Competition, Innovation, and Antitrust. A Theory of Market ... - Intertic

Federico Etro 

COMPETITION, 

INNOVATION, AND 

ANTITRUST 

July 19, 2007 

Springer-Verlag 

Berlin Heidelberg NewYork 

London Paris Tokyo 

Hong Kong Barcelona 

Budapest

Competition, Innovation, and Antitrust 

by Federico Etro

A Francesca, Riccardo e Leonardo

Preface 

In 1934 Springer published a book by Heinrich von Stackelberg, “Market and 

Equilibrium”, which contained pathbreaking studies on oligopolistic markets. 

In particular, it analyzed the behavior of a firm acting as a leader with a first 

mover advantage in the choice of its production level over another firm acting 

as a follower. That analysis became the foundation of the economic theory of 

market leaders and is the starting point of my book. In the following pages 

I develop a generalization of Stackelberg’s idea, with a focus on the understanding 

of the behavior of market leaders under different entry conditions, 

particularly when entry in the market is endogenous. Rather than limiting 

the analysis to the effects of the market structure on the behavior of the 

market leaders, I also study the effects of the behavior of market leaders on 

the market structure. 

In other words, this book can be seen as an attempt to describe endogenous 

market structures where the strategies, the expectations on the 

strategies of the others, and also the entry decisions are the fruit of rational 

behavior. In the last few decades, economic theory has put a lot of emphasis 

on the rational behavior in the choice of actions and strategies and on the 

rational expectations on these choices. Most fields of economic theory have 

embraced both these elements adopting the rational expectations approach 

in models with perfect competition first and imperfect competition later. 

The theory of industrial organization has embraced these elements with the 

adoption of game theory as the standard tool of analysis of the interactions 

between firms. Meanwhile, economists have often neglected the rational behavior 

of the firms in their entry decisions, both in partial equilibrium and 

general equilibrium models. For this reason, microeconomic and macroeconomic 

analyses of markets with imperfect competition have been often limited 

to situations in which the number of firms was exogenously given. The main 

scope of this book is to provide a general microeconomic analysis of markets 

where entry decisions are rational decisions, and to understand the effects of 

endogenous entry on the equilibrium behavior of the firms and on the welfare 

properties of the equilibrium market structure. 

A great deal of this work is inspired by and based on the revolutionary 

contributions of game theoretic analysis to industrial economics and antitrust 

policy in the last three decades. The pathbreaking works of Avinash Dixit,

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Preface 

Michael Spence, Joseph Stiglitz, Paul Milgrom, John Roberts, Drew Fudenberg, 

Jean Tirole, Michael Whinston and others during the 80s made it clear 

how one could study the rational behavior of market leaders and draw welfare 

implications in a solid game theoretic framework. On the policy front, 

the main consequence of these studies was the development of the so-called 

post-Chicago approach to antitrust, which emphasized a number of situations 

in which an incumbent could engage in anti-competitive practices such 

as predatory pricing, bundling, vertical restraints, price discrimination, anticompetitive 

mergers and so on. The game theoretic approach was able to 

emphasize that these practices could harm consumers by excluding other entrants 

or by facilitating collusion. This approach challenged the former school 

of thought associated with the Chicago school and represented by Richard 

Posner, Robert Bork and others who were (and still are) skeptical toward 

antitrust intervention against exclusionary strategies and mergers. 

The classic book by Jean Tirole “The Theory of Industrial Organization” 

(1988) today remains the best exposition of the game theoretic foundations 

of the modern industrial organization, of the strategic interactions between 

firms, and of the policy implications of the post-Chicago approach. In the 

Introduction to the second part of that book, entitled “Strategic Interaction” 

and entirely dedicated to the strategic behavior of firms, Tirole points out a 

fundamental distinction for the behavior of a market leader facing an entrant: 

this leader will be aggressive under strategic substitutability and accommodating 

under strategic complementarity, 1 unless it tries to foreclose entry. 

Since competition in quantities is associated with strategic substitutability 

and competition in prices with strategic complementarity, Tirole’s taxonomy 

of business strategies based on this distinction became a classic result of the 

modern industrial organization and affected most of its subsequent evolution. 

The natural consequence for markets where firms compete in prices is indeed 

a simple one: incumbents adopting aggressive pricing strategies or equivalent 

strategies must have a predatory intent, otherwise they would adopt accommodating 

strategies. Since then, most of the antitrust analysis of exclusionary 

practices was based on related arguments. 

This book develops a general characterization of the strategic interactions 

between firms taking into account alternative entry conditions. The 

traditional analysis of incumbents and entrants that I sketched above has a 

main problem: it largely neglects the role of the endogenous entry of competitors 

in constraining the behavior of the incumbents. Entry in a market 

is endogenous when in equilibrium there are no profitable opportunities to 

1 The strategic variables of two firms interacting in a market are defined strategic 

substitutes when an increase in the variable chosen by one firm induces the 

other firm to adjust its own strategic variable in the opposite direction. They are 

strategic complements when an increase in the strategy of one firm induces the 

other one to adjust its own strategy in the same direction. The terminology is 

due to Bulow et al. (1985).

Preface 

ix 

be exploited by potential entrants. A simple situation in which this occurs is 

when entry is simply free. A more general situation emerges when firms or 

entrepreneurs are active in different markets and the rate of profit mustbe 

equalized across these markets. Another and more realistic situation in which 

entry can be regarded as endogenous is when there are large fixed costs of 

entry or limited sunk costs (traditionally considered barriers to entry) that 

constrain endogenously the entry decision of the firms. Overall, we do believe 

that endogenous entry should be regarded as the standard situation 

in most markets, while exogenous entry only emerges in extreme situations 

where entry is not a decision taken by the firms, but it is determined by other 

institutional or regulatory authorities. 

When entry is endogenous market leaders are always aggressive under 

both strategic substitutability and complementarity, under both competition 

in quantities and in prices, and even under other forms of competition. This 

has radical implications for the pricing strategies, for the choice of strategic 

investments in cost reductions, quality improvements and advertising, for 

the choice of the financial structure, for the decisions to bundle goods or 

price discriminate, for the production decisions in the presence of network 

externalities, two-sided markets and learning by doing, for the adoption of 

vertical restraints, for the decision to merger or collude with a rival, and for 

many other important issues in industrial organization. 

Evidently, the endogenous entry approach has crucial consequences on 

concrete antitrust policy for the analysis of the behavior of market leaders 

and also for merger and collusion issues. When entry is endogenous, incumbents 

are always aggressive, typically without exclusionary purposes, and 

their strategies hardly harm consumers; mergers in markets where entry is 

endogenous take place if and only if they create enough cost efficiencies; and 

cartels between a limited number of firms facing endogenous entry are ineffective. 

The flavor of these results goes back to the Chicago view, but our 

game theoretic analysis is derived from the standard post-Chicago approach, 

which is augmented with endogenous entry. 

The literature on industrial organization is quite fragmented because separate 

analysis is usually undertaken for models of competition in quantities, 

models of competition in prices and models of competition for the market. 

A possible advantage of the approach I adopt in this book is the provision 

of a unified framework for the analysis of market structures. This framework 

encompasses most models of competition in quantities, prices and models of 

competition for the market, and can be used to analyze and compare different 

market structures in a simpler manner. The book contains a large amount 

of unpublished material, especially in the theoretical analysis of Chapters 2 

to 4. The applied analysis in Chapters 5 to 7 is based on policy oriented 

work, some of which was realized as the chief economist of the Task Force 

on Competition established by the International Chamber of Commerce of 

Paris in 2006.

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Preface 

In Chapter 1, I introduce the basic theoretical tools of industrial organization 

and describe the simplest examples of competition and innovation. 

Thestartingpointisamarketinwhichafirm decides how much to produce 

on the basis of demand and cost conditions. In such a context, I describe 

the behavior of a monopolist and compare it with the behavior of two firms 

in a Cournot duopoly; on this basis I introduce the discussion of the fundamental 

subjects of antitrust analysis as mergers, foreclosure and collusion. 

Then, I employ the same model to describe competition between multiple 

firms within the four main market structures analyzed in this book. In the 

first (Nash competition), firms take decisions independently and their number 

is exogenous. In the second (Marshall competition), the number of firms 

is endogenized assuming that firms enter in the market if and only if they 

expect positive profits. In the third (Stackelberg competition), there is again 

an exogenous number of firms but one of them, the leader, takes its decision 

before the others. In the fourth (Stackelberg competition with endogenous 

entry), there is still a leader with a first mover advantage, but the number 

of firms is endogenous and again derived assuming that firms enter in the 

market if and only if they expect positive profits. The same analysis can 

be extended to a model where firms sell differentiated products and choose 

their prices. I analyze such a model adopting the simplest demand and cost 

conditions, and characterizing the same four different forms of competition 

as before: with price competition, however, I show that the behavior of the 

leader is radically different according to whether entry is endogenous or not. 

Finally, I provide a simple example of competition for the market where firms 

invest to increase their relative chances to innovate, I analyze the four different 

equilibria, and apply the result to discuss the incentives of an incumbent 

monopolist to invest in R&D. 

In Chapter 2, I present a general model of competition and I show that 

most models used in industrial organization are nested in this general model. 

Applications include virtually all symmetric models of competition in quantities 

with homogenous and differentiated goods, models of price competition 

with Logit or isoelastic demand, and standard contests or patent races. I discuss 

in some detail how to characterize the Nash equilibrium and the Marshall 

equilibrium for the general model and for its main applications. Then, I extend 

these equilibria with a firm, the leader, which undertakes a preliminary 

investment affecting competition ex post, as in the literature on strategic investments 

started with the contributions of Avinash Dixit and others. This 

general approach allows one to verify what the strategic incentives of the 

leader are to engage in a number of commitments or investments and to 

be aggressive or accommodating in the market. 2 I perform this analysis in 

the presence of an exogenous number of competitors and of an endogenous 

number, and derive the general principle for which market leaders facing en- 

2 A more aggressive strategy reduces the profits of the other firms, a more accommodating 

strategy increases them.

Preface 

xi 

dogenous entry always take those strategic decisions that induce them to be 

aggressive in the market. Then, I apply these results to specific decisions of a 

leader: 1) investments in cost reductions; 2) persuasive advertising (and other 

demand enhancing investments); 3) decisions on the financial structure and 

the optimal equity-debt ratio; 4) preliminary production levels in the presence 

of network externalities and two-sided markets; 5) bundling of goods; 6) price 

discrimination; 7) delegation of pricing decisions to downstream distributors 

for interbrand competition; and 8) horizontal mergers. 

In Chapter 3, I generalize the analysis of the forms of competition in 

which a leader has a first mover advantage and followers decide their strategies 

independently in a subsequent stage. I characterize the Stackelberg equilibrium 

and the Stackelberg equilibrium with endogenous entry within the 

general framework and for alternative forms of competition in quantities and 

in prices. In particular, I derive the general principle for which market leaders 

facing endogenous entry are always aggressive under both strategic complementarity 

and strategic substitutability: they produce more than the rivals 

when competing in quantities and they set lower prices when competing in 

prices. I also derive the conditions under which a market leader is so aggressive 

to adopt an entry-deterring strategy. This happens under constant 

or decreasing marginal costs of production and homogenous goods, independently 

from the size of the fixed costs of production and of the shape of the 

demand function, and it provides a game theoretic foundation for some of the 

insights of the limit-pricing framework associated with Joe Bain, Paolo Sylos 

Labini and Franco Modigliani and of the contestability approach associated 

with William Baumol, John Panzar and Robert Willig. The latter approach 

could be re-interpreted in terms of Stackelberg competition in prices with 

endogenous entry and homogenous goods, but our framework allows us to 

extend its spirit to the more general case of product differentiation. In such a 

case (as when marginal costs are increasing), market leaders prefer to allow 

entry while still adopting aggressive strategies under both quantity and price 

competition. Finally, I show that, when entry is endogenous, the allocation 

of resources is improved by the presence of the leader. The spirit of these 

results extends to the more complex cases with asymmetries between firms, 

multiple leaders or endogenous leadership, and to the case of multiple strategic 

variables. In conclusion, I illustrate how one can apply these results to 

differentpolicyquestions:1)Ireconsider the role of a collusive cartel in the 

presence of endogenous entry, and argue that this is ineffective unless it has 

a leadership role (in which case the cartel coordinates aggressive strategies 

between its members); 2) I review the problem of the optimal state aids and 

trade policy for firms exporting in a foreign country, and I show that the 

traditional results break down when the domestic firms are engaged in competition 

in a market where entry is endogenous (in such a realistic case, state 

aids inducing aggressive export strategies, and in particular export subsidies,

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Preface 

are always optimal); and 3) I analyze the role of privatizations and liberalizations 

in markets for private goods. 

In Chapter 4, I exploit the results of the previous chapters and apply 

them specifically to models of competition for the market. My starting point 

is a simple model in which all firms choose an initial investment that delivers 

drastic innovations according to a stochastic process. Analyzing the usual 

four forms of competition, I show the general principle for which incumbent 

monopolists that are leaders and face endogenous entry in the competition 

for the market, invest in R&D more than any other firm. This outcome overturns 

a standard result of the theory of innovation, due to Kenneth Arrow, for 

which incumbent monopolists would have lower incentives to invest in R&D 

and replace their own technological leadership. The same result on innovation 

byleadersisconfirmed in a more realistic version of the model in which firms 

invest over time, when innovations are non drastic, and especially when they 

are sequential. The investment of the technological leaders in the presence of 

sequential innovations leads automatically to an explanation for the persistence 

of monopolistic positions, which is associated (somewhat paradoxically) 

with free entry in the competition for the market. On this basis, I develop 

a theory of technological progress driven by market leaders which is closely 

related to the original ideas of Joseph Schumpeter on the role of monopolies 

in enhancing growth - ideas that are hardly consistent with the recent literature 

on endogenous technological progress, in which leaders do not invest in 

R&D because of the Arrow effect. Finally, I discuss the relationship between 

competition in the market on one side and competition for the market on the 

other side. 

In Chapter 5, I apply my theoretical analysis to antitrust policy, particularly 

to issues concerning abuse of dominance. First, I review the traditional 

approaches to antitrust policy and emphasize the strengths and the limits of 

the Chicago school and of the post-Chicago approach. Subsequently, I provide 

a first attempt to derive policy implications from the theoretical analysis 

on the behavior of market leaders in the presence of exogenous entry and endogenous 

entry. I emphasize that any inference on the market power of a 

leader from its market share can be highly misleading. Moreover, when entry 

of firms is endogenous, one should be extremely careful in associating aggressive 

pricing strategies by market leaders (or related strategies as bundling) 

with exclusionary purposes. I also note that when firms compete to obtain 

sequential innovations protected by intellectual property rights (IPRs), persistence 

of technological leadership can derive from endogenous entry in the 

competition for the market rather than market power in the competition in 

the market. Therefore, antitrust policy should be careful in evaluating dominant 

positions in dynamic high-tech sectors, and should avoid interfering 

with the protection of IPRs which is the source of investments in R&D and 

technological progress. In conclusion, I apply these ideas to current antitrust 

policy with particular reference to the efficiency defense for dominant firms,

Preface 

xiii 

to the determination or predatory pricing, to bundling as an exclusionary 

strategy, and to issues of IPRs protection. 

In Chapter 6, I apply my theoretical analysis to the markets of the New 

Economy, in particular to the software sector, which is characterized by a 

number of peculiar features analyzed in the book as network externalities, 

two-sided markets, high investments in R&D and a pre-eminent role of the 

leader in both the competition in the market and for the market. This leader 

has been also the subject of antitrust investigations in US and EU, therefore 

I analyze these famous antitrust cases from an economic point of view, and 

try to focus on its main aspects: 1) whether Microsoft is a monopolist; 2) 

whether its bundling strategies are predatory and harm consumers; and 3) 

whether antitrust authorities should force the disclosure of its IPRs to promote 

competition in the software market. I can briefly summarize the results 

of my investigation as follows: 1) evidence from the competition in and for 

software markets witnesses the lack of monopolistic power by Microsoft and 

better defines its role as that of a Stackelberg leader in a market with endogenous 

entry; 2) bundling strategies by Microsoft appear as natural aggressive, 

or pro-competitive, strategies which may harm competitors but create benefits 

to all consumers; and 3) forced disclosure of the IPRs of Microsoft for 

interoperability purposes may severely jeopardize investment in R&D rather 

than promoting it, with negative consequences for the consumers in the long 

run. 

In Chapter 7, I conclude this book by suggesting ways to investigate the 

empirical predictions of the theory of market leaders concerning the pricing 

policy of the leaders, and their decisions on quality, advertising, distribution, 

financing and R&D investments as functions of the entry conditions. I also 

re-interpret my results on the behavior of market leaders from the point of 

view of business administration recommendations for marketing and strategy. 

Finally, I suggest avenues for future theoretical research on market leadership 

and on endogenous entry. 

My initial interest in the role of market leaders and endogenous entry, 

especially in the market for innovations, was inspired by discussions with 

Michele Boldrin at U.C.L.A. While our later research efforts have taken radically 

different directions, I am grateful to him for inspiring motivations. 

At U.C.L.A., between 1998 and 2000, I also benefited from interaction with 

Harold Demsetz, Jack Hirshleifer, David Levine, John Riley, Bill Zame and, 

most of all, with Karina Firme whose wisdom and intelligence has enlightened 

many of my thoughts on these issues (and others as well). I presented 

a prototype model on the behavior of leaders in markets with endogenous 

entry for the first time in a seminar at M.I.T. in November 2000. In that 

occasion, comments by Robert Barro and Daron Acemoglu shaped a lot of 

my subsequent theoretical investigations. I developed the first ideas of this 

book at N.B.E.R. and Harvard University: the rigorous logic and the depth 

of the suggestions of Robert Barro have been crucial for my understanding of

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Preface 

many topics, and my way of thinking about economic issues is largely shaped 

around his free market ideals. At the time, I also benefited from interesting 

discussions with Philippe Aghion, Oliver Hart, David Laibson, Gregory 

Mankiw, Ricardo Reis, Silvana Tenreyro and Joseph Zeira. 

Since then, I have presented parts of this book at different conferences, 

seminars and lectures in many places around the world, including U.C.L.A., 

Harvard University, University of Milan, Bicocca, CERGE and Charles University 

(Prague), European University Institute (Florence), University of Vienna, 

University of Virginia (Charlottesville), the Finnish Competition Authority 

and ETLA (Helsinki), the Roundtable on The Lisbon Agenda and the 

future of Information Technology IPRs (Brussels), the Telecom Conference 

on the Economics of the Information and Communication Technology (Paris), 

the Conference on Competition and Regulation of the Athens University of 

Economics and Business (Corfù), the DIW Roundtable on Competition and 

IPRs (Berlin), the Conference on EU and Greek Competition Policy (Athens) 

and others. I am grateful to many participants for important comments, and 

especially to Jacques Bourgeois, Guglielmo Cancelli, David de Meza, Vincenzo 

Denicolò, David Encoua, Maxim Engers, David Evans, Leonardo Felli, 

Hans Jarle Kind, Joseph Harrington, Massimo Motta, Meir Pugatch, Jennifer 

Reinganum, Patrick Rey, David Ulph and Martti Virtanen. Between 

2002 and 2003, while I was economist for the Ministry of Economy of my 

country and teaching at Luiss University (Rome), I also benefited from interesting 

conversations with Riccardo Faini and Domenico Siniscalco on related 

policy issues. 

A large part of the antitrust implications of my theories is derived from my 

professional experience as a consultant on antitrust issues for international 

organizations and private companies. I am thankful to many brilliant people 

from these organizations and companies with whom I have collaborated since 

2004, especially for providing a unique opportunity to apply, discuss and test 

many of the ideas presented in this book. However, the responsibility for what 

follows is only mine and should not involve any of the institutions I have been 

and am affiliated with. 

Since 2004, I have contributed to organize INTERTIC, the International 

Think-tank on Innovation and Competition (website www.intertic.org), and 

I am extremely grateful to its co-founder and vice-president, Krešimir Žigić: 

interacting with him has been fundamental for many of the ideas presented 

in this book. Simon Anderson, also vice-president of Intertic, has been a continuous 

source of inspiration during the last years: I am extremely grateful 

for many of his precious comments. Similarly, I need to thank all the other 

members of Intertic, and especially Avinash Dixit, Yannis Katsoulacos, Vincenzo 

Denicolò, Barbara Spencer, Stephen Martin and Dennis Mueller for 

their valuable comments. The 2007 Intertic Conference, held at the University 

of Milan, Bicocca (“International Conference on Innovation and Competition 

in the New Economy”, May 4-5, 2007) put together some of the best

Preface 

xv 

international economists working on issues of competition, innovation and industrial 

policy and has been a source of deep inspiration; I am thankful to all 

the participants, and especially to the members of Intertic and to Kris Aerts, 

Rabah Amir, Carlo Cambini, Guido Cozzi, Raymond De Bondt, Giovanni 

Dosi, Nisvan Erkal, Katerina Goldfain, Heli Koski, Kornelius Kraft, Eugen 

Kováč, Daniel Piccinin, Jan Vandekerckhove and Viatcheslav Vinogradov for 

stimulating debate. 

I completed this book at the University of Milan, Bicocca, one of the most 

modern and advanced challenges of graduate and postgraduate education in 

Italy. At its Department of Economics I found the ideal environment to write 

these pages. I am very grateful to all of my colleagues, especially Luigino 

Bruni, Floriana Cerniglia, Emilio Colombo, Mario Gilli, Giovanna Iannantuoni, 

Jean Jacques Lambin, Silvia Marchesi, Graziella Marzi, Mariapia Mendola, 

Ahmad Naimzada, Piergiovanna Natale, Pier Luigi Porta, Luca Stanca 

and Patrizio Tirelli, for many comments and suggestions on preliminary versions 

of the book. 

A special thanks to Flavia Ambrosanio, Massimo Bordignon, Umberto 

Galmarini and Piero Giarda from the Catholic University of Milan, who directed 

me toward the study of economic issues more than ten years ago, and 

helped me with generosity and precious suggestions since then. I would also 

like to thank the Editor of Springer, Niels Peter Thomas, who has been extremely 

kind in supporting this project from the beginning and improving it 

in many ways, and Irene Barrios-Kezic for outstanding editorial assistance. 

Finally, I am extremely grateful to Indira Pottebaum who read the manuscript 

many times and gave me a lot of precious comments. 

While preparing this book, I was teaching industrial organization and 

competition policy to advanced undergraduates and I am thankful to my 

students at the University of Milan, Bicocca, for many questions and comments 

on Chapter 1. This chapter is extremely simplified and can be used 

for a short undergraduate course on oligopoly theory; an updated version for 

teaching purposes can be found at www.intertic.org (where other material related 

to this book can be found as well). Also Chapters 5, 6 and 7, which are 

entirely verbal, should be accessible to anyone who has no formal background 

in economic theory, but is interested in antitrust issues and in the evolution 

of the New Economy, the software market and the Microsoft case. Chapters 

2, 3 and 4, however, are more advanced at a technical level and could be 

used for a postgraduate course on industrial organization or on the theory of 

innovation. Finally, I tried to write each chapter as a self contained treatment 

of a particular topic, therefore the reader may also look at a chapter of his 

or her interest without having to read the previous parts. 

My approach to industrial organization issues is largely affected by studies 

in other fields as macroeconomics, international economics and business 

administration, and it probably reflects the fact that I have never taken a 

course in industrial organization. Also for these reasons, this book should be

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Preface 

seen as a complement of other graduate textbooks in the field, and not as a 

substitute. Tirole (1988) is the “first-mover” and still the leader in the market 

for game theoretic textbooks in industrial organization, but of course it does 

not include two decades of literature (especially on the theory of innovation 

and on the evolution of the post-Chicago approach to antitrust). Many other 

good and diversified textbooks have appeared (or endogenously entered) in 

this market in the following years. Shy (1995) offers a wide review of basic 

models at an advanced undergraduate level. Anderson et al. (1992) and 

Vives (1999) provide more sophisticated analysis respectively of the models 

with product differentiation and of the leading models of oligopolistic interaction, 

but they largely ignore the role of market leaders in their frameworks. 

Martin (2002) provides an excellent guide to many theoretical and empirical 

issues, but (as the other cited books) it contains a limited treatment of many 

aspects that are relevant to the markets of the New Economy, as network 

externalities, multi-sided markets, Schumpeterian theories of innovation and 

the related antitrust issues. Scotchmer (2004) provides a nice overview of 

the theory of innovation, but her analysis does not include the most recent 

progress in the theory of innovation by leaders and of its consequences for 

endogenous technological progress and for R&D policy. Motta (2004) is a 

useful survey of the theoretical and applied literature on antitrust policy before 

the advent of the endogenous entry approach and of the related policy 

implications. Finally, the classic books by Bork (1993) and Posner (2001) on 

the major achievements of the Chicago school could be also used in parallel 

to our treatment, which is largely aimed at formalizing some of the informal 

results of the Chicago view on antitrust policy. 

A last word on the cover of this book, for which I have chosen a painting 

by the Dutch artist Jan Vermeer, The Astronomer, now visible at the Louvre 

Museum in Paris. This masterpiece, painted in 1668, depicts a researcher 

engrossed in scientific investigation, and directing his attention toward a celestial 

globe, 3 metaphor of the sphere of knowledge at a time when a radical 

change of paradigm was taking place in science. The Astronomer seems to be 

pondering about the mysteries of the universe, and is working indoors without 

looking through the window at the heavens, but the penetrating light 

coming from the window is enlightening him, the globe, the astrolabe and 

the focus of his work. Doing scientific research is a bit like touching a piece 

of the sphere of knowledge; the rest, as always, is left for future research. I 

hope you will have as much fun reading this book as I did in writing it. 

Federico Etro 

Department of Economics, University of Milan, Bicocca 

Milan, July 2007 

3 See James A. Welu, 1975, “Vermeer: His Cartographic Sources”, The Art Bulletin, 

Vol. 57 (4), pp. 529-47.

Contents 

Preface ....................................................... 

vii 

1. Competition, Leadership and Entry ....................... 1 

1.1 ASimpleModelofCompetitioninQuantities.............. 4 

1.1.1 MonopolyandAntitrustIssues..................... 5 

1.1.2 NashEquilibrium ................................ 8 

1.1.3 Marshall Equilibrium . ............................ 9 

1.1.4 StackelbergEquilibrium........................... 10 

1.1.5 StackelbergEquilibriumwithEndogenousEntry ..... 12 

1.2 Increasing Marginal Costs and Product Differentiation ...... 15 

1.2.1 U-shapedCostFunctions.......................... 16 

1.2.2 Product Differentiation ........................... 18 

1.3 ASimpleModelofCompetitioninPrices.................. 20 

1.4 ASimpleModelofCompetitionfortheMarket ............ 25 

1.4.1 TheArrow’sParadox ............................. 27 

1.4.2 InnovationbyLeaders ............................ 31 

1.5 Conclusions............................................ 34 

1.6 Appendix ............................................. 36 

2. Strategic Commitments and Endogenous Entry ........... 41 

2.1 MarketStructure....................................... 44 

2.2 Nash Equilibrium....................................... 48 

2.3 Marshall Equilibrium ................................... 49 

2.4 CompetitioninQuantities,inPricesandfortheMarket..... 50 

2.4.1 CompetitioninQuantities......................... 50 

2.4.2 CompetitioninPrices............................. 54 

2.4.3 CompetitionfortheMarket........................ 58 

2.5 StrategicInvestments ................................... 59 

2.5.1 The Fudenberg-Tirole Taxonomy of Business Strategies 61 

2.5.2 StrategicCommitmentswithEndogenousEntry...... 63 

2.6 CostReductionsandSignaling ........................... 66 

2.7 AdvertisingandDemandEnhancingInvestments ........... 70 

2.8 DebtandtheOptimalFinancialStructure................. 72 

2.9 NetworkExternalitiesandTwo-SidedMarkets ............. 76

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2.10 Bundling .............................................. 79 

2.11 VerticalRestraints...................................... 82 

2.12 PriceDiscrimination.................................... 84 

2.13 AntitrustandHorizontalMergers......................... 87 

2.14 Conclusions............................................ 89 

3. Stackelberg Competition and Endogenous Entry .......... 91 

3.1 Stackelberg Equilibrium ................................. 94 

3.2 Stackelberg Equilibrium with Endogenous Entry............ 97 

3.3 CompetitioninQuantities,inPricesandfortheMarket..... 100 

3.3.1 CompetitioninQuantities......................... 100 

3.3.2 CompetitioninPrices............................. 106 

3.3.3 CompetitionfortheMarket........................ 108 

3.4 Asymmetries,MultipleLeadersandMultipleStrategies ..... 109 

3.4.1 AsymmetriesBetweenLeaderandFollowers ......... 109 

3.4.2 MultipleLeaders ................................. 110 

3.4.3 EndogenousLeadership ........................... 113 

3.4.4 MultipleStrategies ............................... 114 

3.4.5 General ProfitFunctions .......................... 116 

3.5 AntitrustandCollusion ................................. 118 

3.6 State-AidsandStrategicExportPromotion................ 120 

3.7 Privatizations.......................................... 123 

3.8 Conclusions............................................ 124 

3.9 Appendix ............................................. 125 

4. Dynamic Competition and Endogenous Entry ............ 131 

4.1 ASimplePatentRacewithContractualCostsofR&D...... 135 

4.1.1 EndogenousEntry................................ 138 

4.1.2 WelfareAnalysis ................................. 141 

4.2 DynamicCompetitionfortheMarket ..................... 142 

4.2.1 NashEquilibrium ................................ 143 

4.2.2 Marshall Equilibrium . ............................ 144 

4.2.3 StackelbergEquilibrium........................... 144 

4.2.4 StackelbergEquilibriumwithEndogenousEntry ..... 146 

4.2.5 Non-drasticInnovations ........................... 148 

4.2.6 StrategicCommitments ........................... 150 

4.3 SequentialInnovations .................................. 151 

4.3.1 EndogenousValueofInnovations................... 152 

4.3.2 EndogenousTechnologicalProgress................. 155 

4.4 Competition in the Market and Competition for the Market . 159 

4.5 Conclusions............................................ 162 

4.6 Appendix ............................................. 165

Contents 

xix 

5. Antitrust and Abuse of Dominance ....................... 171 

5.1 TheTraditionalApproachestoAbuseofDominance ........ 174 

5.1.1 TheChicagoSchool .............................. 174 

5.1.2 ThePost-ChicagoApproach ....................... 176 

5.2 TheTheoryofMarketLeadersandEndogenousEntry ...... 178 

5.2.1 Competition in the Market and Policy Implications . . . 179 

5.2.2 Competition for the Market and Policy Implications . . 186 

5.3 ADigressiononIPRsProtection ......................... 189 

5.3.1 PatentsinDynamicSectorsandInnovations ......... 190 

5.3.2 Open-SourceInnovations .......................... 191 

5.3.3 ConclusionsonIPRsProtection.................... 194 

5.4 ReformingAntitrust .................................... 195 

5.4.1 EfficiencyDefense ................................ 196 

5.4.2 PredatoryPricing ................................ 197 

5.4.3 Bundling........................................ 201 

5.4.4 IntellectualPropertyRights ....................... 203 

5.5 Conclusions............................................ 204 

6. Microsoft Economics ...................................... 207 

6.1 TheSoftwareMarket ................................... 208 

6.1.1 Network Effects .................................. 210 

6.1.2 Multi-sidedPlatforms............................. 212 

6.1.3 Microsoft........................................ 215 

6.2 TheAntitrustCases .................................... 218 

6.2.1 TheUSCase .................................... 218 

6.2.2 TheEUCase .................................... 221 

6.3 IsMicrosoftaMonopolist?............................... 223 

6.3.1 WhyIsthePriceofWindowssoLow? .............. 225 

6.3.2 Does Microsoft StifleInnovation?................... 228 

6.4 Bundling .............................................. 230 

6.4.1 Strategic Bundling . . . ............................ 232 

6.4.2 TechnologicalBundling ........................... 234 

6.5 IntellectualPropertyRights ............................. 235 

6.5.1 Patents, Trade Secrets and Interoperability .......... 236 

6.5.2 LicensesandStandards ........................... 238 

6.6 Conclusions............................................ 240 

7. Epilogue .................................................. 243 

7.1 EmpiricalPredictionsoftheTheoryofMarketLeaders...... 243 

7.2 ImplicationsforBusinessAdministration .................. 252 

7.3 ImplicationsforEconomicTheory ........................ 252 

7.4 Conclusions............................................ 255 

8. References ................................................ 257

xx 

Contents 

Index ......................................................... 275

1. Competition, Leadership and Entry 

Most of the traditional industrial organization literature has studied the way 

market structure affects the behavior of firms. This book is also about how 

the behavior of firms affects the market structure. Therefore we will focus 

on market structures where both the strategies of the firms and their entry 

choices are endogenous. 

We will study the strategies and the entry decisions within a general 

framework and apply the results to different environments, characterized by 

competition in the market and competition for the market. The difference 

between these two forms of competition is simple. When firms compete in 

the market, they choose the price of their products or the production level, 

or even other auxiliary strategies, but the products of all the firms are exogenously 

given. When firms compete for the market, they invest in R&D to 

innovate and create new products or better versions of the existing products. 

Our ultimate objective will be to employ our theoretical results to derive 

some insights on policy issues, and in particular on antitrust issues. For this 

purpose, we will pay a close attention to the behavior of market leaders and 

to the interaction between these firms and the other firms, the followers. 

In this chapter we will study the simplest models of competition one can 

think of. Our purpose is to introduce the reader to the basic tools of the 

theory of oligopoly. Nevertheless, we will also present new insights on the 

behavior of leaders in markets where entry is endogenous. In the rest of the 

book we will generalize these results in many directions, but the spirit of our 

analysis can be grasped from the examples developed in this chapter. 

We will focus on four general typologies of competition and their related 

equilibria. The first typology goes back to the early analysis of Cournot (1838) 

who was the real pioneer of the modern economic analysis and the first one 

to study market structures for homogeneous goods where firms choose their 

output and where the equilibrium between demand by consumers and supply 

by all firms determines the price. While the analysis of Cournot goes back 

to the first half of the XIX century, his equilibrium concept corresponds to 

the one that today we associate with Nash (1950): 1 each firm independently 

chooses its strategy to maximize profits taking as given the strategy of each 

1 Nash (1950) introduced mixed strategy equilibria and provided a general proof 

of the existence of these equilibria.

2 1. Competition, Leadership and Entry 

other firm. This idea can be applied to more general market structures and 

also when firms choose strategies different from their output, for instance 

when they choose their prices, or their investments in R&D. Therefore, we 

will generally refer to a Nash equilibrium when an exogenous number of firms 

compete choosing their strategies simultaneously. This equilibrium concept 

is at the basis of any analysis of strategic interactions between independent 

agents, and in particular at the basis of the theory of industrial organization. 

The second typology of competition extends these models of imperfect 

competition to endogenous entry of firms. A market is in equilibrium only 

when there are not further incentives for other firms to enter into it and 

conquer positive extra-profits. This idea is often associated with the studies 

on competitive markets in partial equilibrium of the second half of the XIX 

century, in particular with Marshall (1890). Therefore, we will refer to this 

equilibrium as the Marshall equilibrium. In modern terms, the concept of 

Nash equilibrium with free entry characterizes this situation. Formal treatments 

have been provided by von Weizsäcker (1980) and Novshek (1980) for 

competition in quantities and (neglecting the strategic interactions) by Dixit 

and Stiglitz (1977) for competition in prices. In general, equilibria with endogenous 

entry are the natural way to think of medium and long run equilibria 

both in partial and general equilibrium. Nevertheless, they have been rarely 

used in industrial organization, where the number of competitors is often 

assumed exogenous to focus on the strategic interactions between predetermined 

competitors, and also in general equilibrium macroeconomic analysis 

with imperfect competition (which often abstracts from entry processes to 

focus on price rigidities). 

The third typology of competition was introduced by Stackelberg (1934) 

who studied markets where a firm has a leadership over the others. While in 

every day talks a market leadership refers to a vague concept of competitive 

advantage, in economic jargon a leadership is associated with a first mover 

advantage, that is the ability to choose strategies and commit to them before 

the other firms. Under Stackelberg competition, the leader can exploit its 

first mover advantage taking into account the reactions of the followers. 2 

Notice that the behavior of a leader in a Stackelberg equilibrium requires 

a commitment power whose credibility is crucial but sometimes not realistic 

(see Schelling, 1960). However, Dixit (1980) and Fudenberg and Tirole (1984) 

have shown that proper preliminary investments can be a valid substitute for 

this commitment: a firm can invest in cost reductions, in advertising, in R&D 

or in other strategic investments to obtain a competitive advantage over the 

other firms. We will return to this possibility in the next chapter, while in this 

one we will analyze the simpler case in which a leader has indeed the ability 

2 Only later on, Selten (1965) introduced the concept of subgame perfect equilibrium 

for dynamic games (and the Stackelberg equilibrium belongs to this class), 

while Harsanyi (1967-68) introduced Bayesian equilibria with uncertainty. For an 

introduction to game theory see Fudenberg and Tirole (1991) or Myerson (1991).

1. Competition, Leadership and Entry 3 

to commit to strategies before the other firms. For example, the leader can 

choose how much to produce before them. Since the equilibrium price depends 

on the production of all the firms, the followers must take in consideration the 

production of the leader when they decide their own production: for instance, 

they may want to produce less if the leader has decided to produce more. 

But the leader is aware of these reactions, and decides its own production 

level taking into account the expected behavior of the followers: for example, 

the leader may want to produce a lot to induce the followers to reduce their 

production. Similarly, a price leader chooses its own price taking into account 

the impact of this choice on the prices adopted by the followers. Imagine that 

the followers are going to increase their prices when they face a price increase 

by the leader: then, the leader may want to choose a high price to start with, 

so that all firmswillendupwithhighprices. 

The last typology of competition completes our taxonomy of the basic 

forms of market interaction combining the analysis of leadership and entry. 

In the second half the XX century there have been some attempts to model 

both these elements. One is the literature on entry deterrence associated 

with Bain (1956), Sylos Labini (1956) and Modigliani (1958), who took into 

consideration the effects of entry on the predatory behavior of market leaders 

mainly in the case of perfectly substitute goods and constant or decreasing 

marginal costs. Another important attempt is associated with the theory 

of contestable markets by Baumol et al. (1982), which shows that, in the 

absence of sunk costs of entry, the possibility of “hit and run” strategies 

by potential entrants is compatible only with an equilibrium price equal to 

the average cost. One of the main implications of this result is that “one 

firm can be enough” for competition when there is at least one aggressive 

potential entrant. This theory and its implications do not apply when goods 

are imperfect substitute or firm compete in quantities rather than in prices, 

which represents a crucial theoretical gap. 

These and other attempts were not developed in a coherent and general 

game theoretic framework. The development of such a framework is the focus 

of this book, whose theoretical contribution is the characterization of the 

Stackelberg equilibrium with endogenous entry and of its applications. This 

equilibrium is characterized by rational strategies adopted in different stages. 

In a first stage, the leader chooses its strategy under rational expectations on 

the strategies that will be adopted by the followers and on the entry decisions 

of these followers. In a second stage the followers decide whether to enter in 

the market or not according to their expectations on profitability. In the 

last stage, the followers simultaneously choose their strategies to maximize 

profits, knowing the strategy of the leader and taking as given the strategies 

of the other followers. 

This introductory chapter presents, in the simplest possible way, some 

examples of these four different forms of competition and equilibria. Our 

initial focus is on models of competition in quantities. After presenting the


basic linear model which assumes constant marginal costs and homogenous 

goods in Section 1.1, we extend it to U-shaped cost functions and to product 

differentiation in Section 1.2. In Section 1.3, we present a simple model of 

competition in prices with a Logit demand function. Finally, in Section 1.4, 

we discuss a simple model of competition for the market (a contest where 

firms compete investing with the purpose of conquering a new market), and 

we analyze the role of incumbent monopolists (with or without a leadership 

in the competition for the market). Section 1.5 concludes. 

1.1 A Simple Model of Competition in Quantities 

Our initial example will be about the simplest situation one can think of: a 

market for a single homogenous good whose supply requires a positive fixed 

cost of production and a constant additional cost for each unit produced, 

which means that the marginal cost of production is constant. To be more 

formal, imagine a good whose demand is linearly decreasing in the price, say 

D(p) =a−p where a>0 is a parameter representing the size of the market. If 

total production by all the firms is Q = P n 

i=1 q i,whereq i is the production 

of each firm i =1, 2, ..., n, in equilibrium between supply and demand we 

must have Q = D(p) =a − p, which provides the so called inverse demand 

function in equilibrium: 

p = a − Q = a − 

nX 

q i (1.1) 

i=1 

Basically, the larger production is, the smaller the equilibrium price must 

be. 

Imagine now that each firm can produce the good with the same standard 

technology. Producing q unitsrequiresafixed cost of production F ≥ 0 and 

a variable cost cq where c ∈ [0,a) is a constant marginal cost of production. 

Notice that, while the average variable cost is constant (equal to c), the 

average total cost (equal to c+F/q) is decreasing in the output. In conclusion, 

the profit function of a firm i is the difference between revenues and costs: 

π i = pq i − cq i − F = (1.2) 

Ã ! 

nX 

= a − q i q i − cq i − F 

i=1 

Before analyzing different forms of competition between many firms in 

this set up, we will investigate a few simple and extreme situations where 

one or two firms only are active in this market and derive some preliminary 

implications for antitrust analysis.

1.1.1 Monopoly and Antitrust Issues 

1.1 A Simple Model of Competition in Quantities 5 

Our first investigation of the market described above focuses on a monopoly. 

Consider a single firm producing q. Itsprofit mustbegivenbyπ =(a − 

q)q − cq − F . Its maximization requires an output satisfying the optimality 

condition ∂π/∂q = a − 2q − c =0, 3 which can be solved for the monopolistic 

output: 

q M = a − c 

2 

The monopolistic price can be derived from the inverse demand function as 

p M = a − q M =(a + c)/2, and the associated profits are: 4 

(a − c)2 

π M = − F 

4 

Imagine now that another firm enters in the market. When the two firms 

compete at the same level, it is natural to imagine that their strategic choices 

are taken simultaneously. In the equilibrium of this duopoly, both firms must 

choose their output levels independently, and these output levels must be 

consistent with each other. The result is a Cournot equilibrium. 

Consider firms i and j. If they compete choosing independently their 

outputs, firm i has the following profit functionπ i =(a − q i − q j )q i − cq i − F , 

and total production is now Q = q i + q j ; of course the profit offirm j is 

the same after changing all indexes. Profit maximization by firm i requires 

∂π i /∂q i =0or a − 2q i − q j = c, from which we obtain the so called reaction 

function: 

q i (q j )= a − c − q j 

2 

This is a rule of behavior for firm i whichcanbeinterpretedintermsof 

expectations: the larger is the expected production of firm j, the smaller 

should be the optimal production of firm i. Firmj will follow a similar rule: 

q j (q i )= a − c − q i 

2 

The geniality of Cournot’s idea is that in equilibrium the two rules must be 

consistent with each other. In terms of expectations, the equilibrium production 

of each firm must be the optimal one given the expectation that the other 

firm adopts its equilibrium production. Mathematically, we can solve the system 

of the two reaction functions to find out the production of each firm in 

3 The second order condition ∂ 2 π/∂q∂q = −2 < 0 guarantees that the profit 

function is concave, so that the solution corresponds to a maximum. 

4 We will assume that F is small enough to allow profitable entry by one firm in 

the market.


equilibrium. It is easy to verify that there is only one consistent equilibrium, 

and it implies that each firm produces the same amount: 

q = a − c 

3 

Accordingly, the equilibrium price is p =(a +2c) /3, andtheprofit ofeach 

firm is: 

(a − c)2 

π C = − F 

9 

Competition increases total production and reduces the price and the profits 

compared to the monopolistic case. For this reason, the firms may engage 

in alternative agreements or strategies that can increase the price and their 

profits. Any practice that leads to higher prices ends up hurting consumers. 5 

The scope of antitrust policy is precisely to avoid this kind of anti-competitive 

behavior. Here, we will sketch the main anti-competitive practices that can 

emerge in such a simple context. 

Mergers. As we noticed, the Cournot duopoly generates lower profits for 

each firm compared to a monopoly. Moreover, also the sum of the profits 

of both firmsislowerthantheprofits of the monopolist. This implies that 

there is an incentive for one firm to merge with the other one, monopolize 

the market and increase total profits. Since this induces a higher final price, 

antitrust authorities should prevent a similar horizontal merger as an attempt 

to monopolize the market. 6 

Abuse of Dominance. There is another possibility for one of the two firms 

to increase its profits. This possibility emerges when this firm can act as a 

leader and choose its output before the second firm. In this case, the leader i 

could chose a output level ¯q which is high enough to convince the second firm 

j to avoid entry. This entry deterring output level can be calculated as follows. 

Consider the reaction function of firm j derived above: this tells us that when 

firm i produces q, firm j finds it optimal to produce q j (q) =(a − c − q)/2 so 

as to obtain profits π j (q) =(a−c−q) 2 /4−F .Now,theleaderi is aware that 

producing ¯q = a − c − 2 √ F will reduce the profits of the other firm j to zero 

(π j (¯q) =0). This is the entry deterring strategy, and it allows the leader to 

remain alone in the market. If this firm has the market power to choose its 

5 In this model with linear demand, consumer surplus is simply the area below the 

demand curve and above the market price, which corresponds to Q 2 /2. Welfare 

is traditionally defined as the sum of consumer surplus and firms’ profits, W = 

Q 2 /2+ n 

i=1 π i. 

6 Notice, however, that in case the merger between the two firms allows to save 

one of the two fixedcosts,thegaininefficiency may overcompensate the loss 

in consumer surplus after the merger (see Williamson, 1968, and Farrell and 

Shapiro, 1990, on a more general analysis of efficiencies in horizontal mergers).


strategy before the rival, it can use this power to increase profits excluding 

entry. 7 Moreover, if this firm remains alone in the market, it could be able 

to restore the monopolistic price in the future. When this is the case, the 

exclusionary strategy ends up increasing the final price, therefore antitrust 

authorities should punish it as a predatory strategy. 

Collusion. A third way to increase profits requires collusion. To see how 

it works in our simple setup, let us go back to the symmetric duopoly. The 

reduction in total profits associated with Cournot competition (compared 

to the monopolistic outcome) was due to the fact that each firm did not 

take into consideration the impact of its own production on the profits of 

the other firm, and hence tended to produce too much from the point of 

view of joint profit maximization. This externality leads to a price reduction 

and to a decline in total profits. For this reason the two firms may try to 

collude and agree on limiting their production at a lower level, possibly at 

the monopolistic level. Under perfect collusion, each one of the two firms 

produces half of the monopolistic output, ˜q =(a − c)/4, andobtainsprofits 

˜π =(a − c) 2 /8 − F . 

However, only a strong and reciprocal commitment could guarantee that 

such a collusive behavior is sustainable, because in the absence of a commitment 

each firm would have incentives to deviate and produce more than 

that. For instance, if a firm is sure that the other one produces at the collusive 

level, this firm can deviate from the collusive strategy and choose an 

output q D that maximizes π =(a − q D − ˜q)q D − cq D − F .Theoptimaldeviation 

is exactly q D =3(a − c)/8. After deviating from the collusive strategy, 

this firm increases its profits to π D =9(a − c) 2 /64 − F , which is above the 

collusive profits, while the profits of the other firm are reduced below them. 

This profitable deviation should not surprise, because there must be always 

aprofitable deviation for each firm when we are not in the Cournot equilibrium. 

Not by chance, we can also provide an alternative definition of the 

Cournot equilibrium as one in which there are not profitable deviations for 

any firm. 

It is important to notice that collusive outcomes can be reached more 

easily when interactions are repeated over time, because deviations can be 

punished in the future, and the threat of punishments can reduce the incentives 

to deviate. The theory of collusion has studied the conditions under 

which monopolistic profits can be sustained in dynamic games. For instance, 

if the same competition is repeated infinite times, each firm discounts the 

future, and each deviation is punished with reversion to the Cournot equilibrium 

forever, collusion is sustainable if and only if firms are patient enough. 

7 Notice, however, that the exclusionary strategy does not necessarily increase the 

price and, even if it increases the price, it does not necessarily reduce welfare 

(measured as consumer surplus plus profits). If the fixed cost of production is 

high enough, entry deterrence may require a higher price but it may be more 

efficient from a welfare point of view.


Of course, collusion could be sustained more easily if harder punishments 

were available (for instance with a reversion to zero profits forever). 8 Since 

collusive cartels allow firms to set higher equilibrium prices, antitrust authorities 

should prevent similar agreements. 

As we have seen, simple games can be useful to understand basic strategic 

interactions and to approach some of the fundamental antitrust issues. 

However, a more complete analysis needs to take into account the presence 

of more than just one or two firms, and possibly also to endogenize entry in 

the market. To these tasks we now turn. 

1.1.2 Nash Equilibrium 

We now move to the study of a generalized Nash competition between many 

firms. In particular, imagine that there are n firms in the same market described 

above. Each firm i will have profits: 

⎛ 

⎞ 

nX 

π i = ⎝a − q i − q j 

⎠ q i − cq i − F (1.3) 

j=1,j6=i 

and will choose its production q i to satisfy the first order condition a − 2q i − 

P n 

j=1,j6=i q j = c, which generates the reaction function: 

q i = a − P n 

j=1,j6=i q j − c 

2 

Notice that this is decreasing in the output of each other firm, ∂q i /∂q j < 0. 

Therefore, when a firm is expected to increase its own production, any other 

firm has an incentive to choose a lower production level. This is a typical 

property of models where firms compete in quantities. 

Thesystemofn conditions provides equilibrium outputs as in the duopoly 

case. However, its solution is immediate if we notice that all firms will produce 

8 Assume that the punishment is reversion to the Cournot equilibrium and that 

the discount factor is δ ∈ (0, 1). Collusion is sustainable if the discounted payoff 

from collusion forever, ˜π +δ˜π +δ 2˜π +... =˜π/(1−δ), is higher than the deviation 

payoff in one period plus the Cournot payoff forever after that, π D +δπ C /(1−δ). 

This requires δ>(π D − ˜π) / (π D − π C). Substituting for the payoffs, one can 

find that collusion is sustainable when δ > 9/17. Thefirst generalizations of 

this result, known as Folk Theorem, are in Friedman (1971) and Aumann and 

Shapley (1976). Of course, collusion could be sustained more easily if punishment 

was harder. Considering the maximum punishment which delivers zero expected 

payoff for the deviator, Abreu (1986) has verified under which conditions such a 

punishment is itself sustainable, relaxing the condition above (see also Fudenberg 

and Maskin, 1986). For a wide treatment on supergames and dynamic games see 

Mailath and Samuelson (2006).


the same output satisfying a − 2q − (n − 1)q = c. This implies the following 

output per firm as a function of n: 9 

q(n) = a − c 

(1.4) 

n +1 

with total production Q(n) =n(a − c)/(n +1), which is increasing in the 

number of firms. The equilibrium price can be derived as: 

p(n) = a + nc 

(1.5) 

n +1 

which is decreasing in the number of firms and approaching the marginal cost 

of production when the number of firms increases. Nevertheless, the profits 

of each firm are constrained by the fixed costs of production: 

π(n) = 

µ 2 a − c 

− F 

n +1 

The profits of each single firm are clearly decreasing when the number of 

competitors is increasing. This suggests that in the medium and long run, 

new firms will enter in the market as long as there are positive profits to 

be made, and they will stop entering when the number of firmsachievesan 

upper bound. This leads us to the next equilibrium concept. 

1.1.3 Marshall Equilibrium 

It is now extremely simple to extend the model to endogenize entry. Formally, 

consider the following sequence of moves: 

1) in the first stage all potential entrants simultaneously decide “in” or 

“out”; 

2) in the second stage all the firms that have entered choose their own 

strategy q i . 

In what follows we will mainly refer to F as to a technological cost of 

production, but one could think of it as including other concrete fixed costs 

of entry or opportunity costs of participation to the market, as the profits 

that an entrepreneur can obtain in another sector. Beyond the particular 

interpretation, the role in constraining entry is the same. 

As we have seen, in the case of a Nash equilibrium the entry of a new 

firm enhances competition leading to a reduction in the profit of each single 

firm in the market. If we assume that entry takes place as long as positive 

profits can be obtained, a Marshall equilibrium should be characterized by a 

number of firms n satisfying a no entry condition π(n +1)< 0 and a no exit 

condition π(n) ≥ 0. When the fixed cost of production is small enough, this 

9 One can verify that both the cases of a monopoly and of the Cournot duopoly 

are particular cases for n =1and n =2.


equilibrium number is quite large. In these cases it is natural to take a short 

cut and approximate the endogenous number of firms with the real number 

satisfying the zero profit condition π(n) =0,thatis: 

n = a √ − c − 1 

F 

This allows one to derive the equilibrium output per firm under Marshall 

competition: 

q = √ F (1.6) 

the total production Q = a − c − √ F , and the equilibrium price: 

p = c + √ F (1.7) 

which implies a mark up on the marginal cost to cover the fixed costs of 

production. When the fixed costs are zero, the outcome corresponds to the 

classic equilibrium with perfect competition in which the price is equal to the 

marginal cost and the number of firmsisindeterminate.Inthemorerealistic 

case in which start up costs for each firm are positive, the equilibrium is 

inefficient and there are too many firms pricing above their marginal cost. 10 

1.1.4 Stackelberg Equilibrium 

Let us now consider the case in which one of the firms has a first mover 

advantage and can choose its output in a first stage before the followers, 

while these choose their own output in a second stage and independently 

from each other. Let us define the production of the leader as q L .Inthe 

second stage each follower decides how much to produce according to the 

first order condition a − q L − q i − P n 

j=1,j6=L q j = c, wheren is the number of 

firms (including the leader). Assuming that all the followers find it convenient 

to be active, in a symmetric equilibrium each follower produces: 

q(q L ,n)= a − q L − c 

n 

10 Adopting the standard definition of welfare (which here corresponds to the consumer 

surplus because all firms earn no profits under free entry), we have: 

W FE = Q2 

2 = (a − c − √ F ) 2 

2 

Notice that in this case the firstbestwouldrequireonesinglefirm producing 

Q = a − c with welfare: 

W FB = 

(a − c)2 

2 

− F


As we noticed before, ∂q(q L ,n)/∂q L < 0: the production of the leader partially 

crowds out the production of the other firms. Accordingly, in the first 

stage the leader perceives its profits as: 

π L =[a − q L − (n − 1)q(q L ,n)] q L − cq L − F 

We can already see what will be the impact of the behavior of the followers 

on the leader: since a higher production of the leader reduces the production 

of the followers, the leader has an indirect (or strategic) incentive to increase 

its production. Such an aggressive strategy reduces the production of the 

followers and shifts profits toward the same leader. Formally, we can rewrite 

the profits of the leader as: 

∙ 

π L = a − q L − (n − 1) (a − q ¸ 

L − c) 

q L − cq L − F = 

n 

µ 

a − c − qL 

= 

q L − F 

n 

which leads to the optimal strategy: 

q L = a − c 

(1.8) 

2 

In this particular example the leader finds it optimal to commit to produce 

at the monopolistic level. As a consequence, each one of the followers will end 

up producing: 

µ a − c 

q 

2 ,n = a − c 

(1.9) 

2n 

The total output becomes: 

µ 

Q =(a − c) 1 − 1 

2n 

and the equilibrium price is: 

p(n) = a µ 

2n + c 1 − 1 

2n 

(1.10) 

which again tends toward the marginal cost when the number of firms increases. 

The profits for the leader and for each follower are respectively: 

π L (n) = 

(a − c)2 

4n 

− F , π(n) = 

(a − c)2 

4n 2 

− F


Of course, entry of followers occurs if positive profits can be obtained. 11 When 

this is the case, we expect that, at least in the medium or long run, followers 

will keep entering in the market until positive profits can be made. Since 

the profits of the followers are decreasing in the number of firms active in 

themarket,theentryprocesswillhaveanaturallimit.Wenowmovetothe 

equilibrium in which entry occurs until all the profitable opportunities are 

exploited by the followers. As we will see, this equilibrium with endogenous 

entry is quite different from the one analyzed here. 

1.1.5 Stackelberg Equilibrium with Endogenous Entry 

Let us finally move to the last case, in which there is still a leader in the 

market, but this is facing endogenous entry of followers. Formally, following 

Etro (2006,a, pp. 147-8) consider the following sequence of moves: 

1) in the first stage, the leader chooses its own output q L ; 

2) in the second stage, after knowing the output of the leader, all potential 

entrants simultaneously decide “in” or“out”; 

3) in the third stage, all the followers that have entered choose their own 

output q i (hence, the followers play Nash between themselves). 

In this case, the leader has to take into account how its own commitment 

affects not only the strategy of the followers but also their entry decision. As 

we have already seen, in the last stage, if there are n ≥ 2 firms in the market 

and the leader produces q L , each follower produces: 

q(q L ,n)= a − q L − c 

n 

This implies that the profits of each follower are: 

µ 2 a − c − qL 

π(q L ,n)= 

− F (1.11) 

n 

which are clearly decreasing in the number of firms. This would imply that 

further entry or exit does not take place when π(q L ,n+1) ≤ 0 and π(q L ,n) ≥ 

0. Moreover, no follower will find it optimal to enter in the market if π(q L , 2) ≤ 

0, that is if not even a single follower can obtain positive profits given the 

output of the leader. This condition is equivalent to: 

q L ≥ a − c − 2 √ F 

Therefore when the leader adopts an aggressive strategy producing more 

than this cut-off level entry will be deterred, but when the leader produces 

11 At least one follower has incentives to enter in the market if π(2) > 0 or F < 

(a−c) 2 /16, otherwise the leader supplies its monopolistic production and no one 

else enters. In what follows we assume away this possibility (which corresponds 

to the case of a “natural monopoly”).


less than the above cut-off the number of entrants will be determined by a 

free entry condition. In this last case, ignoring the integer constraint on the 

number of firms, 12 we can approximate the number of firmsasarealnumber 

that satisfies π(q L ,n)=0. This implies: 

n = a − c − q L 

√ 

F 

(1.12) 

When this is the endogenous number of firms, each one of the followers is 

producing: 

µ 

q q L , a − c − q 

L 

√ = √ F 

F 

which is independent from the strategy of the leader. Hence, the higher the 

production of the leader, the lower the number of entrants, while the production 

of each one of them will be the same. This would imply a constant level 

of total production Q = q L +(n − 1)q(q L ,n)=a − c − √ F , and a constant 

price p = a − Q = c + √ F , which would be equivalent to the equilibrium 

price emerging under Marshall competition. 

After having derived the behavior of the followers, it is now time to move 

to the first stage and examine the behavior of the leader. First of all, let us 

remind ourselves that entry takes place only for a production level which is 

not too high. If this is the case, the profits of the leader must be: 

π L = pq L − cq L − F = q L 

√ 

F − F if qL


The profits of the leader are then: 

π L =2 √ ³ 

F a − c − 2 √ ´ 

F − F (1.17) 

One way to look at this result is by considering the role of the fixed cost of 

production. When this is zero, we are in the standard neoclassical situation 

where perfect competition takes place: the number of firmsisindeterminate 

and the price must be equal to the marginal cost. However, whenever there 

is a small but positive fixed cost of production, the leader finds it optimal 

to produce enough to deter entry. 13 Constant returns to scale (holding for 

F =0) are not an minor approximation: a small departure from them leads 

to a radical change in the market structure. And when the fixed costs of 

production are high, the leader is able to obtain substantial profits. 14 

Another way to look at the result is to imagine that there are some potential 

entrants and we can establish a relation between their number and 

the market equilibrium: when the number of potential entrants is low enough 

(and the free entry condition is not binding) the market is characterized by 

all these firms being active. When there are many potential entrants (and 

entry is endogenized) there is just one firm in equilibrium, the leader. Furthermore, 

it is interesting to compare the free entry equilibrium with and 

without a leader. In the Stackelberg equilibrium with endogenous entry the 

limit price is higher than the equilibrium price in the Marshall equilibrium 

(the mark up p − c is doubled from √ F to 2 √ F ), consequently the consumer 

surplus is reduced. However, welfare as the sum of consumer surplus and 

profits is higher in the Stackelberg equilibrium with endogenous entry than 

in the Marshall equilibrium. 15 

13 This form of entry deterrence is radically different from that emerging in the 

contestable markets theory of Baumol et al. (1982). First, they focused on price 

competition, which led to a limit price assigning zero profits to the leader, while 

our model of quantity competition leads to a limit price assigning positive profits 

to the leader. Second, their equilibrium was the same with exogenous or endogenous 

entry, while the role of the costs of production in endogenizing entry is 

crucial in our model. In the Appendix we will discuss how to endogenize the 

fixed costs. 

14 For instance, imagine that fixed costs are F =(a − c) 2 /25. Then the profits of a 

leader facing endogenous entry can be calculated as π L =(a − c) 2 /5. Compare 

these to the profits of a monopolist in the same market: its profits would be 

π M =(a−c) 2 /4−F = 21(a−c) 2 /100. It can be easily verified that the difference 

betweenthetwoislessthan5%. 

15 Welfare can be now calculated as: 

W S = Q2 

2 + π (a − c)2 

L = − 3F 

2 

It can be verified that welfare is higher under Stackelberg competition with endogenous 

entry for any F

1.2 Increasing Marginal Costs and Product Differentiation 15 

The extreme result on entry deterrence that we have just found holds 

under more general conditions. For instance, as we will see in Chapter 3, 

as long as goods are perfect substitutes, any kind of demand function will 

generate entry deterrence by the leader when entry of followers is endogenous. 

However, when the cost function departs from the linear version (that we used 

until now) and when imperfect substitutability between goods is introduced, 

entry deterrence may not be the optimal strategy anymore. Nevertheless, the 

leader will still play in a very aggressive way, producing always more than 

the followers when their entry is endogenous. To show this we will now turn 

to two related extensions of the basic model. 

1.2 Increasing Marginal Costs and Product 

Differentiation 

The example adopted until now was extremely simple and stylized. Perfectly 

homogenous goods and marginal costs of production that are always constant 

are quite unrealistic features for many sectors. Most traditional markets are 

characterized by more complex shapes of the cost function and by substantial 

differentiation between products. Consider the market for cars. Companies 

like GM, Ford, Toyota, Nissan, VW, Porsche, Renault or FIAT offer many 

different models, sometimes under different brands (for instance Alfa Romeo, 

Lancia, Maserati and Ferrari for FIAT), and always in multiple versions by 

engine size, color, varieties of optional tools, and so on: each product appeals 

toadifferent class of customers and is sold at a different price. Moreover, 

the production of each model has not a constant unitary cost: on one side, 

economies of scale can be reached at the plant level through large production, 

on the other, larger output levels may require additional investments 

in plants, employees, and other inputs. Generally speaking, for each model 

there is a level of production that minimizes average costs, and average costs 

have a U shape around this efficient level. 

The simple model of competition in quantities studied in the previous 

section can be easily extended to take these realistic dimensions into account. 

For simplicity, we will consider the two issues separately. First, we will depart 

from the assumption of constant marginal costs assuming a U-shaped cost 

function, and then we will depart from the assumption of homogenous goods 

introducing imperfect substitutability between goods. 

assumption F


1.2.1 U-shaped Cost Functions 

In many markets, marginal costs of production are increasing at least beyond 

a certain level of output. Jointly with the presence of fixed costs of production, 

this leads to U-shaped average cost functions. Since technology often exhibits 

this pattern, it is important to analyze this case, and we will do it assuming 

a simple quadratic cost function. 

In particular, the general profit forfirm i becomes: 

π i = q i 

⎛ 

⎝a − q i − 

nX 

j=1,j6=i 

q j 

⎞ 

⎠ − dq2 i 

2 − F (1.18) 

where d>0 represents the degree of convexity of the cost function. When 

d =0we are back to the case of a constant marginal cost (zero in such a 

case). When d>0 the average cost function is U-shaped. One can easily 

verify that the marginal cost is increasing and convex, and it crosses the 

average total cost at its bottom, that is at the efficient scale of production: 

the one that minimizes average costs. This efficient scale of production can 

be derived formally as: 

µ dq 

ˆq =argmin 

2 + F r 

2F 

= 

q d 

Let us look now at the different forms of competition. Our four main 

equilibria can be derived as before. In particular, Nash competition would 

generate the individual output: 

a 

q(n) = 

(1.19) 

n + d +1 

for each firm. 16 Under Marshall competition each firm would produce: 

r 

2F 

q = < ˆq (1.20) 

2+d 

with a number of firms approximated by: 

r 

2+d 

n = a 

2F − d − 1 

Notice that the equilibrium production level is below the cost minimizing 

level. This is not surprising since imperfect competition requires a price above 

16 Amir (2005) shows that in this case industry profits have an inverse U shape with 

amaximumforn =1+2d, while welfare always decreases with n. He generalizes 

this dimension in a number of ways and shows that with strong scale economies 

(d


marginal cost and free entry requires a price equal to the average cost and 

above the marginal cost. Since the average cost is always decreasing when it 

is higher than the marginal cost, it must be that individual output is smaller 

than the efficient scale (von Weizsäcker, 1980). 

Under Stackelberg competition, the leader produces: 

a(1 + d) 

q L (n) = 

[2(1 + d)+d(n + d)] 

and each follower produces: 

(1.21) 

a [1 + d + d(n + d)] 

q(n) = 

(1.22) 

[2(1 + d)+d(n + d)] (n + d) 

Notice that, contrary to the basic linear case, here the leader produces less 

than a pure monopolist and its production diminishes with the number of 

entrants. 

Finally, consider Stackelberg competition with endogenous entry (Etro, 

2008). In the last stage an entrant chooses q(q L ,n)=(a − q L )/(n + d), but 

the zero profit condition for the followers delivers a number of firms: 

Ãr ! 

2+d 

n =(a − q L ) 

− d 

2F 

and each entrant produces: 

r 

2F 

q = 

(1.23) 

2+d 

which is the same output as with Marshall competition. Of course this 

happens when there is effective entry, that is when n ≥ 2 or q L < a − 

(2 + d) p 2F/(2 + d). In such a case, total production is Q = a − (1 + 

d) p 2F/(2 + d), and the price becomes: 

r 

2F 

p =(1+d) 

2+d 

Both total production and the equilibrium price are independent from the 

leader’s production. The gross profit function of the leader in the first stage 

can be derived as: 

π L = pq L − d 2 q2 L − F = 

r 

2F 

=(1+d) 

2+d q L − d 2 q2 L − F 

which is concave in q L .Aslongasd is large enough, we have an interior 

optimum and in equilibrium the leader allows other firms to enter in the 

market and produces:


q L = 1+d 

d 

r 

2F 

> ˆq (1.24) 

2+d 

Notice that the leader is applying a simple pricing rule which equates the 

price derived above p =(1+d) p 2F/(2 + d) to the marginal cost, which is 

dq L in this model. Of course, the leader can price at the marginal cost and 

obtain positive profits because its marginal cost of production is above its 

average cost. This can only happen in the region where the average total costs 

are increasing, which implies a production for the leader above the efficient 

scale. 

Finally, the equilibrium number of firms is: 

r µ 2+d 1+d 

n = a 

2F − d 

 

+ d 

Total output and price are the same as in the Marshall equilibrium, therefore 

the consumer surplus is unchanged, but welfare must be higher since the 

leader makes positive profits. 17 

Notice that the leader is producing always more than each follower. While 

the followers produce below the efficient scale, the leader produces above 

the efficient scale. The intuition is as follows. Followers have to produce at 

a price where their marginal revenue equates their marginal cost, and free 

entry implies that the price has to be equal to the average cost. But marginal 

and average costs are the same at the efficient scale, therefore the followers 

must be producing below this efficient scale. Now, since the equilibrium price 

is determined by the endogenous entry condition, it represents the perceived 

marginal revenue for the leader, and the leader must produce where this 

perceived marginal revenue equates the marginal cost, which in this case 

must be above the efficient scale for profits to be positive. 

1.2.2 Product Differentiation 

We now move to another simple extension of the basic linear model introducing 

product differentiation and imperfect substitutability between the goods 

supplied by the firms. We retain the initial assumptions of constant marginal 

costs and competition in quantities. 

For simplicity, consider the inverse demand function for firm i: 

17 In general, the profit of the leader in case of an interior solution is: 

π L = 

F 

d(2 + d) > 0 

In the alternative case of entry deterrence, the leader produces q L = a − (2 + 

d) 2F/(2 + d). Theprofits of the leader are larger under entry deterrence when 

d is low enough or F is high enough.

p i = a − q i − b X j6=i 


q j (1.25) 

where b ∈ (0, 1] is an index of substitutability between goods. Of course, for 

b =0goods are perfectly independent and each firmsellsitsowngoodas 

a pure monopolist, while for b =1we are back to the case of homogeneous 

goods. In this more general framework the profit functionforfirm i is: 

π i = q i 

⎛ 

⎝a − q i − b 

nX 

j=1,j6=i 

q j 

⎞ 

⎠ − cq i − F (1.26) 

The four main equilibria can be derived as usual. In particular a Nash equilibrium 

would generate the individual output: 

a − c 

q(n) = 

2+b(n − 1) 

for each firm. In the Marshall equilibrium each firm would produce: 

(1.27) 

q = √ F (1.28) 

with a number of firms: 

n =1+ a − c 

b √ F − 2 b 

Under Stackelberg competition, the leader produces: 

(a − c)(2 − b) 

q L = 

2 

and each follower produces: 

(1.29) 

(a − c)[2 − b(2 − b)] 

q(n) = (1.30) 

2[2 + b(n − 2)] 

Finally, consider Stackelberg competition with endogenous entry. As long as 

substitutability between goods is limited enough (b is small) there are entrants 

producing q(q L ,n)=(a − bq L − c)/[2 + b(n − 2)]. Setting their profits equal 

to zero, the endogenous number of firms results in: 

n =2+ a − bq L − c 

b √ − 2 

F b 

implying once again a constant production: 

q = √ F (1.31) 

for each follower. Plugging everything into the profit function of the leader, 

we have:


π L = q L [a − q L − b(n − 1)q] − cq L − F = 

= q L 

h 

(2 − b) √ F − (1 − b)q L 

i 

− F 

that is maximized when the leader produces: 

q L = 

2 − b √ 

F (1.32) 

2(1 − b) 

which is always higher than the production of the followers. This strategy 

leaves space to the endogenous entry of firms so that the total number of 

firms in the market is: 

n =2+ a − c 

b √ F − 2 b − 2 − b 

2(1 − b) 

Notice that the leader will offer its good at a lower price than the followers, 

namely: 

µ 

p L = c + 1 − 

2 b √F 0 

Again, this outcome emerges only if the degree of product differentiation is high 

enough. In the alternative case of entry deterrence, the production of the leader 

is q L =(a − c − 2 √ F )/b and the limit price is p L =[c − (1 − b)a +2 √ F ]/b. Entry 

deterrence is optimal for b or F large enough.

1.3 A Simple Model of Competition in Prices 21 

of contestable markets associated with Baumol et al. (1982) shows that a 

single firm sets the price at a market clearing level which equates the average 

total costs and obtains zero profits again. With U-shaped cost functions, the 

Bertrand equilibrium boils down to a price equal to the minimum average 

cost for each firm, since any different strategy either would leave space for 

profitable deviations, or would lead to losses. 19 Things are not that simple 

when products are differentiated, the case to which we now turn. 

Competition in prices is crucial in markets where the products are highly 

differentiated. In this case, as we have already seen in the last section, each 

firm has a limited market power because it supplies a unique product which 

is only partially substitutable with the products of the other firms. Think of 

the fashion market, which is characterized by strong product differentiation, 

segmentation depending on the target customers, and competition in prices. 

Established luxury brands as Armani, Versace, D&G, Gucci, Etro, Yves Saint 

Laurent, Louis Vuitton and others offer different sophisticated clothes at predetermined 

prices in every season. Other companies which target wider markets, 

as Gap, Abercrombie, Benetton, Zara, H&M and so on, provide largely 

differentiated products and engage in analogous or even stronger forms of 

price competition. 20 In this section, we will focus on the peculiarities of similar 

markets where goods are imperfect substitutes and firms choose their 

prices. 

In this introductory analysis of price competition, we will employ a model 

based on a simple form of the demand function, the so-called Logit demand. 

This is particularly interesting because it is simple but flexible enough to 

depict real world demand functions: not by chance it is widely used in econometric 

studies 21 to estimate demand in various industries and in marketing 

analysis. 22 

The simplest form of the Logit demand is: 

D i = 

Ne −λp i 

h Pn 

j=1 e−λpj i (1.33) 

where of course p i is the price of firm i, λ>0 is a parameter governing the 

slope of the demand function, and N is a scale factor that can be thought of 

19 It is immediate to verify that these equilibria correspond to a Stackelberg equilibrium 

in prices with endogenous entry in the case of homogenous goods. Therefore, 

the theory of Stackelberg competition with endogenous entry can be seen as a 

generalization of the theory of contestable markets to product differentiation, 

andtootherformsofcompetition. 

20 For a recent analysis of the fashion industry see Dallocchio et al. (2006). 

21 See McFadden (1974). 

22 The classic reference on product differentiation and price competition is Anderson 

et al. (1992). See also Anderson and de Palma (1992) for the first analysis 

of Nash and Marshall equilibria within the Logit model of price competition.


as the total income or the total number of agents expressing this aggregate 

demand. Since we focus on substitute goods, such a demand for firm i is 

decreasing in the price of the same firm i and increasing in the price of any 

other firm j. The general profit functionforafirm facing this demand and 

producing with a constant marginal cost c and a fixed cost F 0. This important property, 

which holds virtually in all realistic models of competition in prices, suggests 

that a higher price by one firm induces other firms to increase their prices 

as well. In other words, an accommodating behavior of one firm leads other 

firms to be accommodating too. 

To conclude our analysis of the Nash equilibrium, notice that in a symmetric 

situation with a price p for each firm, demand boils down to D = N/n 

and the equilibrium price is decreasing in the number of firms: 

p(n) =c + 

1 

λ (1 − 1/n) 

(1.35) 

In a Marshall equilibrium one can easily derive that the number of active 

firms is: 

n =1+ N λF 

and each one of these sells its product at the price: 

p = c + 1 λ + F N 

(1.36) 

Let us now move to models of price leadership. Of course it can be even 

harder for a firm to commit to a price rather than to a different strategy (as

1.3 A Simple Model of Competition in Prices 23 

the quantity of production). However, price commitments can be reasonable 

in the short run (for instance in seasonal markets), or when there are small 

menu costs of changing prices or it is costly to acquire the information needed 

to reoptimize on the price choice. In the next chapter we will deal with the 

commitment problem in a deeper way and we will suggest that there are 

realistic ways in which a strategic investment can be a good substitute for a 

commitment to a strategy. For now we will assume that a firm can simply 

commit to a pricing strategy and analyze the consequence of this. 

Concerning the Stackelberg equilibrium we do not have analytical solutions. 

However, it is important to understand the nature of the incentives 

of the firms, which is now rather different from the model with competition 

in quantities. Here the leader is aware that an increase in its own price will 

lead the followers to increase their prices, which exerts a positive effect on 

the profits of the leader. Accordingly, the commitment possibility is generally 

used adopting an accommodating strategy: the leader chooses a high price to 

induce its followers to choose high prices as well. 23 The only case in which 

this does not happen is when the fixed costs of production are high enough 

and the leader finds it better to deter entry. This can only be done adopting a 

low enough price: therefore the leader can be aggressive only for exclusionary 

purposes. 

This standard result emphasizes a possible inconsistency within the model 

of price leadership, at least when applied to describe real markets. We have 

suggested that leaders are accommodating when the fixed costs of production 

(or entry) are small, because in such a case an exclusionary strategy would 

require to set a very low price and would be too costly. But these are exactly 

the conditions under which other firms may want to enter in the market: fixed 

costs are low and exclusionary strategies by incumbents are costly. Therefore, 

the assumption that the number of firms (and in particular of the number of 

followers) is fixed becomes quite unrealistic. 

Let us look at the Stackelberg equilibrium with endogenous entry. The 

solution in this case is slightly more complex, but it can be fully characterized. 

First of all, as usual, let us look at the stage in which the leader has already 

chosen its price p L and the followers enter and choose their prices. As before, 

their choice will follow the rule: 

1 

p i = c + 

λ(1 − D i /N ) 

where the demand on the right hand side depends on the price of the leader 

and all the other prices as well. However, under free entry we must have also 

that the markup of the followers exactly covers the fixed cost of production: 

D i (p i − c) =F 

23 Nevertheless, the followers will have incentives to choose a lower price than the 

leader, and each one of them will then have a larger demand and profits than the 

leader: there is a second-mover advantage rather than a first-mover advantage.


If the price of the leader is not too low or the fixed cost not to high, there 

is indeed entry in equilibrium and we can solve these two equations for the 

demand of the followers and their prices in the symmetric equilibrium: 

p = c + 1 λ + F N , D = λF N 

N + λF 

(1.37) 

Notice that neither one or the other endogenous factors depend on the price 

chosen by the leader. Therefore, it must be that the strategy of the leader is 

going to affect only the number of followers entering in equilibrium, but not 

their prices or their equilibrium production. 

The leader is going to perceive this because its demand can now be calculated 

as: 

D L = 

Ne−λp L 

P n 

i=1 e−λp j = Deλ(p−p L) 

Since neither p or D depend on the price of the leader as we have seen before, 

the perceived demand by the leader is a simple function of its own price, and 

its profits can be derived as: 

π L =(p L − c)D L − F = 

=(p L − c)De λ(p−pL) − F 

where we could use our previous results to substitute for p or D. Profit 

maximization by the leader provides its equilibrium price: 

p L = c + 1 λ 0 

which is positive under the assumption that F

1.4 A Simple Model of Competition for the Market 25 

1.4 A Simple Model of Competition for the Market 

The last example we are going to consider introduces us to a topic that 

we will encounter later on in the book in Chapter 4, the competition to 

innovate and therefore conquer a market with new or better products. In 

many high-tech sectors, this is becoming a main form of competition, since 

the life of a product is quite short and R&D investment strategies to conquer 

future markets are much more important than price or production strategies. 

Consider the pharmaceutical sector: in this market companies like Pfizer, 

Bayer, Merck, Hoffmann-La Roche, GlaxoSmithKline and many others invest 

a lot in R&D to develop, test and patent new drugs, while price competition 

over unpatented drugs plays a minor role. 25 

Competition for the market works as a sort of contest. Firms invest to 

innovate and to win the contest. It may be that the first innovator obtains a 

patent on the invention and exploits monopolistic profits for a while on its 

innovation. It may be that the same innovator just keeps it secret and exploits 

its leadership on the market until an imitator replaces it. In both ways the 

expectedgainfromaninnovationiswhatdrivesfirms to invest in R&D. In 

this framework we can also study alternative market structures depending on 

the timing of moves and on the entry conditions. 

Consider a simple contest between firms to obtain a drastic innovation 

which has an expected value V ∈ (0, 1) for the winner and generates no 

gains for the losers. Each contestant i invests resources z i ∈ [0, 1) to win 

the contest. This investment has a cost and, for simplicity, we will assume 

that the cost is quadratic, that is zi 2 /2. The investment provides the contestant 

with the probability z i to innovate. The innovator wins the contest if 

no other contestant innovates, for instance because in the case of multiple 

winners competition between them would drive profits 

Q 

away. Accordingly, 

n 

the probability to win the contest is Pr(i wins)=z i j=1,j6=i [1 − z j] ,that 

is its probability to innovate multiplied by the probability that no one else 

innovates. In conclusion, the general profit functionis: 26 

π i = z i 

n 

Y 

j=1,j6=i 

[1 − z j ] V − z2 i 

2 − F (1.39) 

Consider the Nash equilibrium. The first order condition for the optimal 

investment by a firm i is: 

25 See Sutton (1998, Ch. 8) for a description of competition for the market in the 

pharmaceutical industry. 

26 We adopt a more restrictive assumption, V ∈ ( √ 2F,1). This guarantees profitable 

entry for at least one firm. Indeed, a single firm would invest z = V < 1 

expecting π = V 2 /2 − F>0. Hence,investingz =1and innovating for sure can 

be profitable, but it is not optimal.


z i = 

nY 

j=1,j6=i 

[1 − z j ] V 

which shows that when the investment of a firm increases, the other firms 

have incentives to invest less: ∂z i /∂z j < 0. Eachfirm chooses its own investment 

without taking this externality into account, therefore competition 

for the market generates excessive investment from the firms point of view. 

Forinstance,inthecaseoftwofirms, each one would invest z = V/(1 + V ) 

in equilibrium, while collusion between them would reduce individual investment 

to the lower level ˜z = V/(1 + 2V ), which increases expected profits for 

each one of the two firms. 27 This suggests that a joint venture between firms 

competing for a market may end up reducing aggregate investment. However, 

notice that we cannot evaluate these outcomes from a welfare point of view 

without expliciting the social value of the innovation: if the social value of 

the innovation is high enough, the investment is too low also in the Nash 

equilibrium, and R&D subsidies would be needed to restore social efficiency. 

Let us go back to the general case with n firms competing for the market. 

Now, the equilibrium investment is implicitly given by: 

z =(1− z) n−1 V 

In the Marshall equilibrium we must also take into account the endogenous 

entry condition: 

z(1 − z) n−1 V − z 2 /2=F 

and solving the system of the two conditions we have the number of agents: 

³ 

log V/ √ ´ 

2F 

n =1+ h 

log 1/(1 − √ i 

2F ) 

and the investment: 

z = √ 2F (1.40) 

The investment of each firm increases with the size of the fixed cost of R&D, 

while entry decreases in the fixed cost and increases with the value of the 

innovation. 

27 Also in this case we can verify when collusion is sustainable by extending the 

model to an infinitely repeated game. Imagine that a deviation from collusion is 

punished with reversion to the Nash equilibrium. One can verify that the best 

deviation is z D =(1+V )V/(1 + 2V ), and collusion is sustainable for a discount 

factor δ>(1 + V ) 2 /(2 + 4V + V 2 ): more valuable innovations make it harder to 

sustain collusion.


Consider now a Stackelberg equilibrium. As already noticed, when the 

investment by one firm is increased, the other firms have incentives to invest 

less: then in a Stackelberg equilibrium the leader exploits its first mover advantage 

by investing more than the followers, so as to reduce their investment 

and increase its relative probability of winning. For instance, in a Stackelberg 

duopoly the leader invests z L = V (1 − V )/(1 − 2V 2 ) and the follower invests 

z = V (1 − V − V 2 )/(1 − 2V 2 ). 

In a Stackelberg equilibrium with endogenous entry, as long as the investment 

of the leader z L is small enough to allow entry of at least one firm, the 

first order conditions and the free entry conditions are: 

(1 − z) n−2 (1 − z L )V = z, z(1 − z) n−2 (1 − z L )V = z 2 /2+F 

which deliver the same investment choice by each entrant as in the Marshall 

equilibrium, z = √ 2F , and the number or firms: 

h 

log (1 − z L )V/ √ i 

2F 

n(z L )=2+ h 

log 1/(1 − √ i 

2F ) 

Putting these two equations together and substituting in the profit function 

of the leader, we would have: 

π L = z L (1 − z) n−1 V − z2 L 

2 − F = 

= z √ ³ 

L 2F 1 − √ ´ 

2F − z2 L 

1 − z L 2 − F (1.41) 

which has not an interior optimum: indeed, it is always optimal for the leader 

to deter entry investing enough. This requires a slightly higher investment 

than the one for which thehequilibrium number of firms would be n =2. 

Since n(z L )=2requires log (1 − z L )V/ √ i 

2F =0, we can conclude that the 

leader will invest: 

√ 

2F 

¯z L =1− 

(1.42) 

V 

which is increasing in the value of innovations and decreasing in their fixed 

cost. Therefore, in a contest with a leader and free entry of participants, the 

leader invests enough to deter investment by the other firms and is the only 

possible winner of the contest. 

1.4.1 The Arrow’s Paradox 

Until now we investigated a form of competition for the market where all firms 

were at the same level. Often times, competition for the market is between an


incumbent leader that is already in the market with the leading edge technology 

(or with the best product) and outsiders trying to replace this leadership. 

In such a case the incentives to invest in innovation may be different and it is 

important to understand how. Arrow (1962) was one of the first economists 

to examine this issue in a formal way. He found that incumbent monopolists 

have lower incentives than the outsiders to invest. His insight was simple but 

powerful: while the gains from an innovation for the incumbent monopolist 

are just the difference between profits obtained with the next innovation and 

those obtained with the current one, the gains for any outsider are the full 

profits from the next innovation. Consequently, the incumbent has lower incentives 

to invest in R&D. The expected gains of the incumbent are even 

diminished when the number of outsiders increases. When the latter is high 

enough the incumbent has no more incentives to participate to the competition, 

and, in particular, when entry in the competition for the market is 

free, the incumbent does not invest at all. Such a strong theoretical result is 

of course too drastic to be realistic. Many technological leaders invest a lot 

in R&D, try to maintain their leadership, and they often manage: persistent 

leadership is not that unusual: for this reason the theoretical finding of Arrow 

is considered a paradoxical outcome, the “Arrow’s paradox” indeed. Before 

offering a theoretical solution for this paradox, however, we will extend our 

model to include an asymmetry between an incumbent monopolist and the 

outsiders. 

Imagine a two period extension of the model. In the first period an incumbent 

monopolist can exploit its technology to obtain profits K ∈ (0,V]. 

We can think of K as the rents associated with an initial leading technology 

or some other exogenous advantage. If these rents are constrained by a competitive 

fringe of firms, we can also think that an increase in the intensity of 

competition reduces K. Inthefirst period any firm can invest to innovate and 

conquer the gain V from the next innovation to be exploited in the second period. 

If no one innovates, the incumbent retains its profits K also in the second 

period. This happens with probability Pr(no innovation) = Q n 

j=1 [1 − z j]. 

Then, assuming no discounting, the expected profits of the incumbent monopolist, 

that we now label with the index M, are: 

π M = K+z M 

n Y 

j=1,j6=M 

[1 − z j ] V +(1−z M ) 

nY 

j=1,j6=M 

[1 − z j ] K− z2 M 

2 

−F (1.43) 

in case of positive investment in the contest, otherwise expected profits are 

givenonlybythecurrentprofits plus the expected value of the current profits 

when no one innovates. The profits of the other firms are the same as previously. 

Before analyzing alternative forms of competition, notice that when the 

monopolist is assumed alone in the research activity, its optimal investment 

is z M = V − K. Hence, an incumbent monopolist (with K>0) haslower 

incentives to invest than a firm without current profits (with K =0): the 

so-called Arrow effect is in action. Moreover, if we think that the intensity


of product market competition has a negative impact on the current profits 

K, while it has no impact on the value of the innovation (since this is drastic 

and the innovator will not be constrained by product market competitors), it 

clearly follows that an increase in the intensity of competition reduces K and 

increases the investment of the monopolist and the probability of innovation 

z M .AghionandGriffith (2005) put a lot of emphasis on this effect, which 

they label escape competition effect: 

“competition reduces pre-innovation rents...but not their post innovation 

rents since by innovating these firms have escaped the fringe. 

This,inturninducesthosefirms to innovate in order to escape competition 

with the fringe.” 28 

Now, consider a Nash equilibrium with a general number of firms. If the 

incumbent does not invest, the equilibrium is the same of the symmetric 

model, but the expected profit of the monopolist π M (z M ) must be: 

√ √ 

2F (1 − 2F )K 

π M (0) = K + 

V 

which is increasing in K (decreasing in the intensity of competition) and 

decreasing in the value of the innovation V (since this increases the incentives 

of other firms to innovate and replace the monopolist). 

If the monopolist is investing, however, the first order conditions for the 

monopolist and for the other firms in Nash equilibrium would be: 

z =(1− z) n−2 (1 − z M )V , 

z M =(1− z) n−1 V − (1 − z) n−1 K 

which always imply a lower investment of the monopolist because of the 

Arrow effect. For instance, with two firms we have: 

z M = 

(1 − V )(V − K) 

1 − V (V − K) 

z = 

(1 − V )(V − K)+K 

1 − V (V − K) 

(1.44) 

It is interesting to verify what is the impact of an increase in the intensity of 

product market competition, which lowers current profits K without affecting 

the value of the drastic innovation V : this increases the investment of the 

incumbent according to the escape competition effect, but it decreases the 

investment of the outsider. 29 

28 See Aghion and Griffith (2005, pp. 55-56). An increase of the intensity of competition 

is associated with a lower price of the competitive fringe or with a higher 

probability of entry of equally efficient firms. 

29 Of course, the Arrow effect could be counterbalanced if we introduced a technological 

advantage for the incumbent (Barro and Sala-i-Martin, 1995) or absorptive 

capacity of the incumbent (Wiethaus, 2006,a,b), that is the ability to 

imitate the innovation of an outsider.


When entry of firms is free, investors enter as long as the expected profits 

are positive, that is until the following zero profit condition holds: 

z(1 − z M )(1 − z) n−2 V = z 2 /2+F 

This implies that each one of the other firms invests again z = √ 2F ,and 

we will now show that the incumbent monopolist prefers to withdraw from 

the contest and not invest in R&D. To see this, notice that the monopolist 

should invest less than the other firms, according to its optimality condition: 

z M (1 − z M )= √ 2F (1 − √ 2F )(V − K)/V 

This implies that the optimal investment of the monopolist should decrease 

with K: fromthesamelevelasfortheotherfirms z M = √ 2F when K =0 

toward zero investment z M =0when approaching K = V .Theprofits of the 

monopolist in case of positive investment would be: 

√ √ ∙ ¸ 

2F (1 − 2F ) (V − K)zM + K 

π M (z M )=K + 

− z2 M 

V 

1 − z M 2 − F 

where z M should be at its optimal level derived above. Notice that for K =0 

these expected profits are −F ,sothemonopolistprefersnottoinvestatall, 

and for K = V the expected profits tend to K + √ 2F (1− √ 2F )−F ,whichis 

again lower than the expected profits in case the monopolist does not invest 

at all. It can be verified that this is always the case for any K ∈ (0,V), 30 

hence the monopolist always prefers not to invest and decides to give up to 

any chances of innovation. 

Finally, notice that the escape competition effect disappears: an increase 

in the intensity of competition does not affect the investment of any firm or 

the aggregate probability of innovation. Perfect competition for the market 

eliminates any impact of competition in the market on the investment in 

innovation. 31 

In this simple example, the lack of incentives to invest for the monopolist 

emerges quite clearly. On the basis of this theoretical result, it is often 

claimed that monopolistic markets or markets with a clear leadership are 

less innovative. In a neat article on this topic appeared on the The Economist 

(2004, “Slackers or Pace-setters? Monopolies may have more incentives 

to innovate than economists have thought”, Economic Focus, May 22) this 

issue has been explained quite clearly: 

30 This immediate after comparing profits for the monopolist in case of zero and 

positive investment in Nash equilibrium as functions of K. 

31 Not by chance, Aghion and Griffith (2005) obtained the escape competition effect 

in a model where the incumbent is exogenously the only investor. In the next 

section we present a model where the incumbent is endogenously the only investor 

to verify that both the Arrow effect and the escape competition effect disappear 

in that case.


“By and large, officialdom these days continues to take a dim 

view of monopoly. Antitrust authorities in many countries do not 

shrink from picking fights with companies that they believe are too 

powerful. The biggest target in recent years, first in America and 

now in Europe, has been Microsoft, creator of the operating system 

that runs on some 95% of the world’s personal computers. One of 

the arguments against Microsoft is that its dominance of the desktop 

allows it to squeeze out smaller and (say the company’s critics) more 

innovative rivals. 

Despite this, compelling evidence that monopolists stifle innovation 

is harder to come by than simple theory suggests. Joseph 

Schumpeter, an Austrian economist, pointed out many years ago 

that established firms play a big role in innovation. In modern times, 

it appears that many product innovations, in industries from razor 

blades to software, are made by companies that have a dominant 

share of the market. Most mainstream economists, however, have 

had difficulty explaining why this might be so. Kenneth Arrow, a 

Nobel prize-winner, once posed the issue as a paradox. Economic 

theory says that a monopolist should have far less incentive to invest 

in creating innovations than a firm in a competitive environment: 

experience suggests otherwise. How can this be so? 

One possibility might be that the empirical connection between 

market share and innovation is spurious: might big firms innovate 

more simply because they are big, not because they are dominant? 

Apaper 32 published a few years ago by Richard Blundell, Rachel 

Griffith and John Van Reenen, of Britain’s Institute for Fiscal Studies, 

did much to resolve this empirical question. In a detailed analysis 

of British manufacturing firms, it found that higher market shares 

do go with higher investment in research and development, which in 

turn is likely to lead to greater innovation. Still, the question remains: 

why does it happen?” 

We now turn to this theoretical issue. 

1.4.2 Innovation by Leaders 

In this section we will study innovation contests where a firm can act as a 

leader and commit to an investment level before the other firms (Etro, 2004). 

It is reasonable to imagine that the firm able to commit to an investment 

in R&D before the others is the same incumbent monopolist that has the 

leading edge technology. This will be our assumption. 

Consider Stackelberg competition where the incumbent monopolist is the 

first mover. The symmetric reaction of the other firms to the investment of 

32 Blundell et al. (1999).


the leader is still governed by their equilibrium first order condition z =(1− 

z) n−2 (1−z L )V , where now z L is the investment of the leader, which is known 

at the time of the choice of the other firms. The above rule cannot be solved 

analytically, but it shows again that the investment of the outsider firms must 

be decreasing in the investment of the leader, ∂z/∂z L < 0: the higher the 

latter, the smaller the probability that no one innovates and therefore the 

expected gain from the investment of the followers is reduced. This implies 

that the leader has an incentive to choose a higher investment to strategically 

reduce the investment of the followers. However, the investment of the leader 

does not need to be higher than the investment of the other firms, because 

the Arrow effect is still pushing in the opposite direction. For instance, with 

two firms we have: 

z L = 

VK+(1− V )(V − K) 

1 − 2V (V − K) 

z = 

VK+(1− V )V − V 

3 

1 − 2V (V − K) 

(1.45) 

and the Arrow effect prevails on the Stackelberg effect whenever K>V 3 /(1− 

V ). 

When entry is endogenous, things are simpler. As long as the investment 

of the leader is small enough to allow entry of at least one outsider, the free 

entry condition is z(1 − z) n−2 (1 − z L )V = z 2 /2+F , which delivers again the 

investment z = √ 2F for each outsider. Putting together the two equilibrium 

conditions in the profit function of the leader, we would have: 

π L = K + z L (1 − z) n−1 (V − K) − z2 L 

2 − F = 

= K + z √ ³ 

L 2F 1 − √ ´ 

2F + K 1 − z L V 

√ 

2F 

³ 

1 − √ 2F 

´ 

− z2 L 

2 − F 

whose third element, the one associated with the current profits obtained in 

case no one innovates, is independent from the choice of the leader. Consequently, 

the choice of the leader is taken exactly as in our earlier model (with 

K =0) and requires an investment: 

√ 

2F 

¯z L =1− 

(1.46) 

V 

such that no other firm invests in innovation. Therefore, the profits of the 

leader can be calculated as a function of the value of the innovation π L = 

K +¯z L V +(1− ¯z L ) K − ¯z L 2 /2 − F . 

Welfare comparisons are ambiguous: on one side the aggregate probability 

of innovation is lower under Stackelberg competition with free entry rather 

than in the Marshall equilibrium, on the other side expenditure in fixed and 

variable costs of research is lower in the first than in the second case. 33 

33 However, in a dynamic environment where the value of the innovation is endogenous, 

things would change. While without a leadership of the monopolist,


Moreover, notice that when the monopolist is the leader in the competition 

for the innovation, the Arrow effect disappears, because the choice of 

the monopolist is independent from the current profits. The leadership in 

the competition for the market radically changes the behavior of a monopolist: 

from zero investment to maximum investment. The cited article of The 

Economist (2004) has discussed the relation between this theory and innovation 

by monopolists in real world markets. When entry is endogenous: 

“a market leader has a greater incentive than any other firm to 

keep innovating and thus stay on top. Blessed with scale and market 

knowledge, it is better placed than potential rivals to commit itself to 

financing innovations. Oddly–paradoxically, if you like–in fighting 

to maintain its monopoly it acts more competitively than firms in 

markets in which there is no obviously dominant player. 

The most important requirement for this result is a lack of barriers 

to entry: these might include, for example, big capital outlays to fund 

the building of new laboratories, or regulatory or licensing restrictions 

that make it hard for new firms to threaten an incumbent. If there 

are no such barriers, a monopolist will have an excellent reason to 

innovate before any potential competitor comes up with the next new 

thing. It stands to lose its current, bloated profits if it does not; it 

stands to gain plenty from continued market dominance if it does. 

If the world works in the way Mr Etro supposes, the fact that 

a dominant firm remains on top might actually be strong evidence 

of vigorous competition. However, observers (including antitrust authorities) 

may well find it difficult to work out whether a durable 

monopoly is the product of brilliant innovation or the deliberate 

strangulation of competitors. More confusing still, any half-awake 

monopolist will engage in some of the former in order to help bring 

about plenty of the latter. The very ease of entry, and the aggressiveness 

of the competitive environment, are what spur monopolists 

to innovate so fiercely. 

But what if there are barriers to entry? These tend to make the 

dominant firm less aggressive in investing in new technologies–in 

essence, because its monopoly with the existing technology is less 

likely to be challenged. Over time, however, other companies can innovate 

and gradually overcome the barriers... Meanwhile, the monopolist 

lives on marked time, burning off the fat of its past innovations. 

the value of innovation would be just the value of expected profits from this 

innovation (the innovator will not invest further), with a leadership by the monopolist, 

the value of innovation should take into account the option value of 

future leadership and future innovations: this would endogenously increase the 

value of being an innovator and would increase the aggregate incentives to invest. 

We will return on this important point in Chapter 4.


So much for theorizing. What might the practical implications be? 

One is that antitrust authorities should be especially careful when 

trying to stamp out monopoly power in markets that are marked by 

technical innovation. It could still be that firms like Microsoft are 

capable of using their girth to squish their rivals; the point is that 

continued monopoly is not cast-iron evidence of bad behavior. 

There might be a further implication for patent policy. Patents, 

after all, are government-endorsed monopolies for a given technology 

for a specified period. Mr Blundell and his colleagues found that 

the pharmaceutical industry provided the strongest evidence of correlation 

between market share and innovation. Thus strong patents, 

despite their recent bad press, can be a source of innovation. Generally, 

though, when one company dominates a market, people should 

be careful in assuming that it is guilty of sloth. It may be fighting 

for its life.” 

The idea behind this discussion can bedescribedinsimplertermsasa 

derivation of two sufficient conditions under which monopolists have incentivestoinvestinR&Dandtoinvestmorethanotherfirms: 

1) leadership 

for the monopolist and 2) endogenous entry for the outsiders in the race to 

innovate. We will return on these issues in Chapter 4, and discuss their policy 

implications in Chapters 5 and 6. 

Finally, we confirm that, also when the incumbent monopolist endogenously 

invests in R&D, the escape competition effect disappears: an increase 

in the intensity of product market competition as formalized by Aghion and 

Griffith (2005) does not affect innovation when entry in the competition for 

the market is free. This may suggest that competition for the market could 

be a good substitute for competition in the market, another point on which 

we will return later in the book. 

1.5 Conclusions 

In this chapter we developed some toy models to compare different equilibria. 

Toy models can be quite suggestive and even provide many interesting 

insights, however they often hide very simplistic assumptions and it is hard 

to understand whether certain results hold in general or just under specific 

assumptions. That is why it is now time to generalize our models at a deeper 

level. The objective of the next chapters will be an investigation of the general 

properties of our four alternative equilibria. 

Moreover, in this chapter we developed examples in which firms compete 

strategically in a symmetric way, or in which a firm is a leader and has a 

first mover advantage in the choice of its strategy. Since a commitment to 

a strategy (especially a price strategy) can lack credibility (especially in the 

long run), it is important to verify whether alternative credible commitments

1.5 Conclusions 35 

or strategic investments can sustain results similar to those derived here. In 

Chapter 2 we will approach this issue developing a general model of strategic 

commitments. 

Before moving to this task, however, it is important to summarize what 

we have learned with our toy models. First, we considered simple models 

of competition in quantities. We noticed that market leaders produce more 

output than each one of the other followers, both in the case of exogenous 

entry and in the case of endogenous entry. As we will see, this does not 

always hold with exogenous entry, but it always holds with endogenous entry. 

We also noticed that in certain situations (homogenous goods and constant 

marginal costs) leaders deter entry when entry is endogenous, while in other 

cases (U shaped average cost functions or imperfect substitutability between 

goods) they do not and allow entry. We also noticed that the behavior of 

market leaders under price competition was radically different depending on 

the entry conditions. It is important to understand what drives these results, 

and we will explore this issue in Chapter 3. 

Finally, we looked at a simple model of competition for the market and 

obtained a surprising result. While incumbent monopolists do not have incentives 

to invest in R&D if the competition for innovating is free and symmetric 

between all firms, when these incumbents have a leadership in the competition 

for the market they also have strong incentives to invest and end up 

being the only investors. If this is the case, their leadership should be persistent 

over time and innovation and technological progress would be driven by 

market leaders. In Chapter 4 we will generalize the model of competition for 

the market in realistic ways and will try to evaluate these drastic results.


1.6 Appendix 

1. Taking Care of the Integer Constraint. In the derivation of the 

Stackelberg equilibrium with endogenous entry, homogenous goods and constant 

marginal costs of Section 1.1 we simplified things assuming that the 

number of firms was a real number. Here we verify that the equilibrium is 

exactly the same even if we consider, more realistically, that the number of 

firms in the market must be an integer. We provide a constructive proof since 

this is helpful to understand the general behavior of the profits of the leader 

in a more general version where the integer constraint on the number of firms 

is taken in consideration. 

Given the production of the leader q L and the number of firms n, the 

reaction function and the profits of each follower are the same as before. 

However, the number of firms is a step function of the output of the leader. 

In particular, the number of firms is given by the integer number n ≥ 2 when 

the output of the leader is between s(n) and s(n − 1), where these cut-offs 

are defined as: 

s(n) ≡ a − c − (n +1) √ F 

while only the leader can be profitably in the market (n =1)whenq L >s(1). 

Let us remember that for any exogenous number of firms the profits of the 

leader are maximized at the monopolistic output (a−c)/2, andthereforethis 

profits are increasing before and decreasing after this output level. Given this, 

we can determine the behavior of the profits of the leader in function of its 

output distinguishing three regions. 

The high output region, emerges for a small enough number of firms n 

such that s(n) > (a − c)/2 or n

1.6 Appendix 37 

It can be easily verified that π L (n) >π L (n +1) for any number of firms 

active in this region, therefore it is optimal to choose a production that 

maximizes profits with n =1, that is exactly the entry deterrence output 

s(1) = a − c − 2 √ F . This output delivers the profits: 

π L (1) = 2 √ ³ 

F a − c − 2 √ ´ 

F − F 

The low output region emerges for any high enough number of firms n 

such that s(n − 1) < (a − c)/2, orn>(a − c)/2 √ F .Thisimpliesthatthe 

profits of the leader are always increasing in the output. Trivially, it is never 

optimal to produce less than the monopolistic output. 

The third case emerges for a number of firms such that s(n) < (a−c)/2 < 

s(n − 1), or: 

µ a − c 

n ∈ 

2 √ F − 1; a − c 

2 √ F 

In the interval of production x L ∈ [s(n),s(n − 1)] it is optimal for the leader 

to choose the monopolistic output level, because (only) in this interval profits 

have an inverted U shape. In this interval, the leader produces (a − c)/2 and 

each one of the n−1 followers produces (a−c)/2n as in a standard Stackelberg 

model with an exogenous number of firms. The usual profits of the leader are 

then: 

(a − c)2 

π L (n) = − F 

4n 

and we need to verify that these are always smaller than what the leader can 

obtain with the entry deterrence strategy. Since: 

(a − c) 2 

π L (1) R π L (n) ⇔ n R 

8 √ F (a − c − 2 √ F ) 

the profit maximizing choice of the leader could be in this region if there is 

anumberoffirms n that belongs to the set derived above and that is lower 

than the cut-off just obtained. However, this requires that this cut-off is larger 

than (a − c)/2 √ F − 1 and: 

(a − c) 2 

8 √ F (a − c − 2 √ F ) > a − c 

2 √ − c)2 

− 1 iff F>(a 

F 16 

This is impossible because we assumed F


2. Endogenous Costs of Entry. The theory of Stackelberg competition 

with endogenous entry can also be seen as depicting the way a market 

leader can extract rents from a competitive market in the presence of fixed 

costs of entry. These costs can be interpreted as technological costs that are 

taken as given by the firms. However, they can also be endogenized imagining 

that they characterize the market and that the same leader can choose 

them in a preliminary stage. For instance, by investing in R&D or paying 

for an advertising campaign, or even by establishing certain barriers to entry 

associated with a cost of entry, the leader can set a sort of benchmark: all the 

other firms have to undertake the same investment, pay the same advertising 

campaign or face the same costs of entry to be able to compete in the market 

(Sutton, 1998). 

Imagine that the leader can choose the investment F . Consider for simplicity 

the linear example of competition in quantities of Section 1.1. The 

demand and cost characteristics of this market depend on this investment so 

that the parameters a(F ) and c(F ) are now functions of the endogenous investment. 

This will be chosen to maximize the expected profits of the leader: 

π L (F )=2 √ F 

h 

a(F ) − c(F ) − 2 √ F 

i 

− F 

In general, the choice will imply a positive investment (otherwise the 

leader would expect zero profits). One can also show that from a welfare 

point of view, the leader will choose an excessive investment if this investment 

reduces its equilibrium production, but will choose a suboptimal investment 

in the opposite case. 34 In other words, leaders tend to do too little of good 

things and too much of bad things. 

For instance, imagine that F serves no real purpose other than raising 

the cost of entry (a 0 (F )=c 0 (F )=0). This is the case of what we usually call 

an artificial barrier to entry created by the dominant firm. The leader would 

maximize its expected profits choosing a positive barrier to entry: 

F ∗ (a − c)2 

= 

25 

which delivers the net profits: 

(a − c)2 

π L = 

5 

In other words the leader would create a completely useless barrier associated 

with a fixed cost (born by the leader as well) just to profit expostfrom 

its entry deterring strategy. Of course, in this case the welfare maximizing 

34 This is an immediate consequence of the definition of welfare as a sum of consumer 

surplus and profits. When profits of the leader are maximized the investment 

is excessive if the consumer surplus is decreasing in the investment, that is 

if output is decreasing. Of course this is still a second best comparison.


barrier would be F =0, which would lead to complete rent dissipation and 

marginal cost pricing with zero profits for everybody. The moral of this story 

is that the priority in industrial policy should be to create the conditions for 

free entry and hence to fight against artificial barriers to entry, not to fight 

against leaders per se.

2. Strategic Commitments and Endogenous 

Entry 

In this chapter we will study a general model of market structure and characterize 

the incentives of a firm to adopt different strategic commitments 

to gain a competitive advantage over the rivals. We will develop a unified 

general framework in which standard models of competition in the market 

and for the market are nested, including those analyzed in Chapter 1 and 

others analyzed and extended in Chapters 3 and 4. Virtually all models of 

competition in quantities with homogenous or imperfectly substitute goods 

and with general shapes of the cost function are nested in our general model. 

Also encompassed are a wide class of models of competition in prices (as 

long as the demand function satisfies some regularity conditions), including 

models with a constant expenditure demand function or isoelastic demand 

functions (derived from quasilinear utilities or homotethic utilities àlaDixit 

and Stiglitz), and a wide class of models of competition for the market, whose 

detailed analysis will be postponed to Chapter 4. 

The initial focus of this chapter will be on Nash equilibria and on Marshall 

equilibria, that is on market structures characterized by symmetry between 

an exogenous number of firmsintheformercaseandanendogenousnumber 

of firms in the latter case. Nash competition can be interpreted as a form of 

competition with an exogenously limited number of firms, whose equilibrium 

can be seen as a short term equilibrium of a given market or even as a general 

equilibrium for a market where entry is exogenously constrained (for instance 

by legal or regulatory barriers to entry). A symmetric Nash equilibrium can be 

easily characterized through a single equilibrium profit maximizing condition 

that takes into account symmetry between the firms, for instance a mark up 

rule for the Cournot model of competition in quantities or for the Bertrand 

model of competition in prices. Such a characterization allows one to study 

the comparative statics of the equilibrium variables and hence it is at the 

basis of the analysis of the interaction between exogenous variables (as costs, 

taxes, demand parameters, or even the number of firms in the market) and 

endogenous variables (output, prices, profits). 

Marshallian competition can be interpreted in terms of a medium or long 

run equilibrium in which there are not exogenous barriers to entry. In such a 

context entry is endogenously determined by the presence of profitable opportunities 

to be exploited. When these opportunities are exhausted, the entry

42 2. Strategic Commitments and Endogenous Entry 

process stops. In the Marshall equilibrium, the strategies of the firms and 

the number of firms are jointly determined by a profit maximizing condition 

and by an endogenous entry condition (typically a zero profit condition or a 

no arbitrage condition between entry in different sectors), both taking into 

account symmetry between firms. Also in such a case, we can easily verify 

the impact of changes in demand and supply conditions and other exogenous 

policy parameters on the equilibrium variables, namely output, prices and 

the number of firms. 

Building on this general framework and on this standard characterization 

of equilibria, we will introduce the analysis of market leaders verifying their 

incentives to adopt alternative strategic investments that can create a competitive 

advantage in the subsequent competition with the other firms. 1 As 

we will see, the behavior of the leaders changes when they face an exogenous 

number of competitors or an endogenous number. The first case has been 

characterized at least since the work of Fudenberg and Tirole (1984) and 

Bulow et al. (1985) on duopolies. Suppose that firm i has the gross profits 

Π(x i ,X −i ,k), which depend on its strategy x i , the aggregate statistics X −i 

summarizing the strategies of the other firms, and the preliminary investment 

k. Then, the strategic incentives to invest for this firm depend on the impact 

of the investment on the marginal profitability (Π 13 ), 2 and on the nature 

of the strategic interaction between firms (Π 12 ). Therefore, they are typically 

different in models of competition in quantities, where output choices 

are often strategic substitutes (Π 12 < 0), and in models of competition in 

prices, where strategic complementarity usually holds (Π 12 > 0). On this 

basis, Tirole (1988) has built a taxonomy of business strategies that implies 

four different strategies for the leader: a firm may overinvest or underinvest 

initially to be more accommodating or aggressive subsequently. As shown in 

Etro (2006, a), things simplify drastically when entry of firmsisendogenous, 

because in such a case the strategic incentives to invest are independent 

from the strategic interaction between firms: the optimal investment of a 

firm depends only on whether the investment increases or not the marginal 

profitability, which leads to results that do not dependent on whether prices 

or quantities are the strategic variables. More precisely, when entry is endogenous, 

a firm invests always in the direction that leads to an aggressive 

behavior in the market. Of course, our interest in this outcome relies on the 

belief that in most situations entry in the markets is indeed endogenous, and 

the proper way to analyze the behavior of firms should take this element into 

account. 

The abstract and general rules we just pointed out have a lot of applications 

to industrial organization and related fields, and this chapter will 

analyze a few of them. Fundamental strategic investments are those affect- 

1 See Singh et al. (1998) on the empirical relevance of strategic investments by 

leaders. 

2 Subscripts denote derivatives with respect to the arguments.

2. Strategic Commitments and Endogenous Entry 43 

ing supply, as cost reducing investments or overproduction in the presence 

of learning by doing, and those affecting demand, as investments in quality 

improvements, in advertising, in product differentiation. We will show that 

when entry in the market is endogenous, a market leader has always a strategic 

incentive to overinvest in the first typology of investments because this 

leads to aggressive behavior, while the role of demand enhancing investments 

is more complex. 

Another application concerns the theory of corporate finance: starting 

from the literature on the relation between the optimal financial structure 

and product market competition (Brander and Lewis, 1986) we will examine 

the incentives to adopt strategic debt financing for markets with free entry. 

It turns out that under quantity competition there is always a strategic bias 

toward debt financing, while under price competition there is only when uncertainty 

affects costs, but not when it affects demand. In general, departing 

from the standard Modigliani-Miller neutrality result, a financial tool like 

debt is useful when it constrains equity holders to adopt more aggressive 

strategies in the market, and this is the case when positive shocks increase 

marginal profits. 

Other new applications developed in detail here concern discrete commitments. 

We will examine the case of bundling strategies. In an influential 

paper, Whinston (1990) has studied bundling in a market for two goods. The 

primary good is monopolized by one firm, which competes with a single rival 

in the market for the secondary good. Under price competition in the secondary 

market, the monopolist becomes more aggressive in its price choice in 

the case of bundling of its two goods. Since a more aggressive strategy leads 

tolowerpricesforbothfirms as long as both are producing, the only reason 

why the monopolist may want to bundle its two goods is to deter entry of the 

rival in the secondary market. This conclusion can be highly misleading because 

it neglects the possibility of further entry in the market. We show that, 

if the secondary market is characterized by endogenous entry, the monopolist 

would always like to be aggressive in this market and bundling may be the 

right way to commit to an aggressive strategy: bundling would not necessarily 

exclude entry, but may increase competition in the secondary market and 

reduce prices. 

Many other implications are relevant for antitrust policy. For instance, 

we will consider the theory of vertical restraints for interbrand competition 

(Rey and Stiglitz, 1988; Bonanno and Vickers, 1988), and show that a market 

leader facing endogenous entry would want to delegate distribution to a 

downstream retailer through wholesale prices below marginal cost: in such a 

case we have an example of a pro-competitive vertical restraint. 

Other results that are relevant for antitrust purposes concern the incentives 

to adopt limited interoperability, third degree price discrimination, and 

aggressive pricing in the presence of network externalities or multi-sided markets. 

Finally, we will apply our result to horizontal mergers and show that


they create a strategic disadvantage for firms facing endogenous entry: therefore, 

in markets where entry is endogenous, mergers can only emerge when 

they create large efficiency gains, a point which is largely in line with the 

informal results of the Chicago school. 

The chapter is organized as follows. Sections 2.1 describes our general 

framework and Sections 2.2-2.3 characterize the Nash equilibrium and the 

Marshall equilibrium. Section 2.4 clarifies which models of competition in 

quantities, in prices and for the market are nested in the general framework, 

and derives some properties of these models. Section 2.5 analyzes general 

strategic investments in Nash and Marshall equilibria. Section 2.6-2.13 apply 

the results to a number of industrial organization issues. Section 2.14 

concludes. 

2.1 Market Structure 

A market structure is characterized by a number of firms, their strategies, 

a relationship that links all the strategies with the profit ofeachfirm and 

an equilibrium concept, which requires consistency between all the optimal 

strategies. 

In general, firms can choose many different strategies, for instance they 

can choose the price of their products, their quality, the investment in advertising 

and so on, and they can also choose these and other strategies for 

different products or different periods. However, in this chapter we will refer 

to the case of a single strategy. Imagine that in the market there are n firms 

and that the vector of their strategies is x =[x 1 ,x 2 , ..., x n ] where x i is the 

strategy of firm i. Wemaythinkthatdifferent firms have different features 

and different technological options, and there can be different profit functions, 

say π i (x) for each firm i. A market structure is a set of strategies x for 

n firms with profit functionsπ i (x), suchthatx i =argmaxπ i (x) for each i. 

A large portion of this book will deal with models of competition in the 

market where firms choose their output or their prices to maximize revenues 

net of the production cost c(·), which is increasing in the level of production, 

and net of a fixed cost F ≥ 0. In particular, we will deal with models of 

quantity competition, as those studied in Chapter 1, where the strategy q i 

represents the level of production of firm i, and profits are given by: 

π i (q 1 , .., q i , .., q n )=q i p i (q 1 ,q 2 , .., q n ) − c(q i ) − F 

where p i (·) is the inverse demand, decreasing in the output of every firm. 

Interesting applications that will be described in detail include models with 

linear demand, as those adopted in Sections 1.1-2, models with isoelastic 

demands and homogenous goods, and models with imperfectly substitutable 

goods.

2.1 Market Structure 45 

Another wide class of models is based on price competition and imperfect 

substitution between goods, where the strategy p i represents the price of firm 

i and profits are given by: 

π i (p 1 , .., p i , .., p n )=p i D i (p 1 , .., p i ,..,p n ) − c [D i (p 1 , .., p i ,..,p n )] − F 

with a direct demand function D i (p 1, .., p i , .., p n ) that decreases in the price of 

firm i and increases in the price of the other firms. Applications that will be 

investigated later on include models with the Logit demand (as those studied 

in the example of Section 1.3), models with isoelastic demand functions, 

constant expenditure demand functions and others. 

We will also study forms of competition for the market in which firms 

choose a strategy z i that allows to conquer a market whose value is V 

with a probability that depends also on the choices of the other firms, 

Pr i (z 1 , .., z i ,..,z n ). In such a case, expected profits are: 

E [π i (z 1 , .., z i , .., z n )] = Pr i (z 1 , .., z i ,..,z n )V − c (z 1 , .., z i , .., z n ) − F 

where the cost function c(·) can depend on the investment of each firm. Examples 

include the simple contest we studied in Section 1.4, more complicated 

patent races where firms invest over time and innovate according to complex 

stochastic processes, and also models of rent seeking where the probability 

that an agent obtains a generic rent is the ratio between the agent’s investment 

and total investment by all other agents. 

These market structures are general enough to include most of the realistic 

competitive frameworks analyzed in the theory of oligopoly. However, since 

a main topic of this book is the effect of entry on the strategic interaction 

between firms that have the same production technologies available and that 

face the same demand structure, we need to impose some further restrictions 

on the functional forms to be used. In particular, in the main analysis we will 

focus on models in which all firms have the same cost technology and there 

are not exogenous differences or asymmetries between them. 

Accordingly, we will not deal with spatial models of horizontal or vertical 

differentiation like the Hotelling (1929) duopoly with spatial differentiation. 3 

3 Imagine two firms choosing their prices p 1 and p 2 with the profit functions 

π i (p i ,p j )=p i D(p i ,p j ) where demands are: 

D(p 1 ,p 2 )= (k 1 + k 2 ) 

2 

+ (p 2 − p 1 ) 

2(k 2 − k 1 ) , D(p 2,p 1 )= (2 − k 1 + k 2 ) 

2 

− (p 2 − p 1 ) 

2(k 2 − k 1 ) 

Such an apparently complicated structure can be derived from a very simple 

situation. Imagine that consumers of a single unit of product are uniformly distributed 

along a market of unitary length, that is on [0, 1]. Onthismarkettwo 

firms are located at distances k 1 and k 2 >k 1 from the origin, produce homogenous 

goods at no cost and sell them at prices p 1 and p 2 . Each consumer at 

distance d from the origin will buy the good that minimizes the price plus a cost


Clearly in such a model, the equilibrium prices and profits depend on the 

initial locations of the two firms/products. 4 In other words, profit functions 

and equilibrium outcomes depend on exogenous and firm specific parameters 

which introduce a substantial asymmetry between the firms. Moreover, if we 

were going to evaluate the entry opportunities in such a market, the result 

would be completely dependent on the location of the new entrants compared 

to the location of the incumbents. 5 The reason is that every new firm would 

compete just with its two closest rivals (for the consumers between them) 

and therefore each firm would have a different profit function depending on 

its particular competitors and their features. 6 Such a situation can depict 

markets where geographical location or, in a metaphorical sense, horizontal 

differentiation are a crucial element. However, it badly characterizes many 

other markets where each firm has to compete with all the other firms at 

once since all products in the market are potentially substitutes (which, in 

the applied analysis, is what defines a market). For this reason, our focus in 

this book, in line with the tradition associated with Chamberlin (1933), will 

be on models that allow for competition between symmetric firms. 

Finally, since we are interested in characterizing endogenous entry of 

firms, we will limit our attention to markets where equilibrium profits decrease 

when entry occurs, a realistic feature that is not always verified in 

standard models. 7 

which is quadratic in the distance from the location of the corresponding firm, 

that is good i such that p i +(k i − d) 2 is smallest. This framework allows division 

of consumers between those buying good 1 and those buying good 2, delivering 

the demands above. 

4 Indeed, maximizing the two profit functions with respect to the prices and solving 

for them, one can find the equilibrium with p 1 =(2+k 1 + k 2 )(k 2 − k 1 )/3 and 

p 2 =(4− k 1 − k 2 )(k 2 − k 1 )/3. 

5 Clearly one could endogenize the location decision (for instance, with two firms, 

they would choose maximum differentiation, placing themselves at the borders 

of the market with k 1 =0and k 2 =1). See the fundamental contribution of 

D’Aspremont et al. (1979) for a formal and general treatment, and Anderson et 

al. (1992) for further discussion. 

6 We could easily extend the model to n firms symmetrically distributed along a 

circle where consmers are also distributed uniformly and choose between products 

as before (Vickrey, 1964). The Nash equilibrium would generate the price 

p =1/n 2 for each firm, and the Marshall equilibrium would imply n =1/ 3√ F 

firms selling at the price p = 3√ F 2 . 

7 For instance, we will exclude from our main analysis the basic model of price 

competition with linear demand (associated with Bowley, 1924) as D i = a −p i + 

b j6=i p j. In the Nash-Bertrand equilibrium, this model implies that the profits 

of each firm increase in the number of firms. Something that makes no sense in 

real markets. See Section 3.4.5 on this point.

2.1 Market Structure 47 

More formally, in this book we will focus on a class of market structures 

with profit functions that are symmetric, additively separable and decreasing 

in the strategies of the other firms. For consistency, we will drop separate 

notations for different strategies and adopt a generic strategic variable x i ≥ 0 

for any firm i. Given the strategies x j for all j =1, 2, ..., n, eachfirm i has a 

net profit function: 

π i = Π (x i ,β i ) − F (2.1) 

which depends on two main factors: the strategy of the same firm x i and a 

factor which summarizes the strategies of the other firms β i .Weassumethat: 

Π 1 (x i ,β i ) R 0 for x i S x(β i ) 

for some turning point x(β i ),andΠ 11 (x, β) < 0, or more generally that 

Π (x, β) is quasiconcave in x. Therefore, it is an inverted U curve in x for 

any β. 

The effects (or spillovers) induced by the strategies of the other firms on 

firm i’s profits are summarized by: 

nX 

β i = h(x k ) (2.2) 

k=1,k6=i 

for some function of the strategies of each other firm h(x) that is assumed 

continuous, differentiable, non-negative and increasing in x. The gross profits 

are assumed to decrease in the strategies of the other firms and in their 

summary statistics β, thatisΠ 2 (x, β) < 0. 8 

In general, it could be that Π 12 is positive, so that we have strategic complementarity 

(since this implies ∂Π 1 (x i ,β i ) /∂x j > 0), from now on denoted 

with SC, or negative so that we have strategic substitutability (since this implies 

∂Π 1 (x i ,β i ) /∂x j < 0),denotedwithSSfromnowon.Intheformer 

case x 0 (β i ) > 0, which implies that the reaction functions are upward sloping 

(∂x(β i )/∂x j > 0 for all firms), in the latter x 0 (β i ) < 0, which implies 

that the reaction functions are downward sloping (∂x(β i )/∂x j < 0 for all 

firms). Of course, intermediate cases with non monotone reaction functions 

can emerge as well. An important outcome of the following analysis will concern 

the characterization of the firmsstrategiesunderdifferent conditions. 

For this purpose, let us introduce a behavioral definition: a strategy x is aggressive 

compared to another strategy x 0 if x>x 0 , and is accommodating in 

the opposite case; a firm adopting a strategy x>x 0 is more aggressive than 

a firm adopting a strategy x 0 . 

8 For models of competition in prices an axiomatic foundation for a similar profit 

function can be derived by a demand system that satisfies the Independence 

from Irrelevant Alternatives property (the ratio of quantities demanded of any 

two goods is independent of the existence or price of a third good).


2.2 Nash Equilibrium 

Our first analysis is about competition between n firms. This number is kept 

exogenous and no other firms can enter in the market even if there are profitable 

opportunities to be exploited. This could happen because there are 

legal or institutional constraints on the number of actors in the market, or 

because the underlying technology is only available for a restricted number of 

firms. In a Nash equilibrium every firm chooses its strategy to maximize its 

own profits given the strategies of the other firms and the equilibrium strategies 

must be consistent with each other. In this kind of game, a pure-strategy 

Nash equilibrium exists if the reaction functions are continuous or do not 

have downward jumps. While in general this may not hold, weak conditions 

for existence have been studied for many applications, 9 andinthisgeneral 

framework we will just assume the existence of a unique and symmetric equilibrium.Moreprecisely,wecandefine 

the following concept of symmetric 

equilibrium: 

Definition 2.1. A Nash Equilibrium between n firmsissuchthat:1) 

each firm chooses its strategy x to maximize its profits given the spillovers β 

from the other firms; 2) β =(n − 1)h(x). 

Notice that the last condition guarantees consistency between the fact 

that all firms choose the same strategy x and that the spillovers for each firm 

are at the same level β. We will assume that in equilibrium all firms make 

positive profits, or in other words, that the fixed cost is small enough to allow 

each firm to gain from being in the market. 

To characterize the equilibrium, notice that, given the strategy of each 

other firm, firm i chooses its own strategy to satisfy the first order condition 

Π 1 (x i ,β i )=0. Imposing symmetry in equilibrium between the followers we 

have: 

Π 1 [x, (n − 1)h(x)] = 0 (2.3) 

which completely defines the equilibrium strategy x. WerequireΠ 11 +(n − 

1)Π 12 h 0 (x) < 0 to assume local stability. 10 

To investigate the comparative properties of the Nash equilibrium with 

respect to the number of firms n, which is the only exogenous variable, let us 

totally differentiate the equilibrium condition to obtain: 

dx 

dn = Π 12 h(x) 

{−[Π 11 +(n − 1)Π 12 h 0 (x)]} T 0 if Π 12 T 0 (2.4) 

The related effects on profits are: 

9 See Vives (1999). 

10 In this book we will not deal with dynamic concepts of stability and evolutionary 

learning. On this issue see Fudenberg and Levine (1998).

2.3 Marshall Equilibrium 49 

dΠ 

dn = − Π 2 h(x)Π 11 

{−[Π 11 +(n − 1)Π 12 h 0 (x)]} < 0 (2.5) 

An increase in the number of firms increases the strategic choice of each 

firm if SC holds, and decreases it under SS, 11 while we always have a negative 

impact of entry on the profits of each firm as long as Π 2 < 0. 

2.3 Marshall Equilibrium 

Now we will drop the assumption that the number of firms is exogenous and 

look at the more realistic situation in which firms can actually enter in the 

market if there are profitable opportunities to be exploited. If entry is free, it 

occurs until the gross profits are equal to the fixed costs of production. Nevertheless, 

one could also think of the profits in other sectors as constraining 

entry: according to this “general equilibrium” interpretation, a no arbitrage 

condition between sectors would make sure that net profits are equal in all 

sectors and it would endogenizes entry. 

As we noticed above, the profits for each firm in the Nash equilibrium are 

always decreasing in the number of firms. This implies that when there are 

positive profits in equilibrium with n firms, there is an incentive for outsiders 

to enter in the market. Then we can define a symmetric Nash equilibrium 

with endogenous entry as follows: 

Definition 2.2. A Marshall equilibrium is such that 1) each firm chooses 

its strategy x to maximize its profits given the spillovers β from the other 

firms; 2) the number of firms n is such that all firms make non negative 

profits and entry of one more firm would induce negative profits for all of 

them; 3) β =(n − 1)h(x). 

To characterize the equilibrium, we still have the first order equilibrium 

condition: 

Π 1 [x, (n − 1)h(x)] = 0 (2.6) 

Moreover, we can impose the endogenous entry requirement as a zero profit 

condition. We will neglect the integer constraint on the number of firms: this 

is a good approximation when there are many firms - in general, the exact 

equilibrium number of firms would be the higher integer that is smaller than 

our equilibrium number. 

The endogenous entry condition becomes: 

11 It can be equivalently shown that the effect of any other exogenous parameter 

depends on its impact on the marginal effect of the strategic variable.


Π [x, (n − 1)h(x)] = F (2.7) 

These two equations define the strategy of each firm and the number of firms 

as functions of the fixed cost. Local stability requires now Π 2 h(x) +Π 11 + 

(n − 1)Π 12 h 0 (x) < 0. To study the comparative statics of the system, we 

totally differentiate it with respect to F to obtain: 

dx 

dF = Π 12 

−Π 11 Π 2 

R 0 if Π 12 Q 0 

dn 

dF = Π 11 +(n − 1)Π 12 h 0 (x) 

< 0 (2.8) 

Π 11 Π 2 h(x) 

as long as Π 11 +(n − 1)Π 12 h 0 (x) < 0. Hence, a Marshall equilibrium implies 

strategies decreasing (increasing) in the fixed cost under SC (SS) and 

anumberoffirms decreasing in the fixed cost. An interesting interpretation 

of these comparative statics effects emerges if we think of a general equilibrium 

model where an increase in F corresponds to a positive shock on the 

profitability of the other sectors. Such a shock would make firms more aggressive 

in a market with SS and more accommodating in a market with SC, 

but it would always reduce the number of firms. For instance, if we think of 

markets with competition in prices in general equilibrium, a positive shock 

in one sector has the effect of increasing prices and reducing entry in the 

other sectors, an implication rarely matched by macroeconomic models with 

imperfect competition (since these models typically neglect the endogeneity 

of entry). 12 

2.4 Competition in Quantities, in Prices and for the 

Market 

In this section we will show that general models of competition in quantities 

and in prices and models of competition for the market are nested in our general 

framework, and we will analyze the Nash equilibrium and the Marshall 

equilibrium in these models. 

2.4.1 Competition in Quantities 

In Chapter 1 we examined some simple cases of competition in quantities. 

Here we will examine more general models of this kind. Consider a general 

demand function: 

⎡ 

⎤ 

nX 

p i = p ⎣ x i , h(x j ) ⎦ 

j6=i 

12 Introducing another exogenous parameter, say k, affecting each profit function 

Π(x i ,β i ,k) with Π 3 > 0, the strategies are decreasing in k whenever Π 13 Π 2 > 

Π 3Π 12, whiletheeffect on the number of firms is ambiguous.

2.4 Competition in Quantities, in Prices and for the Market 51 

decreasing in both arguments, and a cost function c(x i ) for firm i,withc 0 (·) > 

0, wherex i is the quantity produced by firm i. Profits are then: 

⎡ 

⎤ 

nX 

π i = x i p ⎣ x i , h(x j ) ⎦ − c(x i ) − F (2.9) 

j6=i 

Using our definitions, the gross profit function can be written as: 

Π (x i ,β i )=x i p (x i ,β i ) − c(x i ) (2.10) 

and it can be easily verified that it is nested in our class of market structures 

(2.1) under weak conditions. This model is general enough to take into 

account different shapes of the cost function and imperfect substitutability 

between goods. In general, it can be characterized by SS or SC since we have 

Π 12 = p x + x i p xβ ,whosefirst element is negative and whose second element, 

proportional to the impact of a change of production of other firms on the 

slope of inverse demand, has an ambiguous sign. 

Here, for simplicity, we will focus on the case where β i = P n 

k=1,k6=i x k, 

that is h(x i )=x i . For instance, assuming linear demand functions as those 

studied in Chapter 1, we would have: 

p i = a − x i − bβ i , b ∈ (0, 1] 

where Π 12 (x i ,β i )=−b 0 

where Π 12 (x i ,β i )=−γ [a + β i − γx i ](x i + β i ) −γ−2 whose sign is positive 

for x i low enough and negative for x i high enough: consequently, the reaction 

functions have an inverse U shape. This demand can be derived from a 

standard constant elasticity utility function: 

U = (a + P n 

J=1 C j) 1−γ 

+ C 0 (2.12) 

1 − γ 

for γ>0.


It is also possible to have situations in which SC holds always. For instance, 

Stackelberg (1934) presented an example with exponential demand 

p = exp [−(x i + β i ) υ ] which generates SC for υ ∈ (0, 1). Nevertheless, we 

should keep in mind that output strategies are complements only in the extreme 

cases in which demand is highly convex. 

A general characterization of Cournot models is beyond our scope, therefore, 

in the rest of this section, we will focus on some particular cases. 

Homogenous goods. In the case of homogenous goods, the Nash-Cournot 

equilibrium condition under symmetry becomes: 13 

p(X)+xp 0 (X) =c 0 (x) 

where total output is X = nx (under the second order condition 2p 0 + xp 00 < 

0). This is the usual rule equating marginal revenue and marginal cost, and 

can be rewritten as a mark-up rule (p − c 0 ) /p = −xp 0 /p, whose right hand 

side is the inverse of the elasticity of direct demand = −(dx/dp)(p/x). 

Therefore, we obtain the following expression for the equilibrium price: 

p(X) = 

c0 (x) 

1 − 1/ 

(2.13) 

Focusing on the linear costs case with a constant marginal cost c, thecomparative 

statics with respect to the number of firms provide: 

dx x(E − 1) 

= 

dn 1+n − nE 

dp [n − E(n − 1)]xp0 

= < 0 

dn 1+n(1 − E) 

where E ≡ −xp 00 (nx)/p 0 (nx) is the elasticity of the slope of the inverse 

demand with respect to the individual output of a firm, which is an index of 

the convexity of the demand function (E =0under linear demand). Notice 

that the second order condition requires E


The price increases less (more) than proportionally if E < (>)1/n, while 

profits decrease in the marginal cost unless E ∈ (2/n, 1+1/n). Noticethat 

this general Cournot model with n firms boils down to the monopoly model 

after imposing n =1, and we can verify that these comparative statics results 

match those emerging in the classic case of a monopoly for n =1.Forinstance, 

under linear demand (E =0), a unitary increase of the marginal cost 

increases by half the monopolistic price, but by two thirds the duopolistic 

price, and so on until full shifting of the marginal cost on the price under 

perfect competition (for n →∞): a more convex demand function leads to 

a larger shift of the cost change on the price. Generally, these results are 

quite useful since they can be used to evaluate the complex impact on the 

equilibrium prices and profits of an increase in costs due to different factors 

as a change in the costs of the inputs of production or in the indirect taxes. 14 

Let us move to the Marshall equilibrium. The two equilibrium conditions 

are now the optimality condition for a representative firm and the zero profit 

condition: 

p(X)+xp 0 (X) =c 0 (x), xp(X) =c(x)+F (2.14) 

Totally differentiating the system we can derive the comparative statics of a 

change in the constant marginal cost. The new effects are: 

dx 

dc = p0 x 2 

n∆ < 0 

dp 

dc = 2x2 p 02 

∆ > 0 dn 

dc = p0 x 

(2 − nE) 

∆ 

Since ∆ ≡ x 2 p 02 (2p 0 + xp 00 ) > 0 by the second order condition, we can easily 

obtain that the cost increase raises the price less (more) than proportionally 

if E)0. Thenumberoffirms is decreasing in the marginal cost except 

in the case of a highly convex demand function. 

Hyperbolic demand. As an example, let us look at the hyperbolic demand: 

1 

p = P n 

J=1 x (2.15) 

j 

which can be derived from a standard logarithmic utility: 

Ã n 

! 

X 

U =log C j + C 0 (2.16) 

J=1 

14 For instance, in the linear case with a specific taxt s and an ad valorem tax t v 

we have: 

p = 

a 

n +1 + n c + t 

s 

 

n +1 1 − t v 

which shows that the price is decreasing in the number of firms and in both 

the taxes. For more results on tax incidence in oligopoly see Delipalla and Keen 

(1992), Myles (1995), and in presence of tax evasion Etro (1997, 1998a,b), Cowell 

(2004) and Marchese (2006).


where C j is consumption of good j and good 0 is the numeraire. 15 It can 

be easily verified that the Nash equilibrium is characterized by a production 

for each firm equal to x =(n − 1)/n 2 c, and by the following price and gross 

profits: 

c 

p = 

Π = 1 1 − 1/n 

n 2 (2.17) 

Notice that profits are now independent from the marginal cost, which is in 

line with our general result (since E =2/n implies dΠ/dc =0), while they 

decrease in the number of firms. In a Marshall equilibrium (assuming F 0 and g 0 (p) < 0: thefirst assumption implies 

that the demand of firm i decreases in the price of firm i, and the remaining 

assumptions make sure that it increases with the prices of the other firms. 

Focusing on the case of a constant marginal cost, we then have the gross 

profits: 

⎡ 

⎤ 

nX 

π i =(p i − c)D ⎣p i , g(p j ) ⎦ − F (2.20) 

j=1,j6=i 

In Chapter 1 we developed an example based on the Logit demand: 

15 Notice that the hyperbolic demand is nested in the non linear one cited above 

for a =0and γ =1.


D i = 

Ne−λp i 

P n 

j=1 e−λp j 

(2.21) 

which belongs to our class of demand functions after setting g(p) =exp(−λp), 

that satisfies g 0 (p) < 0. Andersonet al. (1988) have shown that this demand 

is consistent with a representative agent maximizing the utility: 

µ 1 X n µ 

Cj 

U = C 0 − C j ln 

(2.22) 

λ 

N 

j=1 

when when P n 

j=1 C j = N and −∞ otherwise (total consumption for the 

n goods is exogenous), under the budget constraint C 0 + P n 

j=1 p jC j = Y , 

with C 0 as the numeraire. This interpretation allows one to think of 1/λ as 

a measure of the variety-seeking behavior of the representative consumer. 

Other important cases derive from the class of demand functions introduced 

by Spence (1976) and Dixit and Stiglitz (1977) and derived from 

the h maximization ³ of a utility function of a representative agent as U = 

Pn 

´i 

u C 0 ,V 

j=1 Cθ j under the budget constraint C 0 + P n 

j=1 p jC j = Y , 

where C 0 is the numeraire, u(·) is quasilinear or homothetic, V (·) is increasing 

and concave, and θ ∈ (0, 1] parametrizes the substitutability between 

goods. Consider the utility function: 

⎡ ⎤ 1 

θ 

nX 

U = C0 

α ⎣ Cj 

θ ⎦ 

(2.23) 

j=1 

with θ ∈ (0, 1) and α>0. In this case the constant elasticity of substitution 

between goods is 1/(1 − θ) and increases in θ: for this reason this model 

is often referred to as the CES (constant elasticity of substitution) model. 

Demand for each good i =1, ..., n can be derived as: 

Yp − 1 

1−θ 

i 

D i = 

(1 + α) P n 

θ 

j=1 p− 1−θ 

j 

(2.24) 

which belongs to our general class after setting g(p) =p − 1−θ , which of course 

satisfies g 0 (p) < 0. Similar demand functions and related models of price competition 

have been widely employed in many fields where imperfect competition 

plays a crucial role, including the new trade theory, the newkeynesian 

macroeconomics, the new open macroeconomy, the endogenous growth theory 

and the new economic geography. 16 

We now have to verify that the profit functions derived from this class 

of demand functions are actually nested in our general model with gross 

16 Anderson et al. (1992) have provided a detailed analysis of the foundations for 

the Logit and CES demand functions through three different approaches (rep- 

θ


profits Π (x i ,β i ). For this purpose, we will adopt a simple trick changing the 

strategic variable for each firm i from the price p i to its inverse x i ≡ 1/p i . 17 

Of course, choosing a price or its inverse is just a matter of mathematical 

definition, however it allows us to greatly simplify our discussion. First of 

all, increasing x i =1/p i is now equivalent to reducing the price of firm i in 

both models of competition in quantities and in prices. Moreover, under our 

specification of the demand functions, we can now define: 

µ 1 

h(x i )=g with h 0 (x i )=−(1/x 2 i )g 0 (1/x i ) > 0 

x i 

and rewrite gross profits as: 

µ 

1 1 

Π (x i ,β i )=µ 

− c D ,β 

x i x i 

i 

(2.25) 

The model belongs to our class of consistent market structures (2.1) under 

weak regularity conditions. Moreover SC holds as long as DD 12 0 is the elasticity of the direct demand. Assuming that 

SC holds, we have the comparative statics results: 

dp 

dn ∝ p2 g(p)[D 2 +(p − c)D 12 ] < 0 

dp 

dc ∝ −p2 D 1 > 0 

resentative consumers models as those emphasized here, discrete choice models 

with stochastic utility and a multidimensional generalization of the Hotelling 

model) and of the existence of the related equilibria. For the case of an exponential 

subutility in the Dixit-Stiglitz preferences see Behrens and Murata (2007). I 

am thankful to Avinash Dixit to point this out. 

17 We borrowed this device from Mas-Colell et al. (1995, Ch. 12).


while the effect of a change in the marginal cost on the profits is ambiguous. 

The Marshall equilibrium requires that all firms choose their prices optimally 

and that profits are driven to zero by endogenous entry: 

D [p, (n − 1)g(p)] + (p − c) D 1 [p, (n − 1)g(p)] = 0 (2.27) 

D [p, (n − 1)g(p)] (p − c) =F (2.28) 

Total differentiation of this equilibrium system generates the following comparative 

statics result: 

dp 

dc ∝ −g(p)D [2D 2 +(p − c)D 12 ] > 0 

while the effect of the marginal cost on the number of firmsisambiguous. 

Some examples. As we have seen in Chapter 1, in the case of a Logit 

demand (2.21) under exogenous entry we have: 

p = c + 

n 

(n − 1)λ 

Π = 

N 

λ(n − 1) − F (2.29) 

while the endogenous entry equilibrium implies: 18 

p = c + F N + 1 λ 

n =1+ N λF 

(2.30) 

In the case of a CES demand (2.24), the Nash equilibrium generates the 

following price and profits: 19 

p = 

c(n − θ) 

θ(n − 1) 

Π = 

Y (1 − θ) 

γ(n − θ) 

(2.31) 

This clearly implies a price decreasing in the number of firms and increasing 

more than proportionally in the marginal cost (dp/dc > 1). Gross profits for 

each firm are independent from the marginal cost, decreasing in the number of 

firms and converging to zero when this number grows. Finally, in the Marshall 

equilibrium of the Dixit-Stiglitz model we have: 20 

18 The firstbestwouldrequireonefirm less than in the Marshall equilibrium. The 

second best under the zero profit constraint would require a price p = c +1/λ 

with N/F λ firms. 

19 In this case under specific andad valorem taxation we have: 

p = (c + ts )(n − θ) 

(1 − t v )θ(n − 1) 

which implies overshifting of both taxes. 

20 The first best would require price equal to the marginal cost with Y (1−θ)/F (1+ 

θα) firms. The second best under the zero profit constraint would require a price 

p = c/θ with Y (1 − θ)/F (1 + α) firms.


p = 

cY 

θ [Y − F (1 + α)] 

n = 

(1 − θ)Y 

(1 + α)F + θ (2.32) 

Notice that these equilibria can be compared with those that would 

emerge with the same isoelastic demand function if firms were competing 

in quantities rather than in prices. 21 In that case one could solve for the 

Cournot equilibrium with an exogenous number of firms and obtain a price 

p = cn/θ(n − 1). This is higher than the price obtained above: competition 

in prices reduces the mark up and the profits of the firms compared to competition 

in quantities (this result holds in a more general set up than this). 

Finally, in all these cases the equilibrium price does not converge to the 

marginal cost when the number of firms increases (it converges to c+1/λ with 

the Logit demand and to c/θ with the isoelastic demand). This is possible 

because of product differentiation, which allows firms to maintain a certain 

degree of market power even if there are many competitors in the market; for 

this reason these kinds of models are often referred to as models of monopolistic 

competition - and in general equilibrium applications they are often 

employed neglecting the strategic interactions (so that the number of firms 

does not affect equilibrium prices and profits, and endogeneity of entry is 

irrelevant). 

2.4.3 Competition for the Market 

A large class of models of investment in innovation or competition for the 

market can be studied within our general framework. For instance, in Chapter 

1westudiedasimplecontestwhereeveryfirmcouldobtainaninnovation 

with probability x i ∈ [0, 1] after investing x 2 i /2. The expected profits were: 

π i = x i 

n 

Y 

j=1,j6=i 

(1 − x j ) V − x2 i 

2 − F (2.33) 

That model was nested in our general framework, even if in such a case we 

would need a few steps to realize it: 

π i = x i e n 

j=1,j6=i log(1−xj) V − x2 i 

2 − F = 

= x i e − 

n 

j=1,j6=i log 1 

1−x j 

V − x2 i 

2 − F 

21 Maximizing the utility (2.23) one obtains the inverse demand: 

Yx −(1−θ) 

i 

p i = n 

 

(1 + α) 

j=1 xθ j 

and therefore a profit function which is nested in our general specification (2.1).

2.5 Strategic Investments 59 

Now, setting h(x) =log[1/(1 − x)] which implies h 0 (x) =1/(1 − x) > 0, we 

can rewrite gross profits as: 

Π (x i ,β i )= x iV 

e β i 

− x2 i 

2 

(2.34) 

which is clearly nested in our model (2.1) and implies SS since Π 12 = 

−V/e β i < 0. 

22 

As we have seen in Chapter 1, and as one can easily verify from the first 

order condition under symmetry, the Nash equilibrium is characterized by an 

investment in innovation implicitly given by: 

x =(1− x) n−1 V (2.35) 

while in the Marshall equilibrium, where the number of firms reduces expected 

profits to zero, the investment is: 

x = √ 2F (2.36) 

Another related contest which is nested in our framework is a rent seeking 

contest in which agents invest to obtain rents with a probability given by 

their investment relative to the total one (Tullock, 1967). In Chapter 4 we will 

study more realistic forms of competition for the market where firms invest 

over time and innovations arrive according to a stochastic process depending 

on the investment of each firm (Loury, 1979). While that framework will allow 

us to consider further issues, many basic insights from the simple contest 

outlined here will be conserved. 

2.5 Strategic Investments 

Amainleitmotif of this book is about the behavior of market leaders in different 

forms of competitive environments. In the rest of this chapter we will 

approach this issue extending the framework analyzed until now to strategic 

investments or commitments by the leading firm. With strategic commitments 

we refer to any kind of preliminary decisions that affect the strategic 

condition of the leaders compared to the other firms. In the jargon of marketing, 

we may refer to all those commitments that affect the marketing mix, 

the so-called 4 P’s of marketing: product, price, place and promotion, here 

meaning quality of the good, costs, distribution and advertising (see Kotler, 

1999). In the jargon of strategy, we may refer to all those commitments that 

affect the competitive strategy and provide a competitive advantage to the 

leader (see Porter, 1985). 

22 This model can also be used as a foundation of a simple principle-agent model 

(for an introduction see Milgrom and Roberts, 1992) with which one can study 

hyerarchies within teams (see Goldfain, 2007).


More formally, in what follows we will study markets in which all firms 

compete simultaneously as before, but one of them, the leader, will have a 

chance to undertake a preliminary investment which will affect competition 

ex post. The purpose, of course, is to understand what kind of decisions are 

taken by market leaders, whether they are going to induce an aggressive or 

an accommodating behavior, and how they affect equilibria. The pioneering 

analysis in this field is due to Dixit (1980) and Fudenberg and Tirole (1984), 

who focused on duopolies, while here we will consider the situation in which 

there is an exogenous number of firms n, possibly larger than two. 

Consider the following sequence of moves: 

1) in the first stage a leader, firm L, makes a strategic commitment on a 

variable k (we will often refer to this as to a strategic investment); 

2) in the second stage each follower chooses its own strategy x i and the 

leader chooses its own strategy x L after knowing the commitment of the 

leader. Therefore, all firms, the leader and the followers, play in Nash strategies 

in the second stage. 

In the second stage the profit of the leader is defined by: 

π L = Π L (x L ,β L ,k) − F (2.37) 

where, without loss of generality, we will assume that Π L 3 ≡ ∂Π L /∂k > 0: 

the variable k increases the profitability of the leader. The profit ofeachother 

firm remains: 

π = Π (x, β) − F 

For a given strategic commitment, the second stage is characterized by 

the first order conditions for a Nash equilibrium. For the sake of simplicity, 

we follow Fudenberg and Tirole (1984) assuming that a unique equilibrium 

exists with symmetric strategies for all the firms except the leader and that 

there is entry of some followers for any feasible k. Therefore, we have the 

equilibrium conditions: 

Π L 1 (x L ,β L ,k)=0 Π 1 (x, β) =0 (2.38) 

In general, we will say that the investment makes the leader tough when 

Π L 13 > 0, that is a higher strategic investment k makes the leader more aggressive 

(increases x L ), and makes the followers less (more) aggressive under 

SS (SC). The investment makes the leader soft when Π L 13 < 0.Inwhatfollows 

we will analyze many different kinds of investments, and in each application, 

there will be a cost for these investments. The leader will choose its investment 

by comparing its impact on the profit and its impact on the cost. Our 

interest, however, will be on the strategic effect, that is the effect of the 

investment of the leader on the behavior of the followers, defined as: 

SI(k) =Π L 2 (x L ,β L ,k) ∂β L 

∂k 

(2.39)


If the cost of the strategic investment is given by some positive and increasing 

function f(k), the net profit oftheleaderwillbe: 

π L (k) =Π L (x L ,β L ,k) − f(k) − F 

and the optimality condition will be: 

Π L 3 (x L ,β L ,k)+SI(k) =f 0 (k) 

It is clear that the strategic incentive is the interesting part for our purposes, 

since it tells us how the leader can exploit its commitment capacity in a 

strategic way to affect the equilibrium of the market and obtain more profits. 

To realize this, imagine what would happen if the leader could not choose k 

before competing with the other firms, but had to choose it simultaneously 

with the choice of the market strategies of all firms: then, the strategic incentive 

would not play any role in the choice of the investment (only the direct 

effect would remain). The importance of the commitment capacity relies exactly 

on the possibility of using the investment in a strategic way to affect 

the behavior of the other firms. When SI is positive we will say that there is 

a strategic incentive to overinvest, while when it is negative we will say that 

there is a strategic incentive to underinvest. Of course, overinvestment and 

underinvestment should be thought relative to the direct incentive to invest. 

2.5.1 The Fudenberg-Tirole Taxonomy of Business Strategies 

Let us generalize the standard results of Fudenberg and Tirole (1984) on the 

strategic investment of a leader in duopoly to the case with an exogenous 

number of firms n. The two equilibrium first order conditions (2.38) can be 

easily differentiated to obtain ∂β L /∂k, and hence the strategic incentive: 

SI(k) = h0 (x L )Π L 2 ΠL 13 Π 12 

Ω 

(2.40) 

where Ω is positive by assumption of stability of the system. 23 The sign of 

this incentive is the same as that of −Π 12 Π13, L and we have the following 

traditional result: 

Proposition 2.1. In a Nash equilibrium: 

1) when the strategic investment makes the leader tough (Π13 L > 

0), there is a strategic incentive to over- (under-) invest under 

strategic substitutability (complementarity); 

23 Here: 

Ω = 

Π11 

L 

Π11 +(n − 2) h 0 

(x)Π 

(n − 1)h 0 12 + Π 

L 

(x) 

12 Π 12 > 0


2) when the strategic investment makes the leader soft (Π13 L < 0), 

there is a strategic incentive to under- (over-) invest under strategic 

substitutability (complementarity). 

Now, imagine that in the absence of a strategic incentive to invest, the 

leader was going to choose an investment ¯k such that Π ¡ L x, β, ¯k ¢ = Π (x, β) 

for any x and β. 24 This is a neutrality assumption that allows to derive simple 

and interesting conclusions in a number of applications. It clearly implies 

that only the strategic incentive is going to induce the leader to behave 

in a different way from the other firms. In other words, only the strategic 

commitment can provide the leader with an advantage in the market and in 

the second stage we have: 

x L R x if and only if k R (Q)¯k when Π L 13 > ( 0). In such a case overinvestment is optimal 

when an aggressive behavior in the market induces a less aggressive behavior 

of the other firms (which requires SS: Π 12 < 0): this outcome corresponds 

to what has been called a “top dog” strategy in which the leading firm is 

aggressive to obtain non aggressive strategies of the other firms, a typical 

outcome of models of competition in quantities. 

However, when an aggressive behavior of a firm induces the other firms 

to be aggressive as well (which requires SC: Π 12 > 0), as in models of competition 

in prices, it is optimal to underinvest strategically: this corresponds 

to a “puppy dog” strategy where, in the words of Fudenberg and Tirole 

(1984), underinvestment “accommodates entry by turning the incumbent 

into a small, friendly, nonaggressive puppy dog.” The spirit of puppy dog 

strategies emerges in most models of competition in prices with product differentiation 

25 .Asanexample,Laffont et al. (1998) have shown that a puppy 

24 Within our specification of the cost function for the strategic investment, this 

 

requires Π3 

L x, β, ¯k = f 0 (¯k). 

25 As noticed by Tirole (1988), puppy dog strategies emerge in the Hotelling 

duopoly as well. Considering the location k 1 0 and ∂ 2 π i/∂p i∂k i 

is positive for firm 1 and negative for firm 2. Hencebothfirms have a strategic 

incentive to differentiate products.


dog strategy emerges in (unregulated) markets for interconnected networks 

(for example the telecommunications industry) where an entrant chooses to 

invest strategically in geographical coverage before competing with the incumbent: 

then, the optimal strategy of the entrant is to underinvest to soften 

price competition. 26 A puppy dog behavior can emerge also in an indirect way. 

A typical example is a price protection policy implemented through a “mostfavored-customer 

clause”. This guarantees a firm’s customers that they will 

be reimbursed the price difference with the lowest price offered by other firms: 

as shown by Tirole (1988) this policy softens price competition and increases 

profits. 

When the strategic investment makes the leader soft (Π13 L < 0), the incentives 

take other directions: in the words of Fudenberg and Tirole (1984), the 

“fat cat strategy is overinvestment that accommodates entry by committing 

the incumbent to play less aggressively post entry. The lean and hungry strategy 

is underinvestment to be tougher.” A “lean and hungry look” emergesin 

case of SS (Π 12 < 0). As an example, consider our simple model of Chapter 

1 with competition for the market between an incumbent monopolist and an 

outsider. Because of the Arrow effect, the monopolist with positive profits 

from its leading technology had lower incentives to invest in innovation than 

the outsider, and higher current profits were inducing less investment by the 

incumbent and more by the outsider. In such a case, the incumbent would 

have liked to underinvest in profit enhancing strategies to have a strategic 

incentive to invest more in R&D. 

The “fat cat” strategy emerges in models of price competition (Π 12 > 

0) with a strategic investment that reduces the incentives to be aggressive, 

for instance, as we will see later on, with an investment in nonprice (or 

persuasive) advertising, which typically allows a firm to set high prices after 

having developed a goodwill. 27 For further discussion on the taxonomy of 

strategic investment in duopolies, see the extensive treatment of Tirole (1988, 

Part II). 

2.5.2 Strategic Commitments with Endogenous Entry 

We will now follow Etro (2006,a) and assume that the number of potential 

entrants is great enough that a zero profit condition pins down the effective 

number of firms, n. Tobeprecise,wewilllookatthesubgameperfect 

equilibrium of the game with the following sequence of moves: 

1) in the first stage, firm L enters, pays the fixed cost F and chooses an 

investment k; 

26 See also Cambini and Valletti (2007). 

27 The quotation of Shakespeare from Julius Caesar (Act. 1, Sc. 2) introducing 

Fudenberg and Tirole (1984) is quite suggestive: “Letmehaveaboutmemen 

that are fat.”


2) in the second stage, after knowing the investment of the leader, all 

potential entrants simultaneously decide “in” or“out”: if a firm decides “in”, 

it pays the fixed cost F ; 

3) in the third stage all the firms that have entered choose their own 

strategy x i simultaneously. 

The equilibrium conditions are the two previous first order conditions 

(2.38), and the zero profit condition binding on the followers: 

Π (x, β) =F (2.41) 

We can now prove that a change in the strategic commitment by the leader 

does not affect the equilibrium strategies of all other firms, but reduces their 

equilibrium number. Let us use the definition β L ≡ (n − 1)h(x) to rewrite 

the equilibrium system (2.38)-(2.41) in terms of the three unknown variables 

x, x L and β L : 

Π 1 [x, h(x L ) − h(x)+β L ]=0 

Π1 L [x L ,β L ,k]=0 

Π [x, h(x L ) − h(x)+β L ]=F 

The second equation provides an implicit relationship x L = x L (β L ,k) with 

∂x L /∂β L = −Π12 L /ΠL 11 and ∂x L/∂k = −Π13 L /ΠL 11 > 0. Substituting this 

expression we obtain a system of two equations in two unknowns, x and β L : 

Π 1 [x, h(x L (β L ,k)) − h(x)+β L ]=0, 

Π [x, h(x L (β L ,k)) − h(x)+β L ]=F 

Totally differentiating the system and imposing stability, which requires 

Π L 11 − h 0 (x L )Π L 12 < 0, it follows that x = x(k), β L = β L (k) and x L = 

x L (β L (k),k) are the equilibrium functions with: 

dx 

dk =0 

dβ L 

dk = h 0 (x L )Π L 13 

Π L 11 − h0 (x L )Π L 12 

dx L 

dk = − Π L 13 

Π L 11 − h0 (x L )Π L 12 

and dn/dk =(dβ L /dk) /h(x). This shows that in a Marshall equilibrium, an 

increase in the strategic investment does not affect the equilibrium strategy 

of all the other firms but reduces their equilibrium number. In the initial 

stage, the strategic incentive becomes: 

SI(k) = h0 (x L )Π L 2 Π L 13 

Π L 11 − h0 (s)Π L 12 

(2.42) 

whose sign is just the sign of Π L 13. This delivers our main result: 

Proposition 2.3. In a Marshall equilibrium, when the strategic 

investment makes the leader tough (soft), there is a strategic 

incentive to over- (under-) invest; moreover, the leader is always 

aggressive compared to the followers.


Basically, whenever investment makes the leader tough (Π L 13 > 0) and 

entry is endogenous, it is always optimal for the leader to adopt a “top 

dog” strategy with overinvestment in the first stage so as to be aggressive 

in the final stage. On the other side, when investment makes the leader soft 

(Π L 13 < 0), we always have a “lean and hungry” look with underinvestment, 

but also in this case, the outcome in the final stage is an aggressive behavior 

of the leader. 

To understand the intuition of this simple but general result, let us focus 

on the first case, in which investment makes the leader tough. Let us suppose 

that SC holds: this is the most interesting case because endogenous entry 

overturns the traditional results (but a similar mechanism works under SS 

as well). Under our assumptions a leader may accept the cost of underinvesting 

strategically (compared to the optimal direct investment) to become 

more accommodating, and this would be the optimal thing to do when the 

number of competitors is exogenous. Now, let us consider the consequences 

of an accommodating strategy when entry is endogenous. Since strategies 

are assumed to be complements, accommodation by the leader would induce 

accommodating strategies by the followers as well. The associated increase 

in expected profits would attract entry of other firms, which will also behave 

in an accommodating way. Since entry occurs as long as there are profitable 

opportunities to exploit, the followers must obtain zero profits in equilibrium. 

Therefore, the entry process induced by an accommodating strategy exhausts 

all possible gains for the followers. What about the leader? Its attempt to induce 

accommodation has the cost of distorting its strategy from the optimal 

direct level. Moreover, it wastes all the potential benefits from accommodation 

because it increases entry. Accordingly, underinvestment cannot increase 

the profits of the leader. 

Consider now an aggressive strategy induced by an initial overinvestment 

of the leader. Such a strategy may induce the rivals to be more aggressive 

as well, and this would reduce entry in the market. Therefore, the leader 

distorts its investment strategy from the directly optimal level but succeeds 

in reducing the negative externalities derived from the strategies of the rivals 

because of the reduction in their number. The optimal level of overinvestment 

trades off the costs of the distortion in the investment level and the benefits 

of the reduction of the number of entrants. 

Finally, notice that the same argument would go through in the case the 

investment made the leader soft, but in that case underinvestment would 

induce the optimal aggressive strategy. 

We will now apply the above results to some basic forms of strategic 

commitments as investments in cost reductions, advertising, financial decisions, 

bundling or price discrimination strategies, strategic contracts, strategic 

mergers and so on. There are many other applications that are not discussed 

in this chapter. Our focus will be limited to the applications with 

substantial relevance for the understanding of the behavior of market leaders


and for our future discussions of antitrust issues. We will emphasize how the 

results can drastically change according to whether we assume that entry is 

exogenous or endogenous, but we will mainly pay attention to the case of endogenous 

entry. After all, we do believe that entry of firmsisanendogenous 

choice in most markets, and not an exogenous fact. 

2.6 Cost Reductions and Signaling 

Our first application is to a situation where a firm can adopt preliminary 

investments to improve its production technology and hence reduce its costs. 

Traditional results on the opportunity of these investments for market leaders 

are ambiguous when the number of firms is exogenous, but, as we will show, 

they are not when entry is endogenous. From now on, we will assume for 

simplicity that marginal costs are constant. Here, the leader can invest k 

and reduce its marginal cost to c(k) > 0 with c 0 (k) < 0, while the marginal 

cost cannot be changed for all the other firms. One could think of the cost 

reducing investment as an investment in R&D to improve the production 

technology, but also in terms of learning by doing: past production reduces 

future costs. 28 

Consider first a model of quantity competition. The gross profit ofthe 

leader becomes: 

Π L (x L ,β L ,k)=x L p (x L ,β L ) − c(k)x L (2.43) 

Notice that in such a model, Π L 12 has an ambiguous sign, but we have: 

Π L 13 = −c 0 (k) > 0 

consequently the leader will overinvest in cost reductions when facing a fixed 

number of competitors (as long as SS holds), and will always overinvest and 

produce more than the other firms when entry is endogenous. 

For instance, assume an inverse demand p = a − X, a constant marginal 

cost c(k) =c − √ gk for the leader investing k, andc for the entrants, where 

g measures the productivity of the R&D investment, whose cost is f(k) =k. 

A Nash equilibrium with n firms would imply: 

x L = 

a − nc(k)+(n − 1)c a + c(k) − 2c 

, x = 

n +1 

n +1 

The optimal investment by the leader can be derived as: 

28 This is the typical case of the aircraft industry (Boeing, Airbus), the production 

of chips (Intel) and many other sectors with a fast technological progress. See 

Sutton (Ch. 14) for an analysis of these markets.

2.6 Cost Reductions and Signaling 67 

k = 

(a − c) 2 g 

[(n +1) 2 − ng] 2 

which clearly generates an equilibrium output for the leader that is higher 

than the one of the entrants (notice that SS holds in this example). The 

optimal investment is increasing in the productivity of the R&D technology, 

that is in g. Moreover, if this productivity is high enough, it is optimal to 

induce entry deterrence. 

The bias toward overinvestment in cost reducing technology aimed at an 

aggressive behavior in the market holds also when entry is endogenous, in 

which case the equilibrium production of the leader and of the entrants are: 

√ 

F 

x L = 

1 − g , x = √ F 

and the leader induces such an equilibrium through the preliminary investment: 

k = 

gF 

(1 − g) 2 

in cost reductions. This implies the following rule for the optimal ratio between 

R&D spending k and sales of the leader px L : 

R&D 

Sales = 

g √ F 

(1 − g)(c + √ F ) 

(2.44) 

Of course, this result requires g to be small enough, otherwise entry deterrence 

³ 

would be optimal, and it would require an investment k = a − c − 3 √ ´2 

F /g. 

In this framework, the chance to undertake a strategic investment in a cost 

reducing technology leads to the same outcome we obtained in Section 1.2.1, 

when the leader could simply choose its output before the other firms and 

marginal costs were increasing: the leader is aggressive to produce more than 

the other firms, but the cost of an aggressive strategy (increasing marginal 

costs of production there, costs of R&D investment here) limits the production 

of the leader. A lot of research has extended this model to the realistic 

case of spillovers of the R&D activity of the incumbent on the entrants (for 

instance, see Žigić et al., 2006 and Vandekerckhove and De Bondt, 2007), 

and the tendency toward overinvestment under endogenous entry holds also 

in that case. 29 

29 Assuming that investment k by the leader induces a marginal cost for the entrants 

c−χ √ gk, whereχ ∈ [0, 1) isameasureofthedegreeofspillovers,theequilibrium 

with endogenous entry implies an investment: 

k = 

(1 − χ)2 gF 

[1 − g(1 − χ) 2 ] 2


Consider now the model of price competition where the leader can invest 

to reduce its marginal costs in the same way and its profit function becomes: 

Π L (x L ,β L ,k)=[p L − c(k)] D (p L ,β L ) with p L =1/x L (2.45) 

Now we have: 

Π L 13 = c 0 (k)D 1 p 2 L > 0 

Accordingly, underinvestment in cost reductions emerges when entry is exogenous 

(since SC holds), but overinvestment is optimal when there is endogenous 

entry. Whenever this is the case, the leader wants to improve its 

cost function to be more aggressive in the market and sell its good at a lower 

price. Summarizing, we have: 30 

Proposition 2.4. Under both quantity and price competition 

with endogenous entry, a firm always has an incentive to overinvest 

in cost reductions and to be more aggressive than the others in the 

market. 

This theory of cost reducing investments aimed at inducing aggressive 

behavior toward the competitors and ultimately at decreasing prices, has 

been extended in a genuinely dynamic framework in an important work by 

Žigić et al. (2006). They depart from the static model of quantity competition 

analyzed above and study a dynamic duopoly in which the leader can 

invest over time to reduce the marginal cost gradually. The optimal accommodating 

strategy generates an increasing investment associated with a decreasing 

price. The optimal entry deterring strategy requires a heavy initial 

investment able to deter entry as soon as possible, and a lower investment 

in the subsequent monopolistic phase, which generates a decreasing price in 

the predatory phase and an increasing price in the monopolistic phase. The 

predatory strategy is optimal when the investment is productive enough (g 

is high enough) and the speed of adjustment of the marginal cost (namely of 

its reduction with the investment) is high enough. However, the surprising 

that is decreasing in the spillovers, which dissipate R&D effort from the perspective 

of the leader. Only when spillovers are small enough (χ

2.6 Cost Reductions and Signaling 69 

result is that the sharp decrease in the equilibrium price due to the predatory 

investment in R&D leads to permanent gains for the consumers also in the 

monopolistic phase after predation (when potential entry still constrains the 

R&D activity). 

Our results can also be used to re-interpret models of predatory pricing 

through cost signaling. In a classic work of the modern industrial organization 

(and of the post-Chicago approach to antitrust), Milgrom and Roberts (1982) 

have studied the entry decision of an entrant in a duopoly with an incumbent 

that is already active in the market, and have introduced incomplete information: 

since the study of informational asymmetries is beyond the scope of 

this book, we will just sketch their idea to emphasize the similarities with 

our approach. Imagine that the entrant does not know the cost of the leader, 

which can be a high cost or a low cost, but would like to enter only when 

facing a high cost leader. Milgrom and Roberts study under which conditions 

preliminary strategies of the leader induce entry deterrence. For instance, a 

low cost leader can signal its own efficiency through initial over-production 

or under-pricing (associated with a sacrifice of profits)aslongasthisisrelatively 

cheaper for the low cost leader compared to the high cost one. This 

sorting or single crossing condition, first pointed out by Spence (1974) in a 

different context, 31 is respected here exactly because the marginal profitability 

of production decreases with the marginal cost. In our terminology, this 

corresponds exactly to our condition Π L 13 > 0: when the marginal cost is 

lower (c(k) is lower because the investment k is higher), the marginal benefits 

of an aggressive strategy is higher. This means that the marginal cost 

of an aggressive strategy is lower for a low cost firm. Then, in a separating 

equilibrium, a low cost leader is initially aggressive overproducing enough to 

signal its efficiency and induce the follower not to enter, while a high cost 

leader does not imitate such a strategy because it is more profitable to behave 

monopolistically initially and accommodate entry subsequently. This result 

shows that cost reductions can have a strategic role also in the presence of 

incomplete information about costs. 32 

Notice that even without exclusionary purposes, a leader may like to signal 

its own type to affect post-entry competition with incomplete information on 

costs. Under competition in quantities (and SS), a low cost leader may signal 

its efficiency to reduce the equilibrium output of the entrant and increase 

its own, but under price competition it is a high cost leader that wants to 

signal its inefficiency to induce high prices by the entrant and obtain high 

31 The initial application was to the signaling of productivity through higher education 

(which requires a lower relative effort for more productive agents). For an 

introduction to the economics of asymmetric information see Tirole (1988, Ch. 

9), Hirshleifer and Riley (1992) and Laffont and Tirole (1993). 

32 When the probability that the leader is low cost is high enough a pooling equilibrium 

occurs. In such a case, the high cost leader produces the same monopolistic 

output of the low cost leader, and the entrant does not enter anyway.


profits for both, a point first made by Fudenberg and Tirole (1984). Without 

developing the argument in technical details, we can point out that when 

entry is endogenous there can only be a gain from signaling efficiency for 

a low cost incumbent, since signaling a high cost would not soften price 

competition, but just induce further entry. In the spirit of our model, we 

can conclude by suggesting that also under incomplete information about 

costs, there is a role for a positive strategic investment in cost reductions (for 

signaling purposes) whenever entry in the market is endogenous. And this 

does not necessarily imply exclusionary aims. 

2.7 Advertising and Demand Enhancing Investments 

We will now consider investments which affect the demand function of a 

firm, such as nonprice advertising (aimed at brand positioning and at enhancing 

the goodwill), and investments for quality improvements or product 

differentiation. These investments tend to increase demand and also reduce 

the substitutability between goods. 33 Under endogenous entry, the aim of 

the leader is always to be aggressive in the market, but different strategies 

emerge under quantity and price competition. 

Consider a model of quantity competition characterized by the inverse 

demand p (x L ,β L ,k) for the leader. The marginal effect of investment on 

inverse demand is positive (p 3 > 0), while the one on its slope is negative 

(p 13 < 0), which implies that a higher investment not only increases demand, 

but it also makes it more rigid. 34 In this case, its gross profit becomes: 

Π L (x L ,β L ,k)=x L [p (x L ,β L ,k) − c] (2.46) 

Consequently, we have: 

Π L 13 = p 3 (1 − η) 

where η ≡−x L p 31 /p 3 is the elasticity of the marginal effect of investment on 

price with respect to production. As long as this elasticity is less than unitary, 

which means that investment does not make demand too rigid, we have Π L 13 > 

33 See Tirole (1988, Ch. 2 and Ch. 7) on product selection, quality and advertising, 

andonproductdifferentiation. 

34 This may not be the case for informative advertising (which informs consumers 

abour product price and availability) or other forms of investment that attract 

marginal consumers. Since these consumers are by definition more sensitive 

to price changes, the investment may increase both demand and its elasticity 

(Becker and Murphy, 1993). In general, marketing studies suggest that investments 

in advertising make demand more rigid for a price increase and more 

elastic for a price decrease (Kotler, 1999). A classic work in the field is Lambin 

(1970).

2.7 Advertising and Demand Enhancing Investments 71 

0. While under exogenous entry the investment choice of the leader depends 

on many factors, under endogenous entry overinvestment takes place if and 

only if η 0 

and D 13 > 0 and the gross profit becomes: 

Π L (x L ,β L ,k)=(p L − c) D (p L ,β L ,k) with p L =1/x L (2.48) 

where the crucial cross effect is: 

Π L 13 = − [D 3 +(p L − c)D 13 ] p 2 L < 0 

In this case with an exogenous number of firms the leader would overinvest 

to increase its price and exploit the induced increase in the price of the 

competitors. However, under endogenous entry the behavior of the leader 

radically changes and there is always underinvestment so as to reduce the 

pricebelowthepriceofthefollowers. 36 

35 The model can also be reinterpreted in terms of product differentiation. It is well 

known that, from the 1950s to the 1970s in US, established firms in the readyto-eat 

breakfast cereal industry rapidly increased the number of the brands they 

offered with aggressive purposes against further entry in the market. 

36 Vertical differentiation is another way to interpret our model. For instance, if demand 

depends on the price-quality ratio, according to some function ˆD(p L/k, β L ) 

where k is quality, it is easy to derive Π L 13 < 0: committing to a high quality 

leads to choose high prices. Nevertheless, in Section 3.4.4 we will study a more 

realistic situation in which committing to high quality is the best strategy for a 

leader facing endogenous entry.


Fudenberg and Tirole (1984) have introduced another simple example 

of investment in advertising that is nested in our framework and is derived 

from Schmalensee (1982). Imagine that firms compete in prices on the same 

customers, but the leader, through a costly investment in advertising k, can 

obtain an extra demand D(k) from new customers, with D 0 (k) > 0. This 

simple stylized set up delivers a profit function for the leader: 

Π L (x L ,β L ,k)=(p L − c) D(k)+(p L − c) D (p L ,β L ) 

with p L =1/x L 

while the profits for the other firmsarethesameasbefore.Thecrosseffect 

is now Π13 L = −D 0 (k)p 2 L < 0. Hence, as Fudenberg and Tirole (1984) noticed 

inthecaseoftwofirms, “if the established firm chooses to allow entry, it 

will advertise heavily and become a fat cat in order to soften the entrant’s 

pricing behavior”, but, we add, when entry of firms is endogenous, the leader 

will underinvest in advertising to keep low prices while allowing some firms 

to enter in the market. Summarizing our results for nonprice advertising, we 

have: 

Proposition 2.5. Under quantity competition with endogenous 

entry, a firm has an incentive to overinvest in nonprice advertising 

as long as this does not make demand too rigid; under price competition 

with endogenous entry the leader has always an incentive 

to underinvest in nonprice advertising. 

Once again this result overturns common wisdom obtained by duopoly 

models, especially under price competition. 

2.8 Debt and the Optimal Financial Structure 

We can also apply our results to the theory of corporate finance to study 

the strategic role of the financial structure. As shown by Brander and Lewis 

(1986, 1988) and Showalter (1995, 1999) in models of duopolies with uncertainty, 

when product decisions are managed by the equity holders, debt can 

affect the marginal profitability, and hence there can be a role for a bias in 

the optimal financial structure, departing from the standard neutrality results 

of Modigliani and Miller (1958). 37 The outcome depends on the kind of 

competition, but also on the kind of uncertainty. 

For finance to play a role in product market competition, we need to 

introduce uncertainty on profits. Imagine that the total financing requirement 

37 See Tirole (2006, Ch. 7) for a survey on the relation between corporate finance 

and product market competition, and Brealey and Myers (2002) for a general 

introduction to the theory of the optimal financial structure. Between many 

empirical analysis on alternative financing tools in different contexts, see the 

recent work of Cenciarini et al. (2006).

2.8 Debt and the Optimal Financial Structure 73 

for each firm is fixed and each firm has enough cash to finance production 

entirely without issuing debt. Furthermore, suppose that the credit market 

is perfectly competitive, so that lenders break even. In such a context, the 

Modigliani-Miller neutrality result holds only if the financial structure does 

not affectproductmarketcompetition. 

For simplicity, we will assume that the financial structure of the outsiders 

implies no debt. The leader, however, can adopt a different financial structure 

by issuing positive debt at a preliminary stage. Afterward, the equity holders 

of all firms choose their market strategies, uncertainty is resolved and payoffs 

for equity holders and debt holders are assigned. Assume that the profit 

functions are disturbed by a random shock z ∈ [z¯, ¯z] independently and identically 

distributed according to the cumulative function G(z) with density 

g(z). The initial ownership of the leading firm can decide its debt level k to 

be repaid out of gross profits, if these are sufficient. Once this choice is taken, 

competition takes place, uncertainty is solved and each firm obtains its own 

profits net of the debt or goes bankrupt. 

If the gross profits of the leader can be written as R(x L ,β L ,z) with the 

usual notation, the value of equity, corresponding to the expected profits net 

of debt repayment can be written as: 

E(k) =Π L (x L ,β L ,k) − F = 

Z¯z 

ẑ 

[R(x L ,β L ,z) − F − k] g(z)dz (2.49) 

where the lower bound ẑ is such that gross profits are zero: 

R(x L ,β L , ẑ) − F = k 

Notice that dẑ/dk =1/R z (x L ,β L , ẑ). We assume usual properties for the 

profit function (R xx (x L ,β L ,z) < 0), and we also assume, without loss of 

generality, that the random variable is chosen so that R z (x i ,β i ,z) > 0: this 

implies that the cut-off level of the positive shock ẑ below which bankruptcy 

occurs is increasing in the debt level (dẑ/dk > 0). 

We could think of a model of competition in quantities where: 

R(x i ,β i ,z)=x i p(x i ,β i ,z) − c(x i ,z) 

with p z (x i ,β i ,z) > 0 and c z (x i ,z) < 0: a positive shock increases demand 

or reduces costs. In case of demand uncertainty with the stochastic linear 

demand p = z − X x j and zero marginal costs, we would have ẑ =(k + 

F )/x L + X x j , which is of course increasing in the debt level. In this example 

and generally under weak conditions, a positive shock increases the marginal 

profitability of production (R xz (x L ,β L ,z) > 0). We can also have a model of 

competition in prices with: 

R(x i ,β i ,z)=[p i − c(z)] D (p i ,β i ,z) 

with p L =1/x L


and we allow explicitly for an impact of uncertainty on both demand and 

costs. Our assumptions are compatible with D z (1/x i ,β i ,z) > 0 and c z (z) < 

0: a positive shock increases demand and/or reduces costs. Moreover, under 

mild conditions assumed in what follows, a positive demand shock increases 

the marginal profitability of a price increase (R xz (x L ,β L ,z) < 0), while a 

positive cost shock always decreases it (R xz (x L ,β L ,z) > 0). 

In general we have: 

Π L 1 (x L ,β L ,k)= 

Z¯z 

ẑ 

R x (x L ,β L ,z)g(z)dz − [R(x L ,β L , ẑ) − k] dẑ 

dk 

whose last term is zero by the definition of ẑ. In any equilibrium, the optimal 

behavior of each firm would require that the expectation of its marginal profit 

issetequaltozero.Butnoticethatwhatisrelevantforafirm with a positive 

debt are the expected profits conditional on these being positive after debt 

repayment, and this affects substantially the marginal profits as well. When 

R xz (x L ,β L ,z) is positive, marginal profit increasesinẑ and hence in the debt 

level, and the opposite happens when R xz (x L ,β L ,z) is negative. As always, 

it is crucial to derive the sign of the cross effect: 38 

Π13 L (x L ,β L ,k)=−R x (x L ,β L , ẑ) dẑ 

dk = 

= −R x(x L ,β L , ẑ) 

R 0 if R xz (x L ,β 

R z (x L ,β L , ẑ) 

L ,z) R 0 

This implies that when the number of firms is exogenous and the leader 

accommodates entry, under SS there is a strategic incentive to issue debt 

when a positive shock increases marginal profits (R xz (x L ,β L ,z) > 0) and 

under SC in the opposite case (R xz (x L ,β L ,z) < 0). For instance, under 

competition in quantities there is typically a strategic role for debt financing 

(Brander and Lewis, 1986), while under competition in prices there is a role 

for debt financing only in the presence of demand uncertainty, but not in case 

of cost uncertainty (Showalter, 1995). 39 Things are different, however, when 

entry takes place endogenously until expected profits are zero. In this case 

we can apply Prop. 2.3 and conclude with: 

Proposition 2.6. Under endogenous entry, a firm has an incentive 

to adopt debt financing to be more aggressive in the competition 

whenever a positive shock increases marginal profits. 

38 The sign of the marginal profit atitsboundsẑ and ¯z depends on the sign of 

R xz (x L ,β L ,z). InparticularR x (x L ,β L , ẑ) Q 0 if R xz (x L ,β L ,z) R 0. Forfurther 

details see Etro (2006e). Notice that a bias toward debt financing is equivalent to 

a bias toward risk-taking behavior, a well known consequence of debt contracts 

(at least since Stiglitz and Weiss, 1981). 

39 Debt financing to deter entry can emerge with quantity competition and SS or 

with price competition and cost uncertainty (Showalter, 1999).

2.8 Debt and the Optimal Financial Structure 75 

In general, under quantity competition there is always a strategic bias 

toward debt financing, while under price competition the same bias emerges 

only when uncertainty affects costs, but not when it affects demand. The 

intuition is again related with the role of debt financing in inducing a more 

aggressive behavior in the market, which is always desirable for the leader 

facing endogenous entry. Under quantity competition, debt induces the management 

to care only about the good states of the world (high demand and 

low costs) and therefore to choose aggressive strategies. Similarly, under price 

competition and demand uncertainty a higher debt increases the marginal 

profitability of a higher price strategy. Accordingly, it helps implementing a 

more accommodating strategy in the market: just what a leader would like to 

do when facing exogenous entry, but the opposite of what would be desirable 

in front of endogenous entry. However, under cost uncertainty, the management 

decides the price to maximize profits conditional on a good state of the 

world, meaning low costs, which leads to a bias toward low prices: this is a 

suboptimal strategy with exogenous entry, but an optimal one with endogenous 

entry. 40 

To complete our analysis, notice that the initial ownership would actually 

choose debt to maximize the overall value of the firm, which corresponds to 

the equity value E (k) plus the debt value: 

D(k) = 

Z ẑ 

z 

¯ 

[R(x L ,β L ,z) − F ] g(z)dz + k[1 − G(ẑ)] 

where the first term represents the expected repayment in the case of bankruptcy 

and the second one the expected repayment in case of successful outcome 

for the firm. Taking into account the dependence of the equilibrium on 

debt k, the value of the firm is then: 

V(k) =E(k)+D(k) = 

Z¯z 

z 

¯ 

R [x L (k),β L (k),z] g(z)dz − F (2.50) 

which corresponds to the expected profits of the firm. When a positive shock 

increases the marginal profitability of an aggressive strategy, the optimal financial 

structure requires an amount of debt k ∗ that induces the management 

to behave as a Stackelberg leader in front of the other firms - as we will see 

40 Chevalier (1995) examines changes in supermarket prices in local markets after 

“leverage buyouts” and finds that prices decrease following an LBO in front of 

rival firms which are not highly leveraged, while they increase when the LBO 

firm’s rivals are also highly leveraged. She associates the former result to predatory 

strategies and the latter to a softening of price competition, but she does 

not control for the endogeneity of entry in these local markets, which makes hard 

to evaluate the results.


in the next chapter, this is the best equilibrium the leader can aim for; more 

debt would induce an excessively aggressive strategy. When a positive shock 

decreases the marginal profitability of an aggressive strategy, the financial 

structure cannot improve the performance of the firm: in this case, for instance 

with price competition and demand uncertainty, the optimal financial 

structure requires no debt. Summing up, the optimal ratio between the value 

of debt and the value of equity can be defined as: 

∙ ¸ 

Debt 

Equity =max 0, D(k∗ ) 

E(k ∗ (2.51) 

) 

Notice that this rule has been derived assuming a perfectly competitive credit 

market, free entry in the product market, no taxes and no bankruptcy costs, 

exactly as for the Modigliani-Miller theorem; further generalizatins could be 

considered. 41 

2.9 Network Externalities and Two-Sided Markets 

Many markets are characterized by network externalities, in the sense that 

demand is enhanced by past production and the consequent diffusion of the 

product across customers. This may happen for cultural or social reasons, 

for instance because goods become fashionable when they have been already 

chosen by other customers, or because of technological reasons, for instance 

because the willingness to pay for a good by each consumer depends on how 

many other consumers have the same good. The last situation is typical of 

advanced technological markets: in principle we may attach a high value 

to video phone communication, but until many of our friends will have a 

video phone, we are unlikely to attach a high value to owning one as well. 

The classic study of competition in this kind of markets is due to Katz and 

Shapiro (1985). 42 Here we will focus on a more stylized model of the behavior 

of market leaders in the presence of network externalities. 

We will adopt the simplest model of quantity competition with homogeneous 

goods and introduce a time dimension. Imagine that in a first period the 

leader is alone in the market and produces k facing the inverse demand p(k) 

and a marginal cost c. In the second period other firms compete in quantities 

and the leader faces the inverse demand p(X)φ(k), whereX is total 

41 The model could be extended introducing bankruptcy costs and adding multiple 

periods to examine dynamic strategies for entry deterrence: as shown by a 

wide literature on the so-called “long purse” or “deep pocket” theory of predation, 

when initial aggressive strategies by the incumbent reduce the financing 

opportunities of the entrants, financial predation can indeed be optimal (see 

Holmstrom and Tirole 1997, Hart, 1995, and Tirole, 2006). 

42 See also Amir and Lazzati (2007).

2.9 Network Externalities and Two-Sided Markets 77 

production and φ(k) is some increasing function of past production, which 

is a measure of the diffusion of the good between consumers, and induces 

network externalities. The gross profit function for the leader becomes: 

Π L (x L ,β L ,k)=p(k)k − ck + δ [p (X)φ(k) x L − cx L ] (2.52) 

where δ ≤ 1 is the discount factor, while the net profit oftheotherfirms is 

simply π i = x i p(X) − cx i − F . Since the other firms do not enjoy network 

effects, one can easily show that in a free entry equilibrium the future production 

x L (k) of the leader will be increasing in its initial production with 

∂x L /∂k = −cφ 0 (k)/φ(k) 2 p 0 (X) > 0. 43 Moreover, in equilibrium we have the 

cross effect: 

Π13 L = δcφ0 (k) 

> 0 

φ(k) 

which, according to our general principle, shows that the leader will always 

engage in initial overproduction to be more aggressive when the market opens 

up to endogenous entry. We can also derive a simple expression for the optimal 

initial production: 

p(k)+kp 0 (k) =c − δp ¡ X)φ 0 (k ¢ x L (k) − δ cφ0 (k)x L (k) 

φ(k) 

(2.53) 

This rule equates the marginal revenue of initial production to its effective 

marginal cost, which includes the myopic marginal cost c, a second term that 

represents the direct benefit due to the network effects on future demand 

(determining what is sometimes called a penetration price), and a last term 

representing the indirect (strategic) benefits due to the commitment to the 

adoption of a more aggressive strategy in the future. Notice that in the presence 

of network externalities, an incumbent expecting strong competition in 

the market may want to price well below marginal cost not with the purpose 

of excluding any other firm to enter in the market, but to be able to compete 

aggressively in the future: this is more likely when the marginal costs of 

production are low and the discount factor is high. Summarizing we have: 

Proposition 2.7. In markets with network externalities an incumbent 

has an incentive to overproduce initially so as to be more 

aggressive when endogenous entry takes place in the future. 

Themodelabove,canbere-interpretedinaninterestingwaywhenwe 

assume that the externality function is simply φ(k) =k. Thisimpliesthatnet 

43 We focus on an interior equilibrium, but it is clear that a corner solution can 

emerge: such a tipping equilibrium is actually typical in markets with network 

effects (see Cremer et al., 2000).


profits in the competitive market are proportional to kx L .Tofix ideas, imagine 

that the firms under consideration produce local newspapers. The leader 

decides a capacity production for k copies of its local newspaper, but also 

sells advertising space on the newspaper in quantity x L and in competition 

with other newspapers (located elsewhere and with their own local readers). 

Of course, advertising is more valuable when a newspaper has more readers, 

and more precisely what matters is exactly the number of interactions between 

readers and advertisement, which is simply k · x L .Thisisthesimplest 

example of a two-sided market because newspapers sell two products (news 

and advertising) to different customers, and there are network effects between 

them (actually only in one direction in this example, since we assumed that 

readers are indifferent to the size of advertisement space on the newspapers). 

As first pointed out by Rochet and Tirole (2003) and Armstrong (2006), 

in such a two-sided market firms charge the different sides in different ways 

with the aim of enhancing network effects: in general the aim is to get on 

board many agents from the side whose size creates more value for the other 

side. In our example, for instance, the direct effect of the sales of newspapers 

(and maybe related bundled gadgets) on the profits from advertising induces 

a production beyond the myopic monopolistic output level. However, here we 

want to point out a new strategic element: a leader facing competition on one 

side (advertising), will have an additional indirect incentive to overproduce 

on the other side (newspapers), to enhance the value of the platform and to 

be aggressive in the competition with other firms (for the advertising). 44 

Similar situations emerge in many multi-sided markets where platforms 

compete on the volume of transactions between different groups of buyers and 

sellers (think of credit cards, operating systems) 45 and multiple factors can 

44 One can verify that the same happens under price competition, which is the usual 

assumption in models of two-sided markets. However, under SC, overproduction 

by the leader is strictly related with the endogeneity of entry. When the number 

of competitors is exogenous, a leader would like to commit to (relatively) high 

prices for the newspapers so as to be accommodating in the competition for 

advertising space against other newspapers: only when entry is endogenous the 

need of being aggressive in the advertising market induces to price newspapers 

at a (relatively) low price. See Section 6.1.2 for further discussion. 

45 For instance, consider a variant of the previous example where both sides are 

now charged for each interaction, and c is the marginal cost of an interaction, so 

that: 

Π L (x L,β L ,k)=[p(k)+p(X) − c] · k · x L 

In case the leader is just a monopolist, k and x would be chosen to satisfy the 

Rochet-Tirole (2003) optimality condition: 

p(k)+p(x) − c = p(k)+p(x) 

(k)+(x) = p(k) 

(k) = p(x) 

(x)

2.10 Bundling 79 

induce different strategic behavior toward different sides. Market relations 

easily become complex when network effects act in both directions (in the 

case of informative advertising, readers may have positive externalities from 

more advertising in the newspapers), and especially when one or both sides 

engage in multi-homing (in case of national newspapers, readers may read 

more than one of them). In Chapter 6 we will discuss some of these issues 

within concrete applications. 

2.10 Bundling 

There has been a lot of attention in the economic literature on the rationale 

for bundling products rather than selling them separately. 46 A fundamental 

reason for this is that many antitrust cases have focused on such a practice as 

an anti-competitive one. Therefore, in this section we will try to understand 

when market leaders adopt bundling as a strategic device for exclusionary 

purposes. 

According to the traditional leverage theory of tied good sales, monopolists 

would bundle their products with others for competitive or partially 

competitive markets to extend their monopolistic power. Such a view as 

been criticized by the Chicago school (Bork, 1993, Posner, 2001) because 

it would erroneously claim that a firm can artificially increase monopolistic 

profits from a competitive market. Bundling should have different motivations, 

as price discrimination or creation of joint economies, whose welfare 

consequences are ambiguous and sometimes even positive. Whinston (1990) 

has changed the terms of the discussion trying to verify how a monopolist can 

affect the strategic interaction with its competitors in a secondary market by 

bundling. His main finding is that bundling tends to strengthen price competition 

against these competitors, therefore the only reason why a monopolist 

could bundle is to deter entry in the secondary market. However, here we 

will show that, when entry is endogenous, bundling may become the optimal 

“top dog” (aggressive) strategy. 

where (x) =−p(x)/xp 0 (x) is the elasticity of demand: the side whose demand 

is more elastic should be charged relatively more because this keeps demand 

on both sides balanced and maximizes the volume of interactions for a given 

total price. Now, imagine that the leading platform competes on one side, but 

can commit to output k on the other side. Since Π13 

L = p 0 (k)k


Imagine that a monopolistic market is characterized by zero costs of production 

and unitary demand at price v, which corresponds to the valuation 

of the good alone. Another market is characterized by standard price competition, 

a fixed cost F and a constant marginal cost c. Grossprofits for the 

monopolist without bundling are: 

π M = v +(p M − c) D (p M ,β M ) − F (2.54) 

while profits for the other firms are π i =(p i − c) D (p i ,β i ) − F .InBertrand 

equilibrium with endogenous entry the monopolist enjoys the profits π M = v. 

Under bundling, demand for the monopolist is constrained by demand 

for the other good, which is assumed less than unitary. The bundle price 

corresponds to P M = v 0 + p M ,wherev 0 ≥ v is the valuation of the primary 

good when bundled with a secondary good of the same firm: this maybe 

higher for efficiency reasons, complementarities or network externalities of 

different kind. In such a case, the profits for the monopolist become: 

π MB =(P M − c) D(P M − v 0 ,β M ) − F 0 =(p M + v 0 − c) D (p M ,β M ) − F 0 

where F 0 ≤ F is the fixed cost of production in case of bundling: this may 

also be lower than before because of cost efficiencies. The other firms have 

the same objective function as before. In Bertrand equilibrium the monopolist 

chooses the price P M = p M + v 0 satisfying: 

(P M − c)D 1 [p M , (n − 1)g(p)] + D [p M , (n − 1)g(p)] = 0 (2.55) 

while each one of the other firms chooses p satisfying: 

(p − c)D 1 [p, g(p M )+(n − 2)g(p)] + D [p, g(p M )+(n − 2)g(p)] = 0 (2.56) 

If endogenous entry holds, the number of firms satisfies also: 

(p − c)D [p, g(p M )+(n − 2)g(p)] = F (2.57) 

so that the profit of the monopolist bundling the two goods becomes π MB = 

(P M − c) D [p M , (n − 1)g(p)]. Noticethatifwedefine β = g(p M )+(n−2)g(p) 

the equilibrium spillovers received by the entrants as a consequence of the 

price chosen by their competitors, the equilibrium conditions (2.56)-(2.57) 

jointly determine p and β independently from the price of the monopolist. 

Using β M = β + g(p) − g(p M ) we can rewrite the equilibrium first order 

condition of the monopolist as an implicit expression for p M = p M (v 0 ),and 

immediately derive that the equilibrium price of the secondary good decided 

by the monopolist has to be decreasing in v 0 . 47 

47 In particular we have: 

dp M 

= −D 1 [p M ,β+ g(p) − g(p M )] 

< 0 

dv 0 ∆


Clearly, bundling is optimal if π MB > π M . We need to verify under 

which conditions this happens. Before doing that, let us look at the way in 

which bundling changes the strategy of the monopolist. Since ∂π MB /∂p M − 

∂π M /∂p M = v 0 D 1 < 0, bundling makes the monopolist tough. This implies 

that the monopolist is led to reduce the effective price in the secondary market 

by choosing a low price of the bundle. Since SC holds, a price decrease 

by the monopolist induces the other firms to reduce their prices. Under exogenous 

entry, as in the Whinston (1990) model with two firms, this reduces 

profits of all firms in the secondary market, hence bundling is never optimal 

unless it manages to deter entry. Under endogenous entry, however, this result 

can change: bundling can now be an effective device to outplace some 

of the other firms without fully deterring entry in the secondary market, but 

creating some profits for the monopolist in this market through an aggressive 

strategy. In particular, bundling is optimal if the low price of the bundle 

increases profits in the competitive market more than it reduces them in the 

monopolistic one. It is easy to verify that bundling is optimal if: 

[p M (v 0 ) − c] D [p M (v 0 ),β M ] − F 0 >v− v 0 D [p M (v 0 ),β M ] 

whose left hand side is the gain in profits in the competitive market and 

whose right hand side is the loss in profits in the monopolistic market: 

Proposition 2.8. Under price competition with endogenous entry 

in a secondary market, a monopolist in a primary market can 

have an incentive to bundle both goods to be aggressive. 

It is important to remark that, in this case, bundling does not need to 

have an exclusionary purpose as assumed by the leverage theory of tied good 

sales. The reduction in the price of the two bundled goods together can also 

benefit consumers. This is even more likely when they are complements, when 

there are network externalities between products, or when bundling creates 

efficiency effects. 

Bundling is an example of a discrete strategy: a firm either bundles two 

goods or not. A similar story can be used to evaluate a related discrete 

strategy, the choice of product compatibility and system compatibility, orinteroperability: 

as Tirole (1988, p. 335) has correctly noticed, “a manufacturer 

that makes its system incompatible with other systems imposes a de facto 

tie-in.” Typically, product compatibility softens price competition because 

consumers can mix and match products of different firms: these products endogenously 

become complements, while they would be substitutes in case of 

incompatibility. Since price cuts are more profitable when competing products 

are substitutes rather than complements, interoperability softens price 

competition. 

where ∆ ≡ 2D 1 +(p M +v 0 −c)[D 11 −g 0 (p M)D 12]−g 0 (p M)D 2 < 0 by the stability 

of the equilibrium system. In other words, the price of the bundle increases less 

than proportionally with v 0 or the monopolist offers the bundle with a discount 

on the secondary good compared to its competitors.


Therefore, according to the standard outcome under price competition 

with an exogenous number of competitors, the only reason why a leader would 

choose a low level of interoperability would be to induce their exit from the 

market. On the contrary, our results suggest that, when entry in the market 

is endogenous, a leader may favour a limited level of interoperability for 

adifferent purpose than entry deterrence: just because this strategy would 

strengthen price competition and enhance the gains from a low pricing strategy 

in the system competition, that is the competition between alternative 

systems. 

2.11 Vertical Restraints 

Vertical restraints are agreements or contracts between vertically related 

firms. They include franchise fees, that specify a non-linear payment of the 

downstream firm for the inputs provided by the upstream firm with a fixed 

fee and a variable part (so that the average price is decreasing in the number 

of units bought), quantity discounts and various forms of rebates, that 

often play a similar role to the one of the francise fees, exclusivity clauses 

and other minor restraints. When these restraints improve the coordination 

of a vertical chain, they are typically welfare improving, however, when they 

affect interbrand competition, that is competition between different products 

and different vertical chains, they can induce adverse consequences on consumers: 

namely they can be used to keep prices high and, therefore, they 

should be punished by the antitrust authorities. This is the standard result 

of the theory of strategic vertical restraints in interbrand competition (Bonanno 

and Vickers, 1988; Rey and Stiglitz, 1988), which suggests that, as long 

as firms compete in prices, a firm has incentives to choose vertical separation 

and charge his retailer a francise fee together with a wholesale price above 

marginal cost to induce an accommodating behavior. 

Consider an upstream firm that produces a good at marginal cost c and 

fixed cost F , and delegates its distribution on the market to a downstream 

firm through a contract implying a fixed fee Υ and a wholesale price w for the 

good. The downstream firm sells this same good at the price p D to maximize 

net profits: 

π D =(p D − w)D(p D ,β D ) − Υ (2.58) 

while the other firms, that are vertically integrated and face the same cost 

structure, have the standard profit function π i =(p i − c)D(p i ,β i ) − F .The 

upstream firm can preliminarily choose the optimal contract, meaning the 

wholesale price w and the fee Υ that maximize net profits: 

π U =(w − c)D(p D ,β D )+Υ − F (2.59)

2.11 Vertical Restraints 83 

It is always optimal to choose w such that the profits of the downstream firm 

are maximized, and the fee that fully expropriates these profits. Of course, 

achoicew = c would be neutral for the market outcome. However, Bonanno 

and Vickers (1988) have shown that, if competition is between an exogenous 

number of firms, it is optimal to choose a high wholesale price w>cto soften 

price competition, and increase prices compared to the outcome in which the 

firm is vertically integrated. This is the classic example of an anti-competitive 

vertical restraint adopted by a market leader through strategic delegation of 

accommodating pricing. 48 

When entry in the market is endogenous, the market leader cannot operate 

as above, because high wholesale prices would put the downstream firm 

out of the market. A market leader can still gain from delegating pricing decisions, 

but the optimal contract is now radically different. In particular, we 

know from our general results, that competition in prices with endogenous 

entry between the downstream firm and the other firms would lead to a price 

p D (w) increasing in the wholesale price for the downstream firm, a price for 

the other firms p = p D (c) and an endogenous value for β; moreover,bothp 

and β would be independent from w, andβ D (w) =β + g(p) − g(p D (w)). One 

can verify that the optimal contract solves the problem: 

max π U =(w − c)D [p D (w),β D (w)] + Υ − F 

{w,Υ} 

s.v. : π D =[p D (w) − w] D [p D (w),β D (w)] − Υ ≥ 0 

and requires a wholesale price for the retailer smaller than the marginal cost 

and implicitly given by: 49 

w ∗ = c + (p D − c)D 2 g 0 (p D ) 


In such a case, the vertical restraint leads to a lower price for the consumers 

and there is no ground for conjecturing any anti-competitive behavior. 

50 Therefore, also in the case of vertical restraints affecting interbrand 

competition, entry conditions are crucial to derive proper conclusions. 

2.12 Price Discrimination 

When firms sell the same good at different prices for different consumers, they 

are adopting a policy of price discrimination, which is often regarded as an 

anti-competitive practice by antitrust authorities dealing with exclusionary 

or exploitative abuses by dominant firms: for this reason, in this sction we will 

try to understand the motivations for the adoption of price discrimination. 51 

Typically, this increases profitability, but it also allows to differentiate prices 

betweenconsumerswithadifferent willingness to pay. Moreover, notice that 

price discrimination requires a certain commitment, because similar goods 

mustbesoldnotonlyatdifferent prices for different consumers, but also 

in different packages and with different advertising. In theory, when firms 

enjoy perfect information on the preferences of the consumers and can set a 

price equal to the maximum willingness to pay of each consumer, they can 

fully extract the consumer surplus, something known as first degree price 

discrimination. However, the usual forms of discrimination are much more 

limited. 

A large literature has focused on the more realistic case of incomplete 

information, in which firms offer different deals and customers choose their 

favorite:atypicalexampleofthissecond degree price discrimination involves 

price-quantity bundles, often involving quantity discounts. A market often 

analyzed in the literature is the insurance market, where high risk types demand 

more insurance and low risk types demand less insurance (but firms do 

not know who is who). In such a market, simple price competition with free 

entry leads to a market failure because high risk types drive out low risk types 

and the market collapses (Akerlof, 1970). In such a case, different prices for 

different quantities naturally emerge in a competitive framework. Rothschild 

and Stiglitz (1976) have shown that a free entry equilibrium of this kind is 

characterized by low risk types accepting limited insurance associated with a 

low price and high risk types accepting full insurance at a higher price. Such 

a separating equilibrium works because high risk types prefer their contract 

rather than imitating the low risk types and obtain cheaper but limited in- 

50 A similar result emerges also in models of competition in quantities, but this 

is less surprising since it confirms the outcome of delegation games with an 

exogenous number of competitors. 

51 See Tirole (1988, Ch. 3) for an introduction to price discrimination.

2.12 Price Discrimination 85 

surance. 52 On the contrary, a pooling equilibrium cannot exist because a firm 

may deviate by offering a contract which is profitable if accepted just by the 

low risk types. 

The relevance of this theory of competitive price discrimination due to 

asymmetric information has been challenged on empirical ground because we 

rarely observe a positive correlation between risk and insurance, even in the 

automobile insurance market (Chiappori and Salanie’, 2000). However, this 

should not surprise because this (as many other insurance markets) is not 

a one shot market, but is characterized by short term contracts which are 

periodically updated. In a dynamic version of the Rothschild-Stiglitz model, 

pooling equilibria with experience rating naturally emerge (Etro, 2000), and 

they exactly mimic the bonus-malus policy that characterizes this market 

everywhere: initial contracts are standard for anybody, but future contracts 

are updated in a Bayesian fashion according to the performance of the drivers 

(which is public knowledge). 53 Notice that also this form of dynamic price 

differentiation based on observable features (the accident record) is a form of 

price discrimination, still emerging in an equilibrium with endogenous entry. 

When firms discriminate on the basis of observable characteristics, we talk 

about third degree price discrimination. Wecanprovideasimpleexample 

of the role of this form of price discrimination within our framework. For 

simplicity, imagine that all firms compete simultaneously for a common set 

of consumers, whose demand is D A (p i ,β i ) for each firm i, and the leader 

also serves a local market with demand D B (p i ) (weassumethathastoserve 

52 While Rothschild and Stiglitz (1976) limited their analysis to two types of consumers, 

the model can be extended to multiple types: in such a case the equilibrium 

price function is nonlinear and can involve quantity discounts (Etro, 

1999, 2000). Hence, the empirical literature started with Cawley and Philipson 

(1999), who tested (and rejected) the convexity of the price function in insurance 

marketsishighlymisleading: contrary to their erroneous claim, bulk discounts 

can perfectly characterize the equilibrium price of competitive insurance markets 

with asymmetric information (exacly as they can characterize the optimal 

monopolistic price discrimination; see Maskin and Riley, 1984). 

53 To gain insights on the nature of the pooling equilibrium in a two period 

Rothschild-Stiglitz model (Etro, 2000), let us suppose that a pooling contract 

is offered in the first period by all firms. The usual problem is that a new firm 

may deviate by offering a contract which is profitable if accepted just by the low 

risk types. In the one period model this kind of contract always exists. In the 

two period model, however, the high risk types have a new incentive to accept 

a similar deviation (and make it unprofitable), since by doing that, they would 

gain a reputation as low risk types and the associated second period contract 

with cheap full insurance. If agents are patient enough, any deviation is accepted 

by both types and so it is not profitable: hence the pooling contract is an equilibrium. 

Of course, also separating equilibria with immediate revelation of the 

risk types exist for low discounting.


both markets simultaneously). The leader can commit to a policy of price 

discrimination, and then choose two separate prices p A L and pB L for the same 

good sold at different kinds of customers. The marginal cost of production is 

c for all firms. The profits of the leader are then: 

π L = p A LD A (p A L,β L )+p B L D B (p B L ) − c[D B (p B L )+D A (p A L,β L )] − F (2.61) 

while the profits of the other firms are simply: 

π i = ¡ p A i 

− c ¢ D A (p A i ,β i ) − F 

Otherwise the leader can adopt a uniform pricing policy and choose a unique 

price p L for both kinds of customers, with the same profit functionasabove. 

The idea behind the commitment to discriminate is that price discrimination 

requires a small preliminary investment in package diversification and 

separate advertising for the products sold for the different kind of customers. 

Consider the case of an exogenous number of firms. Choosing price discrimination, 

the leader sets the two prices, say p A L >pB L , and obtains monopolistic 

profits in the local market and (given symmetry) the same profits 

as the other firms in the symmetric Bertrand equilibrium for the common 

market. Choosing uniform pricing, the leader chooses an intermediate price 

p L ∈ (p B L ,pA L ) in Bertrand equilibrium, and SC implies that also the other 

firms will reduce their equilibrium prices. Ultimately, the leader reduces its 

profits in the local market and strengthens competition in the common market. 

Clearly, in this case, price discrimination is the optimal choice, since 

it allows the leader to maximize profits in the local market and to soften 

competition in the common one. 

Consider endogenous entry now. Under price discrimination, all firms 

choosethesamepricep A L in the common market and entry drives profits 

to zero in this market, while the leader enjoys only its monopolistic profits 

in the local market setting the optimal price p B L . Assume again that the demand 

conditions are such that p A L >pB L . In this case, by adopting uniform 

pricing, the leader will choose an intermediate price between p B L and pA L ,and 

will obtain two results: on one side, profits in the local market will decrease 

because pricing is above monopolistic pricing, on the other side, profits in the 

common market will increase because the leader is endogenously committed 

to aggressive pricing, which is always optimal in a market where entry is 

endogenous. If the former loss is smaller than the latter gain, it is optimal to 

adopt uniform pricing rather than committing to price discrimination. 54 

This simple example is just aimed a suggesting that price discrimination 

can have a role in softening price competition (compared to uniform pricing) 

inducing negative consequences for consumers: this effect, however, is less 

54 Notice that this can happen because the loss from a small deviation from monopolistic 

pricing is a second order loss, while the gain in the common market is 

a first order gain.

2.13 Antitrust and Horizontal Mergers 87 

likely to emerge in markets where entry is endogenous, since in these markets 

an aggressive uniform pricing strategy can be optimal. In conclusion, we may 

have a possible new case for the association of price discrimination by market 

leaders with anti-competitive purposes. 55 

2.13 Antitrust and Horizontal Mergers 

We have seen that even when they face endogenous entry of competitors, 

market leaders can obtain positive profits by adopting certain strategic commitments. 

One may think that a preliminary merger with other firms and 

a subsequent cooperation in the strategic decisions may serve a similar role. 

When the number of firms in the market is given, this is typically the case. 

Moreover, a merger induces a more accommodating behavior which exerts 

an indirect effect on the other firms. When SS holds the other firms become 

more aggressive, when SC holds they become more accommodating as well: 56 

for this reason, loosely speaking, mergers tend to be more profitable under 

competition in prices. However, once again, the situation changes when entry 

is endogenous. In such a case the merger can affect entry, which creates a 

new effect, often taken into account in antitrust policy considerations, but 

not in the theory of mergers until now. 57 In our context, a merger induces 

accommodation by the merged firm, which attracts entry and reduces the 

profits of the merged firm: consequently, there is no any strategic rationale 

for mergers when entry in the market is endogenous. 58 

Consider a merger between two firms, say firms k and j. Thenetprofits 

of the merged firms become: 

π Merger = Π (x k ,β k )+Π ¡ x j ,β j 

¢ 

− ˜F 

55 Notice that a different situation emerges if the demand conditions are such that 

under price discrimination we have p A L


where ˜F is the new fixed cost of production. Using the fact that β j = β k + 

h(x k ) − h(x j ) for k, j =1, 2, wehavethefirst order conditions: 

Π 1 (x k ,β k )+Π 2 (x j ,β j )h 0 (x k )=0 k, j =1, 2 (2.62) 

which clearly shows an accommodating behavior for both strategies. As we 

know, such a behavior creates a strategic disadvantage when entry in the 

market is endogenous. The equilibrium after the merger is characterized by 

two identical strategies for the merged firm, x k = x j = x M ,astrategyfor 

the followers x, and respective spillovers β M and β such that: 

Π 1 (x M ,β M )+Π 2 (x M ,β M )h 0 (x M )=Π 1 (x, β) =0, Π(x, β) =F 

This implies x M β: the equilibrium strategy of the other firms 

isalwaysthesameafterthemerger,buttheaccommodatingbehaviorofthe 

merged entity induces further entry so as to decrease its gross profits below 

those of each independent firm. Nevertheless, the merger can still be profitable 

if π Merger > 0, whichrequires ˜F < 2Π(x M ,β M ). In a market where entry 

is endogenous, the only way a merger can be profitable is by creating cost 

efficiencies. 59 This conclusion exactly matches the informal insights of the 

Chicago school on horizontal mergers (Bork, 1993, Posner, 2001), and can be 

summarized as follows: 

Proposition 2.10. In a market with endogenous entry, a horizontal 

merger induces accommodating behavior of the merged firm and 

attracts entry of other firms: the merger is profitable if and only if 

it creates enough cost efficiencies to compensate for the strategic 

disadvantage of the merged firm. 

Notice that in models of competition in quantities and prices, as long 

as the merged firm does not deter entry, the equilibrium after the merger 

implies the same total production or the same price indexes as before (see 

also Chapter 3). Therefore, consumer surplus is not affected by the merger. 

Since the latter takes place only when there are significant cost efficiencies, 

it follows that horizontal mergers in markets where entry is endogenous are 

welfare improving. 60 

59 For instance, in the linear model of competition in quantities of Section 1.1, 

the merged firm would produce the same as the two separate firms, therefore 

the merger could be profitable only if ˜F < F. In the model with imperfect 

substitutability of Section 1.2.2, a merger between two firms would lead them to 

produce 2 −b times as before and to reach the joint profits π Merger =(2− b)(2 + 

b − b 2 )F/2 − ˜F which are positive if product differentiationisstrongenough(b 

or ˜F small). 

60 The Erkal-Piccinin model extends the analysis to more complex demand functions: 

under competition in prices with a demand system derived from the 

quadratic utility function (2.11), a merger increases the prices of the merged



This chapter has examined Nash and Marshallian competition within a general 

framework, and it has studied the strategic incentives of market leaders 

to undertake preliminary investments that can affect competition. A main result 

of this investigation has been that the behavior of market leaders facing 

endogenous entry is always biased toward the implementation of aggressive 

strategies. As we noticed in the examples of Chapter 1, this result confirms 

what we found in models of Stackelberg competition with endogenous entry, 

that is in models where the leader does not undertake full fledged investments 

to constraint subsequent decisions, but simply commits to strategies before 

the other firms. Since the ultimate results are analogous, we can safely look at 

models of Stackelberg competition with endogenous entry as reduced forms 

of the more general models of Marshallian competition with strategic investments 

analyzed in this chapter. The advantages of the first kind of models 

are that they are simpler, they allow to derive clear welfare comparisons with 

the corresponding models of Marshallian competition, and they allow further 

extensions. For this reason, in the next chapter we will move on to the study 

of general models of Stackelberg competition in the market with and without 

endogenous entry. In Chapter 4 we will do the same for general models of 

Stackelberg competition for the market with and without endogenous entry. 

firms and reduces the prices of the other firms while increasing entry (nevertheless, 

in the absence of cost efficiencies, the impact on consumer surplus is 

typically negative).

3. Stackelberg Competition and Endogenous 

Entry 

In the 1930s, Stackelberg (1934) pioneered the study of a market structure 

where a firm has a leadership over the rivals. Market leaders obtain a stable 

advantage on the followers when they are first movers in the choice of the 

strategy. It is well known that the commitment of the leaders may not be 

credible when initial strategies can be easily revised over time. However, a 

commitment represents a credible advantage in markets with a short horizon 

or when strategies are costly to change. For instance, in some markets a 

certain production level is associated with preliminary investments in the 

preparation of projects, machinery, and on the allocation of different inputs. 

It may be costly to change these factors of production afterwards: being a 

first mover on the output choice in these markets can represent a fundamental 

strategic advantage. In other markets, prices are sticky in the short run due 

to small menu costs or to costly acquisition of information, or because a 

price change can induce adverse reputational effects on the perception of the 

customers: in these cases, being the first mover in the price choice provides 

the leader with a credible commitment in the short run. Finally, in sectors 

where firms compete for the market, a preliminary investment in research 

and development represents a solid commitment to an innovation strategy. 

In general, the economic concept of leadership associated with the timing of 

the decisions can be seen as a simple representation of situations in which 

preliminary investments, as those studied in the previous chapter, provide a 

strategic advantage to a firm. 

The modern game theoretic analysis of competition between market leaders 

and followers started from the seminal contribution of Dixit (1980), 1 who 

focused, as with most of the subsequent literature, on a duopoly. When a market 

leader faces a single follower, two basic situations can emerge. If the fixed 

costs of production for the follower are high, the leader finds it optimal to 

deter entry, for instance by choosing a high output level that leaves too little 

demand for the follower, or by choosing a low price against which the follower 

cannot profitably compete. If the fixed cost of production is low enough, for 

instance if it is zero, the leader cannot profitably deter entry, and has to 

compete on the market with the entrant. There are two possible outcomes, 

and they depend on the form of competition, or more precisely, on the kind 

1 See also Spence (1977) and Dixit (1979).

92 3. Stackelberg Competition and Endogenous Entry 

of strategic interaction. Under strategic substitutability, that typically holds 

with competition in quantities, the leader is aggressive: for instance, produces 

a lot so as to gain market share compared to the rival. Under strategic complementarity, 

that typically holds with competition in prices, the leader is 

accommodating: for instance, chooses a high price so as to induce the rival to 

choose a high price as well. Ultimately, whether strategic complementarity or 

substitutability holds is an empirical question, but its answer is not obvious, 

as it is often not obvious what the strategic variables are that are under the 

control of firms in the real world. For this reason the results of the theory 

appear too vague to be of practical interest for unambiguous descriptions of 

the behavior of market leaders and for policy recommendations. 

The above analysis of the competition between a leader and a follower, as 

already said, holds when the fixed cost of production for the latter is low, so 

that entry deterrence is not an option for the leader. However, in this exact 

situation, net profits for the followers are likely to be high and they could 

attract other firms in the market. For this reason, an analysis limited to an 

exogenous number of firms (the leader and a single follower, or two followers, 

or any other given number of followers) can be quite misleading. In most 

markets, we can regard the number of competitors as an endogenous variable, 

which depends on the interaction between the market leader and the other 

firms, and not as an exogenous variable. In this chapter, we will examine the 

case in which a leader faces an endogenous number of followers. The results, 

based on Etro (2002, 2008), are quite simpler: the leader always behaves in an 

aggressive way, choosing higher production or lower prices than the followers. 

In particular, if each firm has a profit function Π(x i ,X −i ), where the aggregate 

statistics X −i = P j6=i x j summarize the strategies of the other firms, 

an interior equilibrium can be characterized quite simply. The choice of each 

entrant satisfies the normal optimality condition Π 1 =0, while the choice of 

the leader satisfies Π 1 = Π 2 . For instance, under competition in quantities 

and homogenous goods, this implies that the entrants equate marginal cost 

and marginal revenue, while the leader equates marginal cost and price. Its 

profits are positive because production is in the region of increasing average 

costs. We will also verify under which conditions the leader finds it optimal 

to be so aggressive as to deter entry, and we will see that the conditions for 

such an outcome are not very demanding: under competition in quantities 

and homogenous goods the equilibrium implies just one firm,theleader,as 

long as there are increasing, constant or even slightly decreasing returns to 

scale. 2 

The analysis of Stackelberg competition with endogenous entry is somewhat 

related with three older theoretical frameworks. The first is the initial 

literature on entry deterrence associated with the so-called Bain-Modigliani- 

Sylos Labini framework. However, even if the initial contributions by Sylos 

2 As we have already seen in Chapter 1, with a linear demand p = a − X and a 

constant marginal cost c, the equilibrium implies the limit price p = c +2 √ F .

3. Stackelberg Competition and Endogenous Entry 93 

Labini (1956), Bain (1956) and Modigliani (1958) took in consideration the 

effects of entry on the behavior of market leaders, they were not developed 

in a coherent game theoretic framework and were substantially limited to 

the case of competition with perfectly substitute goods and constant or decreasing 

marginal costs (which not by chance, as we will see, are sufficient 

conditions for entry deterrence). 

The second is the dominant firm theory, which tried to explain the pricing 

decision of a market leader facing a competitive fringe of firms taking 

as given the price of the leader. 3 Assuming that the supply of this fringe is 

increasing in the price, the demand of the leader is total market demand net 

of this supply. The profit maximizing price of the leader is above marginal 

cost but constrained by the competitive fringe. While such a model is not 

fully consistent with rational behavior of the parts in a game theoretic perspective, 

it provides interesting insights on the behavior of market leaders 

under competitive pressure. 

The third is the theory of contestable markets by Baumol et al. (1982), 

which focuses mainly on homogenous goods and shows that, in the absence 

of sunk costs of entry, the possibility of “hit and run” strategies by potential 

entrants is compatible only with an equilibrium price equal to the average 

cost. One of the main implications of this result is that “one firm can be 

enough” for competition when there are aggressive potential entrants. 4 

None of these frameworks provides indications on the behavior of market 

leaders in general contexts, but nevertheless they have been quite helpful in 

providing insights on the role of competitive pressure in markets with leaders. 

3 See Carlton and Perloff (2004) and Viscusi et al. (2005, Ch. 6) for an introduction 

and Kahai et al. (1996) for an empirical application to the case of AT&T. See 

also the work of Gaskins (1971) on dynamic limit pricing under threat of entry; 

I am grateful to Avinash Dixit for attracting my attention on this work. 

4 Baumol et al. (1982) note that the contestable outcome can be described as the 

game in which firms first choose prices simultaneously and then choose output (or 

capacity) if they enter (choosing positive output implies entry decision). They 

also claim that the theory of perfect contestable market can be viewed as a 

generalization of the Bertrand game to markets with increasing returns to scale. 

Inthecaseofalineardemandp = a − X and a constant marginal cost c, the 

contestable-market equilibrium requires a price of the incumbent equal to the 

average cost (p = a − x = c + F/x), therefore: 

p = 1 2 

 

a + c − 

(a − c) 2 − 4F 

which is always lower than the equilibrium price under Stackelberg competition 

in quantities with endogenous entry. The contestable-market equilibrium can be 

also interpreted as a Stackelberg equilibrium in prices with endogenous entry and 

homogenous goods. Of course, our theory applies beyond the case of homogenous 

goods.


In this chapter we will develop a general theory of Stackelberg competition 

with endogenous entry within the framework developed in the previous chapter, 

and we will analyze complex situations where there are multiple leaders, 

where the leadership itself is endogenous, where there are multiple strategies 

to be chosen, and where there are more general profit functions. Finally 

we will analyze a few applications concerning collusive cartels and antitrust 

policy, strategic export promotion and privatizations. 

The chapter is organized as follows. Section 3.1 studies pure Stackelberg 

competition where entry is exogenous, while Section 3.2 studies Stackelberg 

competition with endogenous entry. Section 3.3 applies these models to general 

forms of competition in quantities and in prices. Section 3.4 extends the 

model in different directions. Section 3.5 derives some implications for collusion 

between firms. Section 3.6-7 concludes our analysis with a digression on 

commitments created by government policy as state aids to exporting firms 

and privatizations. Section 3.8 concludes. 

3.1 Stackelberg Equilibrium 

In this section we will study a general version of a simple and well known 

game: Stackelberg competition. The number of firms in the market, n, is 

exogenous, for instance because legal or institutional constraints limit entry, 

or because a certain technology is available only for a limited number of 

firms, or is protected by intellectual property rights. What is crucial for the 

following analysis is that no other firms can enter in the market even if this 

is profitable. One of the firms, the leader, can choose its own strategy before 

the other firms. These other firms, defined as followers, choose simultaneously 

their own strategies taking as given the strategy of the leader. Therefore, this 

is a Stackelberg game with one leader and n−1 followers, and we are looking 

for its subgame perfect equilibrium. 

Imagine that each firm i has the profit function: 

π i = Π(x i ,β i ) − F with β i = 

nX 

j=1,j6=i 

h(x j ) (3.1) 

where Π is unimodal in the first argument x i , which is the strategy of the 

same firm, and decreasing in the second argument β i , which summarizes the 

strategies of the other firms through a positive and increasing function h(·). 

In Chapter 1 we analyzed a few examples of this environment: models 

of Stackelberg competition in quantities with linear demand and with homogenous 

goods or imperfect substitutability between goods, models with 

U-shaped average cost functions, models of competition in prices with a Logit 

demand, and simple models of competition for the market. In those examples 

the leader in the market was exploiting the first mover advantage in different

3.1 Stackelberg Equilibrium 95 

ways. For instance, in models of competition in quantities and of competition 

for the market we found out that the leader was aggressive compared to the 

followers (producing or investing more), while in models of competition in 

prices the leader was accommodating (choosing higher prices and producing 

less). Here we generalize those findings in a rule for the behavior of the market 

leaders. 

We will focus on the case in which interior equilibria emerge, that is all 

firms are active in the market and obtain positive profits, and the leader does 

not find it optimal to deter entry. This case emerges whenever the fixed costs 

are low enough. 5 We can define the equilibrium in the following way: 

Definition 3.1. A Stackelberg Equilibrium between n firms is such that 1) 

each follower chooses its strategy x to maximize its profits given the spillovers 

β from the other firms and the strategy of the leader x L ;2)theleaderchooses 

its strategy x L to maximize its profits under rational expectations on β L ;3) 

β =(n − 2)h(x)+h(x L ) and β L =(n − 1)h(x). 

As usual, the equilibrium can be solved by backward induction. Given 

the strategy of the leader, defined as x L , all the followers choose their own 

strategies to satisfy the first order conditions: 

Π 1 (x i ,β i )=0 for any i (3.2) 

In this kind of game, for a given number of firms, a pure-strategy equilibrium 

exists if the reaction functions are continuous or do not have downward jumps 

(see Vives, 1999). Unfortunately this may not be the case due to the presence 

of fixed costs, but weak conditions for existence have been studied for many 

applications. 6 In this general framework we will just assume the existence 

of a unique symmetric equilibrium where all the followers choose the same 

strategy x. 7 In the symmetric equilibrium we have: 

Π 1 [x, (n − 2)h(x)+h(x L )] = 0 (3.3) 

This expression provides the strategy of the follower x as a function of the 

strategy of the leader and of the number of firms, x = x(x L ,n). Totally 

differentiating the equilibrium first order condition, it follows that: 

dx 

Π 12 (x, β) h 0 (x L ) 

= 

dx L − [Π 11 (x, β)+(n − 2)h 0 (x)Π 12 (x, β)] 

5 The next section will deal with the case in which the fixed costs of production 

are high enough (or the number of potential entrants is high enough), that only 

a limited and endogenous number of firms actually enters in the market. 

6 For instance, see Amir and Lambson (2000) on Cournot games with perfectly 

substitute goods and Vives (1999) for a survey. 

7 This happens in all of our examples and, in general, under a standard contraction 

condition, Π 11 +(n − 2)h 0 (x) |Π 12 | < 0. Thisalwaysholdsforn =2.Withmore 

than one follower, weaker conditions for uniqueness are available for particular 

models.


whose denominator is positive under the assumption of stability. Hence, a 

more aggressive strategy of the leader (an increase in x L ) makes the followers 

more aggressive under the assumption of SC (Π 12 > 0), and less aggressive 

under SS (Π 12 < 0). 

In the first stage, the leader takes this into account and maximizes: 

π L = Π L (x L ,β L ) − F (3.4) 

where β L =(n − 1)h [x(x L ,n)]. Therefore, in the case of an interior solution, 

we obtain the first order condition: 

Π1 L (x L ,β L )+Π2 L (x L ,β L ) ∂β L 

=0 (3.5) 

∂x L 

and we assume that the second order condition is satisfied. Using our expression 

for dx/dx L we have: 

Π1 L (x L ,β L )= (n − 1)h0 (x)h 0 (x L )Π 12 (x, β) Π2 L (x L,β L ) 

[Π 11 (x, β)+(n − 2)h 0 (3.6) 

(x)Π 12 (x, β)] 

whose term on the right hand side has the sign of Π 12 (x, β). Comparing the 

equilibrium condition for the followers and that for the leader, it is immediate 

to derive: 

Proposition 3.1. A Stackelberg equilibrium with exogenous entry 

implies that the leader is aggressive compared to the followers 

under strategic substitutability and accommodating under strategic 

complementarity. 

The intuition for this result is straightforward. 8 When the leader foresees 

that a more aggressive strategy will induce the followers to be more aggressive, 

it is optimal to be accommodating, which happens under SC. When the 

leader foresees that a more aggressive strategy will induce the followers to 

be more accommodating, it is then optimal to be aggressive, which happens 

under SS. From this general principle we can make sense of our results in 

Chapter 1: in the models of competition in quantities, the leader was aggressive 

because higher production was pushing toward a lower production 

for the followers, while in the model of competition in prices, the leader was 

accommodating because a higher price was pushing toward higher prices for 

the followers as well, increasing the profits of all firms. As we will see later on 

in detail, these are the typical outcomes of these two forms of competition, 

while competition for the market can lead to a different behavior of the leader 

depending on many market features, a point that we will revisit in the next 

chapter. 

8 Contrary to the model of Fudenberg and Tirole (1984), here we do not have 

a preliminary investment that affectsthestrategy,butwehaveapreliminary 

strategy tout court. In the terminology of the last chapter, it is as if we are 

alwaysinthecasewhereΠ L 13 > 0.

3.2 Stackelberg Equilibrium with Endogenous Entry 97 

3.2 Stackelberg Equilibrium with Endogenous Entry 

Letusmovenowtothecaseinwhichthenumberoffirms in the market is not 

an exogenous variable, but it actually depends on the profitable opportunities 

in the market. As long as there are positive profits to be made in the market, 

firms enter and compete with the leader and the other firms. 9 Therefore, 

the number of competitors is endogenously determined by the technological 

conditions, by the nature of the strategic interaction, and by the preliminary 

strategy of the leader. 

More precisely, following Etro (2002, 2008), we will look at the subgame 

perfect equilibrium of the game with the following sequence of moves: 

1) in the first stage, a leader, firm L, enters,paysthefixed cost F and 

chooses its own strategy x L ; 

2) in the second stage, after knowing the strategy of the leader, all potential 

entrants simultaneously decide “in” or“out”: if a firm decides “in”, 

it pays the fixed cost F ; 

3) in the third stage all the followers that have entered choose their own 

strategy x i (hence, the followers play simultaneously). 

We can define the new equilibrium in the following way: 

Definition 3.2. A Stackelberg equilibrium with endogenous entry is such 

that 1) each follower chooses its strategy x to maximize its profits given the 

spillovers β from the other firms; 2) the number of firms n is such that 

all followers make non negative profits and entry of another follower would 

induce negative profits for all of them; 3) the leader chooses its strategy x L 

to maximize its profits under rational expectations on x and n; 4)β =(n − 

2)h(x)+h(x L ) and β L =(n − 1)h(x). 

To characterize this equilibrium we look at the last stage again. In this 

stage, in the case of an interior equilibrium, we still have a standard first 

order condition for the followers: 

Π 1 [x, (n − 2)h(x)+h(x L )] = 0 (3.7) 

Since dΠ/∂dn = Π 2 h(x) < 0 under our assumptions, entry reduces gross 

profits until they reach the fixed costs and further entry is not profitable 

anymore. Therefore, ignoring the integer constraint on the number of firms, 

we can impose the endogenous entry condition as a zero profit condition: 

9 The exogeneity of the leadership, that is of the identity of the leader and also 

of the number of leaders, can be a realistic description for markets with an 

established dominant firm, or where entry at an earlier stage was not possible for 

technological or legal reasons, for liberalized markets that were once considered 

natural monopolies or those where intellectual property rights play an important 

role. Later, we will extend the model to multiple leaders and to endogenous 

leadership.


Π [x, (n − 2)h(x)+h(x L )] = F (3.8) 

Leaving a formal treatment to the Appendix, we will provide here an intuitive 

and constructive argument to characterize the Stackelberg equilibrium 

with endogenous entry which will be useful in the applications of the next 

section. The system (3.7)-(3.8) can be thought of as determining the behavior 

of the followers in the second and third stages, namely as determining x and 

n as functions of the leader’s first stage action. But we can also look at these 

two equations in a different way: they can be solved for the two unknowns 

x and β. The pair (x, β) will only depend on the fixed cost of production 

and not on the strategy of the leader. Given (x, β), there is a unique locus of 

(x L ,n) pairs that satisfy the equilibrium relation β =(n − 2)h(x)+h(x L ).In 

other words, the strategy of the followers is independent from the strategy of 

the leader, while their number must change with the latter. The invariance 

property (dx/dx L =0) is quite important since it shows that what matters 

for the leader is not the reaction of each single follower to its strategy, but 

the effect on entry. This is exactly the opposite of what happened in the 

Stackelberg equilibrium. When entry is exogenous the leader takes as given 

the number of followers and looks at the reaction of their strategies to its own 

strategy. When entry is endogenous the leader takes as given the strategies 

of the followers and looks at the reaction of their number to its own strategy. 

Let us now move to the first stage and study the choice of the leader. As 

long as entry takes place, the perceived spillovers of the leader can be written 

as 

β L =(n − 1)h(x) =(n − 2)h(x)+h(x)+h(x L ) − h(x L )= (3.9) 

= β + h(x) − h(x L ) 

which depends on x L only through the last term, since we have just seen that 

the pair (x, β) does not depend on x L . We can use this result to verify when 

entry of followers takes place or does not. It is immediate that entry does not 

occur for any strategy of the leader x L above a cut-off ¯x L such that n =2 

or, substituting in (3.9), such that: 

β = h(¯x L ) (3.10) 

which clearly implies ¯x L ≥ x. Entry occurs whenever x L < ¯x L .Insucha 

case, the leader chooses the optimal strategy to maximize: 

π L = Π L [x L ,β+ h(x) − h(x L )] − F (3.11) 

which delivers the first order condition: 10 

10 Notice that the second order condition is: 

D L = Π L 11 − 2Π L 12h 0 (x L ) − Π L 2 h 00 (x L )+Π L 22h 0 (x L ) 2 < 0 

that we assume to be satisfied at the interior optimum.

3.2 Stackelberg Equilibrium with Endogenous Entry 99 

Π L 1 [x L , (n − 1)h(x)] = Π L 2 [x L , (n − 1)h(x)] h 0 (x L ) (3.12) 

In this case the equilibrium values for x L , x and n are given by the 

system of three equations (3.7)-(3.8) and (3.12). In general, the profitfunction 

perceived by the leader is an inverted U relation in x L for any strategy below 

the entry deterrence level ¯x L , and it takes positive values just for x L >x. 

Beyond the cut-off ¯x L , it is downward sloping (as long as the market is not a 

natural monopoly). Hence, the strategy ¯x L is optimal only if it provides higher 

profits than at the local optimal strategy for x L < ¯x L (see the Appendix for 

the details). If we focus our attention on the qualitative behavior of the firms, 

we can conclude as follows: 

Proposition 3.2. A Stackelberg equilibrium with endogenous 

entry always implies that the leader is aggressive compared to each 

follower,andeachfollowereitherdoesnotenterorchoosesthesame 

strategy as in the Marshall equilibrium. 

The main result is that when entry in a market is endogenous, the leader 

of this market behaves always in an aggressive way, independently from the 

kind of strategic interaction that takes place with the followers. In particular, 

an accommodating behavior, which is typical of models of price competition 

(where SC holds) when entry is exogenously limited, will never emerge when 

the decision to enter in the market is endogenously taken by a sufficiently 

large number of potential entrants. Of course, this result is reminiscent of 

what we found in the previous chapter: there leaders were always undertaking 

preliminary investments that were inducing an aggressive behavior in the 

market, here they directly undertake aggressive strategies in a preliminary 

stage. We can conclude that the aggressiveness of leaders facing endogenous 

entry is a fairly general result. 

Comparative statics. We could now investigate the way our equilibria are 

affected when we change some of the parameters, as we did in the previous 

chapter for the Nash and Marshall equilibria. Unfortunately, the comparative 

statics with respect to a generic parameter affecting the profit functions are 

quite complicated for both the Stackelberg equilibrium and the Stackelberg 

equilibrium with endogenous entry. In the second case, we can make some 

progress focusing on changes in the fixed cost. It turns out that results are 

typically the opposite if SS or SC holds. For simplicity, let us assume Π 22 ≥ 0, 

which will hold in most of our examples. 11 The main results are summarized 

in: 

Proposition 3.3. Consider a Stackelberg equilibrium with endogenous 

entry where entry occurs. Under SS, a) if Π 12 >Π 11 /h 0 (x), 

11 Π 22 > 0 holds in the case of quantity competition and perfectly substitute goods 

as long as demand is convex, in our examples of price competition, and in the 

patent races of the next chapter.


the strategy of each firm is increasing and the number of firms is 

decreasing in F , b) otherwise, the strategy of entrants (leader) is 

increasing (decreasing) in F . Under SC, c) if Π12 L < (=)Π22Π L 1 L /Π2 L , 

the strategy of entrants and their number are decreasing while the 

strategy of the leader is increasing in (independent from) F , d) 

otherwise, the strategy of each firm is decreasing in F . 

These results are more interesting when we interpret entry as a “general 

equilibrium” phenomenon determined by the profits available in other sectors. 

In this case, F can be re-interpreted as the profits available in another 

sector and a no arbitrage condition between sectors determine the entry decisions. 

As in the Marshall equilibrium case, a positive shock in another sector 

(increasing F ) tends to reduce entry and induce more aggressive strategies 

by the entrants under SS and more accommodating strategies under SC, but 

the strategies of the leaders may react in the opposite way (or remain unchanged). 

In the next section we will verify these results in models of quantity 

and price competition, and briefly in a simple model of competition for the 

market (generalized in the next chapter). 

3.3 Competition in Quantities, in Prices and for the 


In the previous sections we characterized equilibria in markets with pure 

Stackelberg competition and with Stackelberg competition and endogenous 

entry in a general way. In Chapter 1 we analyzed a number of simple applications. 

In this section we will adopt an intermediate level of sophistication. 

3.3.1 Competition in Quantities 

The classic model of leadership due to Stackelberg (1934) is associated with 

competition in quantities and one firmcommittingtoitsownoutputbefore 

the other firms. Let us consider this situation under the following specification 

of the profit function: 

π i = x i p (x i ,β i ) − c(x i ) − F (3.13) 

where x i is the output of firm i, we allow for imperfect substitutability between 

goods (the inverse demand is decreasing in both arguments) and we 

employ a general cost function. 

Exogenous entry. Let us first focus on the case of exogenous entry. Given 

the output of the leader x L , the equilibrium output of each follower will 

satisfy the profit maximizing condition: 

p (x, β)+xp 1 (x, β) =c 0 (x)


where we remember that β = (n − 2)h(x) +h(x L ). The leader is aware 

that its strategy affects the choice of the followers according to the impact 

dx/dx L that can be derived from the above condition, and can choose its 

output taking this into account. 12 In Chapter 1 we solved for the Stackelberg 

equilibrium in the cases of a quadratic cost function with a linear demand 

and in the case of a linear cost function with a linear demand and imperfect 

substitutability between goods. Beyond those examples things are already 

quite complex. 

To obtain more useful results, let us focus on the standard case of homogenous 

goods and constant marginal costs. Totally differentiating the equilibrium 

condition: 

p(X)+xp 0 (X) =c 

where X is total output, we obtain: 

dx −(1 − E) 

= 

dx L [n − E(n − 1)] 

Here E ≡−xp 00 (X)/p 0 (X) is the elasticity of the slope of the inverse demand 

with respect to the production of a follower, which we already encountered 

in the previous chapter, and which measures the degree of convexity of the 

demand function. For instance, in the case of a linear demand, like the one we 

studied in the example of Chapter 1, this elasticity was zero: in that case, an 

increase in the output of the leader was reducing the output of each follower 

by 1/n. A negative impact emerges whenever this elasticity is small enough, 

but for a high enough elasticity, the impact may turn out to be positive. 

Given the perceived reaction of the followers, the leader chooses its output 

to maximize profits π L =[p(X) − c] x L − F , which provides the optimality 

condition: 

∙ 

p(X)+x L p 0 (X) 1+(n − 1) dx ¸ 

= c 

dx L 

Joining the two equilibrium first order conditions and using the slope of 

the reaction function, we can easily obtain a new general expression for the 

equilibrium output of the leader as a function of the equilibrium output of 

the followers: 13 

12 If fixed costs of production are high enough, the leader can engage in entry 

deterrence, but now we focus on the case in which entry takes place. 

13 We can also solve for the equilibrium price under Stackelberg competition: 

p(X) = 

c 

1 − 1/ L [n − E(n − 1)] 

where L = −p(X)/p 0 (X)x L is the elasticity of demand perceived by the leader. 

We could also calculate the market share of the leader, which is larger than 50% 

whenever E


x L = x [n − E(n − 1)] (3.14) 

We can easily verify that in the case of a linear demand (E =0), the leader 

produces n times the output of the followers, a result we already encountered 

in Chapter 1. When the demand is concave the leader produces even more 

than that, while in case of a convex demand the leader produces less than 

that. Finally, notice that in the particular case in which E =1the first mover 

advantage disappears and the leader produces exactly the same as each one 

of the followers. This is not such an extreme result, as we will see in the 

following example. 

Consider the case of a hyperbolic demand p =1/X, which can be derived 

from the logarithmic utility (2.16). After some tedious calculations, the 

Stackelberg equilibrium can be solved for the production levels: 

x L = 2n − 3 

4c(n − 1) 

x = 2n − 3 

4c(n − 1) 2 

Accordingly, the equilibrium price and the gross profits for the leader and 

the followers are: 

p = 

2c(n − 1) 

2n − 3 

Π L = 

1 

4(n − 1) 

Π = 

1 

4(n − 1) 2 

First of all, notice that in the case where there are just two firms, the first 

mover advantage disappears: the choices of the two firms are strategically 

neutral in the Cournot duopolistic equilibrium (rather than complements or 

substitutes), and there is not an alternative commitment that can increase 

the profits of the leader. 14 When the number of firms increases, the output 

of the leader increases compared to the oneofthefollowers:indeed,wecan 

verify that x L =(n − 1)x, whichsatisfies our general rule (3.14) for any 

number of firms. It follows that, with the exception of the duopoly case, we 

are always in a region where SS holds. Finally, one can also verify that total 

production is the same as under Cournot competition when there are just 

two firms, but it is higher whenever the number of firmsislargerthantwo. 

Endogenous entry. Let us move to the case of endogenous entry in the 

model of quantity competition with a leadership. Consider again the general 

profit function (3.13). The equilibrium first order condition for the followers 

and the endogenous entry condition are: 

p (x, β)+xp 1 (x, β) =c 0 (x) 

xp (x, β) =c(x)+F 

14 This is in line with our previous general result, since under this demand function 

the elasticity of the inverse demand is E =2x/X, whichsatisfies our general 

rule (3.14) for n =2only when x L = x.


and they pin down the production of the followers x and their spillovers β 

independently from the production of the leader. Consequently, the profits of 

the leader can be rewritten as: 

π L = x L p (x L ,β L ) − c(x L ) − F 

= x L p [x L ,β+ h(x) − h(x L )] − c(x L ) − F 

whose maximization delivers the optimality condition: 

p(x L ,β L )+x L [p 1 (x L ,β L ) − p 2 (x L ,β L )h 0 (x L )] = c 0 (x L ) (3.15) 

This relation provides the equilibrium production of the leader if goods are 

poor substitutes or the marginal cost is increasing enough, conditions that 

guarantee the existence of an interior solution. It emerges quite clearly that 

the leader is going to produce more than any follower. 

In particular, when goods are homogenous and the inverse demand is simply 

p(X), the equilibrium condition for the leader boils down to an equation 

between the price and its marginal cost. In such a case, the equilibrium is 

fully charcterized by the following conditions: 

p(X) = 

c0 (x) 

1 − 1/ = c(x)+F 

x 

= c 0 (x L ) (3.16) 

where the first equality is a traditional mark up rule for the followers (with 

elasticity of demand), the second equality is the endogenous entry condition, 

andthethirdonedefines the pricing rule of the leader. Notice that while the 

followers produce below the optimal scale (defined by the equality between 

marginal and average cost), the leader produces above this scale and obtains 

positive profits thanks to the increasing marginal costs. 

In Chapter 1 we studied an example of this result in the case of linear 

demand (p = a − X) and linearly increasing marginal cost (equal to dx), 

where profits were given by (1.18). The equilibrium output of the leader and 

the followers were: 

x L = 1+d 

d 

r 

2F 

2+d 

x = 

r 

2F 

2+d 

This simple set up with homogenous goods allows us to compare welfare 

under alternative forms of competition, namely Marshallian competition and 

Stackelberg competition with endogenous entry. Since we know from Mankiw 

and Whinston (1986) that the Cournot case is characterized by too many 

firms producing too little, it is clear that Stackelberg competition does better 

on both dimensions. Hence, it is welfare improving to assign a leadership 

position to some firms despite this will give them a dominant position with 

associated extra-profits. This is a general result since our model implies that 

total production is always the same under Stackelberg and Cournot competition 

when there is endogenous entry, but a leader produces more than the


followers and consequently there are fewer firms in the Stackelberg case. The 

associated reduction in wasted fixed costs comes back in the form of profits 

for the leader. In conclusion, consumer surplus is the same, but welfare is 

higher under Stackelberg competition with endogenous entry: 

Proposition 3.4. Under endogenous entry and homogenous goods, 

as long as there is entry of some followers, Stackelberg competition 

in quantities is always Pareto superior with respect to Cournot 

competition. 

Another simple example of the aggressive behavior of the leader that we 

analyzed in Chapter 1 emerged in the model with product differentiation 

(demand p i = a − (1 − b)x i − bX) and constant marginal cost (c), where 

profits were given by (1.25), and the equilibrium output of the leader and the 

followers were: 

x L = 

2 − b √ √ 

F x = F 

2(1 − b) 

Again the leader produces more than the follower and sells at a price above 

its marginal cost. The consequence is that entry of followers is reduced. Since 

consumers value product differentiation in such a model the welfare consequences 

are more complex. Nevertheless, the reduction in the price of the 

leader more than compensates the reduction in the number of varieties and 

consumer surplus is strictly increased by the leadership. 15 Therefore, in this 

case the consumers strictly gain from the aggressive pricing strategy of the 

leader even if this induces some firms to exit and reduces the number of 

varieties provided in the market. 

Let us now move to the kind of equilibrium that can emerge when the 

interior solution characterized above does not maximize the profits of the 

leader. When goods are homogenous or highly substitute, or when the marginal 

cost is decreasing, constant or not too much increasing, the optimality 

for the leader implies a corner solution with entry deterrence and: 

15 Using the quadratic utility function (2.11) and the related demand function, in 

equilibrium we have: 

⎡ 

⎤ 

U = Y + 1 n 

⎣ x 2 i + b 

x i x j 

⎦ 

2 

i=1 i 

j6=i 

where Y is the exogenous income of the representative agent. One can verify 

that the gain in consumer surplus from the presence of a leader when entry is 

endogenous is: 

∆U = 

b(2 − b)F 

8(1 − b) > 0 

andthegaininwelfareis∆W = ∆U + π L . I am thankful to Nisvan Erkal and 

Daniel Piccinin for insightful discussions on this point.


xp [x, h(¯x L )] = c(x)+F ⇐⇒ ¯x L = β − x (3.17) 

We saw an example of this outcome in Chapter 1 within the basic model 

with homogeneous goods, linear demand (p = a − X) and constant marginal 

costs c, where profits were given by (1.2). In that case, the equilibrium output, 

produced entirely by the leader was: 

¯x L = a − c − 2 √ F 

Moreover,inthatcasewenoticedthat welfare was greater under Stackelberg 

competition with entry deterrence rather than Cournot competition 

with free entry because total production was reduced but the profits of the 

leader and the savings in fixed costs were enough to compensate the lower 

consumer surplus. 

Another simple case emerges with the hyperbolic demand (p = 1/X) 

and with constant marginal cost c. Now, the Stackelberg equilibrium with 

endogenous entry requires entry deterrence with production: 

³ 

1 − √ ´2 

F 

¯x L = 

c 

In the case of general demand functions for homogenous goods, we can actually 

find a simple sufficient condition for entry-deterrence which only depends 

on the shape of the cost function: 

Proposition 3.5. Under endogenous entry and homogenous goods, 

whenever marginal costs of production are constant or decreasing, 

Stackelberg competition in quantities always delivers entrydeterrence 

with only the leader in the market. 

This result can contribute to clarify the old debate on limit pricing. Entry 

deterrence through this forms of limit pricing is the equilibrium strategy for 

leaders facing endogenous entry for any demand function as long as goods 

are homogenous (or highly substitutable) and returns to scale are constant 

or decreasing. 16 As both our examples show, the entry deterrence production 

is decreasing in the fixed cost, since this cost helps the leader to exclude 

the rivals. When the fixed cost diminishes the equilibrium output of the 

leader increases, and when it approaches zero, the equilibrium approaches 

the competitive outcome with a price equal to the marginal cost (indeed 

both ¯x L = a − c in the case of linear demand and ¯x L =1/c inthecaseof 

hyperbolic demand correspond to a price p = c). Nevertheless, this efficient 

output level is still entirely produced by one single firm, the leader. 

16 This corresponds to the result of the contestable markets theory of Baumol et al. 

(1982). However, that theory generates a limit price which implies zero profits 

for the leader. For instance, with the hyperbolic demand the limit pricing would 

equate inverse demand and average cost (p =1/x = c + F/x), which implies 

x =(1− F )/c > ¯x L.


3.3.2 Competition in Prices 

The role of price leadership is often underestimated for two main reasons. 

The first is that commitments to prices are hardly credible when it is easy 

and relatively inexpensive to change prices. While this is true for long term 

commitments, it is also true that short term commitments can be credible 

in most markets. The macroeconomic literature on price stickiness has developed 

a number of arguments on why this may be the case, ranging from small 

menu costs of price adjustments to costs in the acquisition of information to 

reoptimize. The second reason for which a price leadership may poorly describe 

the behavior of market leaders is probably more pervasive and relies 

on the absence of a first mover advantage in simple models of competition 

in prices. For instance, in standard duopolies, a price leader obtains lower 

profits than its follower, and for this reason neither one nor the other firm 

would like to be a leader: there is actually a second mover advantage. As we 

will see, this result disappears and the first mover advantage is back when 

entry in the market is endogenous. 

In our general class of models with price competition the profit function 

is given by: 

π i =(p i − c) D (p i ,β i ) − F (3.18) 

where p i is of course the price of firm i, and the demand function is decreasing 

in both arguments, with β i = P j6=i 

g(p) for some positive and decreasing 

function g. Notice that the model is nested in our framework (3.1) after 

setting x i =1/p i as the strategic variable (see Section 2.4.2 for a discussion). 

Exogenous entry. Let us consider first the case of exogenous entry. Stackelberg 

equilibrium with n firms is characterized by the following equilibrium 

optimality conditions for the followers and the leader: 17 

D (p, β)+(p − c)D 1 (p, β) =0 

∙ 

µ ¸ dβL 

D (p L ,β L )+(p L − c) D 1 (p L ,β L )+D 2 (p L ,β L ) =0 (3.19) 

dp L 

where dβ L /dp L < 0 can be derived by the optimality condition of the followers 

as long as SC holds. While the equilibrium conditions soon become quite 

complex, the positive last term shows that the leader chooses a price above 

the one of the followers, inducing a general increase in prices compared to 

the Nash-Bertrand equilibrium between the same firms.Thechoiceofahigh 

price by the leader is aimed at softening price competition, but it also leads 

the followers to make more profits by choosing a lower price and stealing 

market shares from the leader. 

17 If fixed costs of production are high enough, the leader can engage in entry 

deterrence, but here we will focus on the case in which entry is accommodated.


Endogenous entry. Let us now look at the Stackelberg equilibrium with 

endogenous entry. The optimality condition for the followers and the endogenous 

entry condition are: 

D (p, β)+(p − c)D 1 (p, β) =0 

(p − c) D (p, β) =F 

and they pin down the price of the followers p and their spillovers β =(n − 

1)g(p), so that the profit of the leader becomes: 

π L =(p L − c)D [p L , (n − 1)g(p) − g(p L )] − F = 

=(p L − c)D [p L ,β+ g(p) − g(p L )] − F 

Profit maximization delivers the equilibrium condition: 

D(p L ,β L )+(p L − c)[D 1 (p L ,β L ) − D 2 (p L ,β L )g 0 (p L )] = 0 (3.20) 

which implies a lower price p L than the price of the followers, since the last 

term is negative. This is a crucial result by itself since we are quite familiar 

with associating price competition and accommodating leaders setting 

higher prices than the followers: this standard outcome collapses under endogenous 

entry. Moreover, the leader is now obtaining positive profits, while 

each follower does not gain any profits: the first mover advantage is back. 

In Chapter 1 we have seen an example based on the Logit demand (2.21), 

where the equilibrium prices were: 

p L = c + 1 λ 

p = c + 1 λ + F N 

Moreover, using the microfoundation pointed out by Anderson et al. (1992) 

in terms of the quasilinear utility (2.22), one can show that this equilibrium 

is Pareto efficient compared to the correspondent Marshall equilibrium: the 

reduction in the price of the leader reduces entry, leaves unchanged consumer 

surplus and increases firms’ profits, inducing an increase in total welfare. 

In the case of the isoelastic demand (2.24) derived in the last chapter from 

the utility function (2.23), we obtain the following prices: 

p L = c θ 

p = 

cY 

θ [Y − F (1 + α)] 

where of course the leader applies a lower mark up than each follower. 18 It 

can be verified that in any version of the Dixit-Stiglitz model where 1/(1−θ) 

18 As we already noticed, we could analyze competition in quantities within the 

same model - one can obtain the inverse demand from (2.23). Since there is 

product differentiation, also that case would entail a higher output for the leader, 

and consequently a lower price.


is the constant elasticity of substitution between goods and c is the marginal 

cost of production, as long as entry is endogenous, the leader will choose the 

price p L = c/θ and the followers will choose a higher price. Indeed, free entry 

pins down the price index that is perceived by the leader, whose optimization 

problem is of the following kind: 

max(p L − c)D L ∝ (p L − c)p − 1 

1−θ 

L 

which always delivers the price above. As a consequence, the leader produces 

more than each follower and the number of followers is reduced compared 

to the Marshall equilibrium. Once again, however, consumer surplus is not 

changed because the price index is unaffected. Since the leader obtains positive 

profits, overall welfare is increased. We summarize these results as follows: 

Proposition 3.6. In a model of price competition with Logit demand 

or Dixit-Stiglitz demand and endogenous entry, a leader sells 

its variety at a lower price than the entrants, inducing a Pareto improvement 

in the allocation of resources. 

In all of these models we can verify the existence of an unambiguous 

ranking of market structures from a welfare point of view. Indeed, from the 

best to the worst case for welfare we have: 1) endogenous entry with a leader; 

2) endogenous entry without a leader; 3) barriers to entry without a leader; 

4) barriers to entry with a leader. If we look at consumer surplus only, case 

1) and 2) deliver the same utility for the consumers, but the rest of the 

ranking is unchanged. This welfare results have important consequences for 

the evaluation of market leaders and for antitrust policy: we will return on 

them in Chapter 5. 

3.3.3 Competition for the Market 

In Chapter 1 we studied a simple model of competition for the market where 

firms were investing to obtain a reward V . Under the specification: 

π i = x i 

n 

Y 

j=1,j6=i 

(1 − x j ) V − x2 i 

2 

(3.21) 

with x i investment in R&D for firm i, we found that because of SS, a Stackelberg 

equilibrium was characterized by a leader investing more than each 

follower, while a Stackelberg equilibrium with endogenous entry was characterized 

by only the leader investing: 

√ 

2F 

¯x L =1− 

V 

These results are not general, since more realistic descriptions of the market 

for innovations can lead to different results. Nevertheless, as we will see in the 

next chapter, which focuses entirely on competition for the market, a leader 

always invests more than any other firm when entry is endogenous.

3.4 Asymmetries, Multiple Leaders and Multiple Strategies 109 

3.4 Asymmetries, Multiple Leaders and Multiple 

Strategies 

The results of the previous sections can be extended in many directions to be 

able to describe market structures in a more realistic way. This section will 

consider a few directions: introducing a technological asymmetry between 

the leader and the followers, extending the model to multiple leaders, endogenizing 

the same leadership status, allowing for multiple strategies and 

considering more general profit functions. Our main focus, at this point, will 

be on the case where entry is endogenous, which we believe to be more relevant 

in most markets. 

3.4.1 Asymmetries Between Leader and Followers 

In this section, following Etro (2002), we assume that the leader has the profit 

function: 

π L = Π L (x L ,β L ,K) − F 

where K is a new parameter specific totheleader(itmaywellbeavector 

of parameters). The basic assumptions are Π3 

L ≡ ∂Π L /∂K > 0 and 

Π L (x, β, 0) = Π i (x, β). Notice that, while this specification may look like the 

one analyzed in Chapter 2, here we are talking about an exogenous parameter 

K, not an endogenous one. We are interested in understanding how exogenous 

asymmetries affect the behavior of market leaders, and not how market 

leaders endogenously create asymmetries to affect their behavior (which was 

the purpose of the analysis of the previous chapter). 

A first mover advantage is often associated with some asymmetry between 

the leader and the followers. For instance, in the simple model of competition 

for the market of Chapter 1 we extended the basic model to consider leaders 

that were also incumbent monopolists with a flow of current profits affecting 

their expected profits. In other cases, it is natural to link the first mover 

advantage with some technological or market advantage, for instance a lower 

marginal cost c(K) for the leader (with c 0 (K) < 0), or other differences as 

those suggested in the previous chapter. 

In general, when entry is endogenous we obtain a strategy of the leader 

which depends on K, x L = x L (K), and hence the number of entrants, but 

not their individual strategy, also depends on K. One can show: 

Proposition 3.7. An asymmetric Stackelberg equilibrium with 

endogenous entry implies that the leader is aggressive whenever 

Π13 L ≥ Π23(Π L 1 L /Π2 L ) or K is small enough. 

The intuition is the following: an increase in the advantage of the leader 

(that is in K) induces a higher incentive to aggressiveness if it raises the


marginal benefit from it more than the change in its marginal cost. Indeed 

the sufficient condition could be rewritten as ∂(Π1 L /Π2 L )/∂K ≤ 0, thatis 

the marginal rate of substitution between x L and β L is decreasing in K. If 

this condition does not hold, it means that x 0 L (K) < 0, therefore for a great 

enough K (a strong enough asymmetry) the leader may be accommodating 

(x L (K) 

0 and Π23 L = 0, and under competition in prices we have Π13 L > 0 and 

Π23 L < 0. Similarly one can examine other kinds of exogenous asymmetries 

(as those we examined in the previous chapter on the demand side, in the 

financial structure, in complementary markets, and so on) and verify how the 

incentives of the leader to be aggressive are changed. 

3.4.2 Multiple Leaders 

Until now we considered a simple game with just one leader playing in the 

first stage. Here we will consider the case in which multiple leaders play 

simultaneously in the first stage. Hence the timing of the game becomes the 

following: 1) in the first stage, m leaders simultaneously choose their own 

strategies; 2) in the second stage, potential entrants decide whether to enter 

or not; 3) in the third stage each one of the n − m followers that entered 

chooses its own strategy. In the next section we will discuss how to endogenize 

m. 

When entry is endogenous we should consider two different situations: one 

in which entry of followers is not deterred in equilibrium and one in which the 

leaders deter entry. Consider first the case in which the number of leaders m is 

small enough, or the cost of deterrence is large enough that entry of followers 

takes place in equilibrium. In such a case, the behavior of the leaders can be 

characterized in a similar fashion to our basic analysis. Moreover, contrary 

to what happens when the number of firms n in the market is exogenous (in 

that case the number of leaders m affects their strategic interaction, their 

strategies and their profits), with endogenous entry the number of leaders 

does not affect their strategies, still given by (3.12), and their profits: 

Proposition 3.8. Under Stackelberg competition with m leaders, 

as long as there is endogenous entry of some followers, each leader 

is aggressive compared to each follower and its strategy and profits 

are independent from m. 

This confirms the spirit of our results with a single leader. Each one of 

the leaders now behaves in an aggressive way compared to the followers and 

also independently from the other leaders. For instance, under competition 

in quantities and increasing marginal cost, each leader produces the same


output that equates the marginal cost to the price, and the equilibrium price 

equates the optimal mark up of the followers to the fixed cost of production. 

While the profit of each leader is not affected by the number of leaders, 

thenumberofentrantsisclearlydecreasedbyanincreaseinthenumberof 

leaders. 

The situation is more complicated if there is entry deterrence in equilibrium. 

In the case of an exogenous number of firms, entry deterrence is a sort 

of public good for the leaders, which may introduce free-riding issues in their 

behavior. Gilbert and Vives (1986) have analyzed this issue in a model with 

m leaders facing a potential entrant, while Tesoriere (2006) has extended the 

model in Etro (2002) to analyze the case of m leaders facing endogenous entry. 

The result can easily be seen through a simple example with two leaders. 

Let us analyze a model of competition in quantities with a linear inverse 

demand p = a − X, constant marginal cost c, m =2and endogenous entry 

of followers. Remember that the entry deterring output in this model is ¯x = 

a − c − 2 √ F . Consider the best response of one leader, say L 1 .Iftheoutput 

of the other leader, say L 2 , is already above the entry deterrence level, x L2 > 

¯x, the best strategy is clearly x L1 =0. However, whenever the output of 

the second leader is below the entry deterring level, it is always optimal to 

produce at least enough to deter the entry of any follower, which implies 

x L1 ≥ ¯x − x L2 . Nevertheless, it may be optimal to produce more than this 

when the standard Cournot best response, namely x L1 =(a − c − x L2 ) /2, 

generates a higher output than the level that is sufficient to deter entry, which 

happens for x L2 >a− c − 4 √ F . An analogous rule drives the best response 

for the second leader. In summary, the best response function for a leader L i 

with i, j =1, 2 is: 

x Li (x Lj )= 

( 

h 

max 

) 

0 

i 

if x Lj ≥ ¯x 

if x Lj < ¯x 

a − c − 2 √ F − x Lj ; a−c−xLj 

2 

that can be rewritten as: 

⎧ 

⎨ 0 x Lj ≥ a − c − 2 √ ⎫ 

F 

x Li (x Lj )= (a − c − x 

⎩ 

Lj ) /2 if x Lj ∈ [a − c − 4 √ F ; a − c − 2 √ ⎬ 

F ) 

a − c − 2 √ F − x Lj 

x Lj


x Li = a − c − 2 √ F , x Lj =0 

Moreover, there are other possible equilibria with both the leaders active 

in the market. We need to distinguish two cases depending on the size of the 

fixed cost. When the fixed cost is high enough, the standard equilibrium of the 

Cournot duopoly is an equilibrium of Stackelberg competition in quantities 

with endogenous entry and two leaders, since it implies a high enough output 

so that further entry is deterred. Since in a symmetric Cournot duopoly each 

firm (each leader here) produces: 

x L1 = x L2 = a − c 

3 

this equilibrium requires that profits are positive for both firms, or F < 

(a − c) 2 /9, and that total output is enough to deter entry of any follower, 

2(a − c)/3 > ¯x or F>(a − c) 2 /36. Whenthefixed cost is lower than this last 

cut-off, however, the two best response functions overlap in an intermediate 

region where aggregate production is just enough to deter entry, and we have 

a continuum of equilibria with x L1 + x L2 = a − c − 2 √ F and such that both 

firms produce enough to obtain positive profits. This requires: 

x L1 = a − c − 2 √ h 

F − x L2 and x L2 ∈ a − c − 4 √ F ;2 √ i 

F 

In summary, Stackelberg equilibria in quantities with two leaders and 

endogenous entry in the case of linear demand and marginal cost are always 

characterized by entry deterrence with the following possible configurations 

of production by the leaders: 

⎧ 

⎪⎨ 

x Li = a − c − 2 √ F , x Lj =0 for any F< 4(a−c)2 

x L1 =(a − c) /3 and x L2 =(a − c) /3 if F ∈ 

⎪⎩ any x Li = a − c − 2 √ h 

F − x Lj ∈ a − c − 4 √ F ;2 √ i 

F 

h 25 

(a−c) 

2 

36 

; (a−c)2 

9 

i 

if F< (a−c)2 

36 

Tesoriere (2006) generalizes this example to m leaders, showing that endogenous 

entry of followers is always deterred, 20 and there is always an equilibrium 

with just one leader producing the entry deterrence output and the 

remaining leaders producing zero. Furthermore, the symmetric Cournot equilibrium 

between all the m leaders can be an equilibrium when total Cournot 

output of the m leaders exceeds the entry deterrent output, and there can 

be a continuum of equilibria with aggregate production equal to the entry 

deterrent level when the fixed cost of production is low enough. Hence, underinvestment 

in entry deterrence cannot occur when entry is endogenous, 

while overinvestment in entry deterrence can occur (but leaders always obtain 

strictly positive profits). Once again, this outcome remains in the spirit 

of our results about the aggressive behavior of market leaders. 

20 As we have seen from the case of a single leader, under constant marginal costs, 

entry deterrence occurs for any demand function. 

⎫ 

⎪⎬ 

⎪⎭


3.4.3 Endogenous Leadership 

After developing a Stackelberg model with multiple leaders and endogenous 

entry of followers, it is natural to verify what happens when there is endogenous 

entry of leaders as well. 

The simplest way to endogenize the number of leaders is by adding an 

initial stage of the game where firms decide simultaneously whether or not to 

become a leader. 21 Any firm can make an investment, say I, whichprovides 

the status of a leader in the market, while any firm that does not invest 

can only enter in the market as a follower: in other words, commitment to 

strategies is costly. As Prop. 3.8 suggests, as long as there is entry of followers, 

it must be that all leaders obtain the same level of positive profits (which 

is independent from the number of leaders m). Therefore, if the investment 

needed to become a leader is small enough, there must always be incentives 

to invest to become leaders when this does not deter entry of followers. Then, 

consider the largest number of leaders compatible with some entry, say M. 

Given this number of leaders, another firm may invest in leadership and 

subsequently engage in Nash competition with only the other leaders (entry 

of followers is now deterred by construction). If such an entry is profitable, 

the equilibrium must imply only leaders in the market and an endogenous 

number m ∗ >M derived from a free entry condition with a fixed cost F + I 

(clearly this happens whenever the cost of leadership is zero or small enough). 

If this is not the case, the only equilibrium implies m ∗ = M firms investing in 

leadership and a residual competitive fringe of followers: once again, as Prop. 

3.8 still implies, all leaders would be aggressive compared to each follower. 

Another interesting situation emerges when entry is sequential, leading 

to a hierarchical leadership. While a general treatment of sequential games 

is complex, Vives (1988) and Anderson and Engers (1994) have fully characterized 

sequential competition in quantities with linear costs and isoelastic 

demand, and with an exogenous number of firms. 22 Their analysis makes clear 

that in the case of endogenous entry the only possible equilibrium would imply 

entry deterrence. 23 

21 See Hamilton and Slutsky (1990). 

22 See Prescott and Visscher (1977) for an early discussion. Economides (1993) studies 

free entry in a game with simultaneous entry at the first stage and sequential 

quantity decisions between the entrants. 

23 Tesoriere (2006) studies the following extension of Etro (2002): at a first preplay 

stage firms simultaneously decide whether or not to enter the market and 

at which period t ∈ T , then at each stage t =1, 2, ..., T ,eachfirm that has 

chosen to enter at stage t decides how much to produce, knowing the production 

chosen by all the firms that entered in the previous periods, taking as given that 

of the other firms that enter at the same time t, and anticipating correctly the 

strategies of the later movers. Focusing on the case of constant marginal costs, he 

shows that at any Subgame Perfect Nash Equilibrium, endogenous entry occurs


3.4.4 Multiple Strategies 

In this section we will show that a weaker version of the result on aggressive 

leaders generalizes when firms choose multiple strategic variables. 

Imagine that each firm chooses a vector of K ≥ 1 strategic variables 

x i =[x i1 ,x i2 , ..., x iK ] ∈ < K + , and its well behaved profit function can be 

written as: 

⎡ 

⎤ 

π i = Π ⎣x i ; X h(x j ) ⎦ − F (3.22) 

j6=i 

with h : < K + → < + differentiable and increasing in all its arguments. Examples 

are models in which the leader sells more than one good, models with 

multimarket competition or competition in quality and price, models with 

multiple inputs in the production function, patent races with multiple investments 

and so on. Clearly these are very important cases in real world 

industries. Results on the behavior of leaders in similar markets with an exogenous 

number of firms are complicated and ambiguous since they depend 

on all the possible cross derivatives and therefore on many specific properties 

of the markets (see Bulow et al., 1985). Nevertheless, under endogenous 

entry, a weaker version of our result still holds. 

Define firm i “on average” more aggressive than firm j if h(x i ) >h(x j ). 

Then, in equilibrium we have a vector x for the followers which is independent 

from the leader’s strategies, and the following equilibrium conditions for the 

strategies of the leader: 

∂Π L (x L ,β L ) 

∂x Lk 

= 

µ ∂h(x) 

∂x Lk 

∂Π L (x,β L ) 

∂β L 

≤ 0 for all k (3.23) 

These conditions do not imply that the leader is more aggressive in all the 

strategies, but that it must be more aggressive in some strategies. Moreover, 

they allow us to derive: 

immediately and simultaneously, and that any of the following configurations is 

an equilibrium: 

1) one of the firms enters in t =1and produces the entry deterring output; 

2) m firms enter in t =1and produce the entry deterring output in aggregate, 

when the Cournot equilibrium with m firms would imply a lower aggregate 

output than the entry deterring output; 

3) m firms enter in t = 1 and produce as in a Cournot equilibrium with 

m firms, when this implies an aggregate output which is larger than the entry 

deterring output. 

No other configuration is sustainable as equilibrium, but the above characterization 

of equilibria already exhibits multiplicity. At any of the possible equilibria, 

however, only market leaders produce: when the leadership is endogenous, 

sequential production is never observed.


Proposition 3.9. A Stackelberg equilibrium with endogenous entry 

and multiple strategic variables always implies that the leader 

is on average more aggressive than each follower. 

To see how to use this result we develop two examples. 

Capital/labour choices. Let us extend the simplest model of competition 

in quantities with a production function using two inputs, say capital k i 

and labour l i according to a Cobb-Douglas specification x i = ki αlη i with 

0


leader will be more aggressive than the followers on average, which means 

that h(θ L ,q L ) >h(θ, q). But this implies g(1/θ L ) >g(1/θ) or, using the fact 

that g is a decreasing function, that θ L >θ. We can then conclude that in a 

Stackelberg equilibrium in price and quality with endogenous entry the leader 

supplies a good with a better quality-price ratio than each other follower. 24 

3.4.5 General Profit Functions 

In this chapter we examined the behavior of firms with a first mover advantage 

over their competitors in the choice of the market strategy. A general result 

that emerges in the presence of endogenous entry is that leaders tend to 

behave in an aggressive way, in particular they choose lower prices and higher 

output than their followers. While we noticed that the spirit of this result is 

robust to a number of extensions, at least under some regularity conditions, 

we are aware that we had to impose a considerable amount of symmetry in 

the general model adopted in this book to obtain the simple results described 

until now. 25 For instance, our simple results do not apply to models where 

profits depend on the number of firms in a more complex way 26 or when 

conjectural variations of the firms are not restricted to the Nash case. 

Nevertheless, as shown in Etro (2008), also in a more general framework 

there is still a tendency of the market leaders to be aggressive toward a fringe 

of competitors that endogenously enter in the market. In particular, generalizing 

our analysis to the case of demand functions exhibiting strong forms of 

loveforvariety,wehaveverified that the tendency toward an aggressive pricing 

of the leaders facing endogenous entry remains, but the behavior of the 

followersisnowaffected. For instance, consider the classic case of imperfect 

substitutability with linear demands p i = a − x i + b P j6=i x j, that we studied 

many times in this book and that can be derived from a quadratic utility 

function as (2.11). Inverting the system, we obtain the direct demands: 

b 

1−b 

D i = a − p i + 

1+b(n − 1) 

P 

j6=i (p j − p i ) 

(3.24) 

24 Similarly, in a generalized version of the Logit model (1.34) with demand for good 

i equal to D i = Ne u n 

 

i 

/ 

j=1 eu j 

,whereu i = q i − λp i parameterizes utility 

from purchasing good i, a leader facing endogenous entry would choose quality 

and price so as to provide higher utility to the consumers than the followers. 

Analogous results emerge if quality does not affect marginal costs but it affects 

fixed costs. On quality choices in the Logit model see also Anderson et al. (1992, 

Ch. 7). 

25 For a critique to the generality of our characterization of Stackelberg equilibria 

with endogenous entry, and to the implications that can be drawn from it, see 

Encaoua (2006). 

26 As with the demand function of Shubik (1980), which, however, does not generate 

love for variety (see Erkal and Piccinin, 2007a).


It can be verified that the profit function associated with this case is not 

nested in our general framework. Nevertheless, it is well behaved and it is 

decreasing in the number of firms for given strategies. Since prices are strategic 

complements, the Stackelberg equilibrium with an exogenous number of 

firms is characterized by a higher price for the leader compared to the followers. 

Contrary to this, the Stackelberg equilibrium with endogenous entry is 

characterized by a lower price for the leader compared to the followers. Moreover, 

the price of the leader is below the equilibrium price in the Marshall 

equilibrium, while the price of the followers is above it and the number of 

products is reduced. 27 In the long run, prices turn into strategic substitutes: 

the reduction in the price of the leader induces the followers to increase their 

prices. 28 

Finally, we hope that these simple models of market leadership could be 

useful for normative purposes. Understanding the way markets work under 

different entry conditions is important not only to derive policy implications 

for competition policy, a topic on which we will turn in Section 3.5 and in 

Chapter 5, but also to understand how government policy should deal with a 

number of issues concerning foreign markets and domestic ones, a hot topic 

in the days of intense globalization, on which we will focus in Sections 3.6 

and 3.7. 

27 Assume zero marginal costs. The optimality condition of the followers and the 

endogenous entry condition imply the following equilibrium relation between the 

price of the followers p and the number of firms n: 

 

F (1 − b)[1 + b(n − 1)] 

p = 

[1 + b(n − 2) 

A reduction in the price of the leader p L reduces entry and, according to this 

relation, it increases the price of the followers. The profit oftheleaderis: 

 

 

p L 

b(n − 1) 

π L = 

a − p L + 

1+b(n − 1) 

1 − b (p − pL) − F 

where both n and p depend on p L .Since∂π L /∂nb pL =p< 0, itisoptimalfor 

the leader to reduce the number of firms compared to the Marshall equilibrium. 

This implies a lower price of the leader and a higher price of the followers in 

the Stackelberg equilibrium with endogenous entry compared to the price of the 

Marshall equilibrium. 

28 These result derive from joint work with Nisvan Erkal and Daniel Piccinin. Notice 

that with a Shubik demand a leader facing endogenous entry would reduce its 

price and the followers would reduce their prices as well (prices are strategic 

complements in both the short and long run). As a consequence the number of 

varieties provided in the market would decrease. Nevertheless, consumer surplus 

would strictly increase because of the generalized reduction in prices.


3.5 Antitrust and Collusion 

Our analysis of the behavior of a market leader and of multiple market leaders 

in this and in the previous chapter has been useful to introduce our discussions 

of antitrust issues concerning abuse of dominance. Nevertheless, the same 

principles can be exploited to investigate other antitrust issues as well. In 

this section we will focus on price fixing cartels. 

One of the main objectives of antitrust policy is the elimination of forms of 

collusion between firms aimed at increasing prices. As we have seen in Chapter 

1, a collusive cartel for the choice of prices or quantities between an exogenous 

number of firms ends up increasing prices and harming consumers. When a 

restricted number of firms collude, they can still implement accommodating 

strategies and increase their equilibrium prices and profits (especially if they 

act as leaders). The reaction of the other firms to their collusive strategies can 

be either aggressive under SS or accommodating under SC, but the outcome 

is qualitatively similar to the previous one: when it takes place, collusion in 

a market with an exogenous number of firms tends to harm consumers. This 

book does not have much to add to this important principle. In this section 

we will examine a different, but related, issue: the impact of collusion between 

arestrictednumberoffirms in a market where entry is endogenous. In such 

a case, collusion has unusual effects. 

More formally, let us consider a collusive cartel between m firms, where 

their strategies x k for k =1, 2, ..., m, are chosen to maximize the joint profits: 

mX 

π Cartel = Π(x k ,β k ) − mF (3.25) 

k=1 

while the other firms i = m +1, ..., n, maximize their simple profits π i = 

Π(x i ,β i ) − F and enter until these net profits are zero. 

In a hypothetical Nash equilibrium between the cartel and the outsider 

firms, each member of the cartel would implement an accommodating strategy 

according to the joint optimality conditions: 

Π 1 (x k ,β k )+ 

mX 

q=1,q6=k 

Π 2 (x q ,β q )h 0 (x k )=0 for k =1, 2, ..., m (3.26) 

while the outsiders would stick to the usual optimality conditions Π 1 (x i ,β i )= 

0. Notice that the accommodating strategies of the members of the cartel 

would attract entry until the cartel becomes a lossmaker: in Marshall equilibrium, 

a simple commitment to collusion is not profitable when entry is 

endogenous (this is another application of our results in Chapter 2, since the 

collusive commitment makes the members of the cartel more accommodating). 

However, a commitment to join in a cartel can be profitable when the 

members of the cartel act as leaders in the competition with the other firms.

3.5 Antitrust and Collusion 119 

More formally, consider a game in which the cartel plays first, then the followers 

enter, and finally the followers play simultaneously. In this case, the 

optimality condition of the followers and their zero profit condition pin down 

their strategy x and their spillovers β independently from the strategies of 

the cartel. 29 Therefore, taking into account that the expected spillover of a 

member of the cartel is β k = P j6=k h(x j)=β + h(x) − h(x k ),theoptimal 

strategies of the cartel solve the problem: 

max 

x 1,...,x m 

π Cartel = 

mX 

Π [x k ,β+ h(x) − h(x k )] − mF (3.27) 

k=1 

The corresponding optimality conditions are: 

Π 1 (x k ,β k )=Π 2 (x k ,β k )h 0 (x k ) for k =1, 2, ..., m (3.28) 

But these conditions exactly correspond to the condition defining the equilibrium 

strategy of a leader (or more leaders) in the Stackelberg equilibrium with 

endogenous entry, namely (3.12). On this basis, we can apply all the results 

derived in the rest of this chapter. In the case of competition in quantities, a 

collusive cartel in a market where entry is endogenous would coordinate an 

increase in the output of its members so as to increase their market shares 

and improve the allocation of resources. In the case of competition in prices, 

the cartel would coordinate a reduction of the prices of its members to increase 

their market shares, and this would lead to an improvement in the 

allocation of resources. 30 We can summarize our result as follows: 

Proposition 3.10. In a market with endogenous entry, a collusive 

cartel is not effective unless it acts as a leader: in such a case, as 

long as there is endogenous entry of some followers, each member 

of the cartel is aggressive compared to each follower. 

Paradoxically, collusion by cartels acting as leaders in markets where entry 

is endogenous turns out to be profitable, sustainable 31 and also procompetitive. 

This result should not be overemphasized from a policy point of 

view. It suggests that harmful collusion between a restricted number of firms 

of a market cannot occur when there is endogenous entry of other firms in the 

market - as already pointed out within the Chicago view (Bork, 1993, Posner, 

2001). However, most of the time, collusive cartels involve all the firms of an 

oligopolistic market and are harmful to consumers: their avoidance should be 

the main focus of antitrust authorities. 

29 We focus on the case in which the number of members of the cartel is small and 

entry takes place in equilibrium. If this is not the case, the cartel deters entry. 

30 Under competition for the market an R&D cartel acting as a leader under endogenous 

entry would enhance investments in R&D for its members. 

31 Since the cartel with m members implements the same strategies as in the Stackelberg 

equilibrium with m leaders and endogenous entry, collusion is always sustainable.


3.6 State-Aids and Strategic Export Promotion 

Globalization leads to the intensification of competition on international markets 

and requires a deeper understanding of the effects of industrial policy 

at large in the international environment. In this section we will present a 

digression on the optimal state aid policy for exporting firms with particular 

reference to subsidies for exports, a topic on which there are contrasting 

views at both the policy and theoretical level. 

In the EU there are strong limitations to state aids distorting competition 

and affecting trade among member countries. Nevertheless, the EU 

heavily subsidizes exports of agricultural products and the aircraft industry 

(Airbus), France has a long tradition in supporting its “national champions” 

with public funding, Italy in supporting the Made in Italy. TheUShaveimplemented 

strong forms of export subsidization through tax exemptions for 

a fraction of export profits, foreign tax credits, export credit subsidies and 

even an exemption from antitrust law for export cartels (the Webb-Pomerene 

Act exempts export associations from antitrust investigations as long as their 

actions do not restrain trade in the US and do not restrain the export trade 

of other domestic competitors). Nevertheless, at least in theory, the WTO 

forbids direct forms of export subsidization for industrial production. 

In front of such a complex and contradictory scenario, it is important to 

understand whether state aids to exporting firms and export subsidies are 

beneficial (as unilateral policies) and what are their consequences for international 

markets. Economic theory is largely ambiguous on this point. In 

the neoclassical trade theory with perfect competition, for instance, export 

subsidies are not optimal because they deteriorate the terms of trade; more 

precisely, since export taxes are equivalent to import tariffs, their optimal 

value can be derived as 1/, where is the elasticity of demand (see Helpman 

and Krugman, 1989). In case of imperfect competition, export promotion assumes 

a strategic dimension, so its main aim becomes shifting profits toward 

the domestic firms. A large body of literature has studied oligopolistic models 

with a fixed number of firms competing in a third market. In this case, 

the optimal unilateral policy is an export tax under price competition (or 

whenever SC holds; see Eaton and Grossman, 1986). Under quantity competition, 

an export subsidy can be optimal (Spencer and Brander, 1983), but 

only under restrictive conditions. The ambiguity of these results represents a 

major problem to derive policy implications. 32 

When entry in the international market is free, however, the theory of 

market leaders suggests that only a commitment able to turn the strategy of 

the domestic firm into a more aggressive one is going to increase its profits. 

More precisely we can apply Prop. 2.3 and conclude that it is (unilaterally) 

optimal to implement any form of strategic export promotion that increases 

32 See Maggi (1996) for an important contribution which endogenizes the mode of 

competition in the strategic trade literature.

3.6 State-Aids and Strategic Export Promotion 121 

the marginal profitability of the domestic firms: this may include direct or 

indirect state aids for exporting firms, policies that boost demand or decrease 

transport costs, export subsidies, R&D subsidies for exporting firms or related 

strengthening of their IPRs (Etro, 2007,a). Here we will focus our attention 

on the optimal export subsidies following Etro (2006,f). 

To fix ideas with an example, imagine Harley & Davidson, Ducati and 

Honda selling their motorbikes in a third unrelated market, say Australia. 

Consider the optimal unilateral policy of the US government toward H&D. 

According to the traditional view, the US government should tax exports 

of H&D. This would force H&D to increase its prices in Australia, which 

would lead Honda to increase its prices as well, and would generate higher 

American net profits from sales of H&D bikes in Australia, together with 

a tax revenue to be distributed between American citizens. The fallacy of 

this argument relies on neglecting that other international companies, say 

Yamaha, Suzuki, Kawasaki, BMW or Aprilia, would be ready to enter in the 

Australian market for motorbikes whenever prices are high enough to promise 

positive profits. And when this is the case an export tax can only penalize 

H&D. When entry in the Australian motorbike market is endogenous, as we 

actually could expect, the optimal US trade policy is to subsidize Harley’s 

exports. Always. 

More formally, adopting the usual notation, it is immediate to verify that a 

(specific) export subsidy s increases the marginal profitability of the domestic 

firm, say firm H. For instance, under competition in quantities we have: 

Π(x H ,β H ,s)=[p(x H ,β H )+s] x H − c(x H ) (3.29) 

and Π 13 =1, while under competition in prices we have: 

Π(x H ,β H ,s)=(p H + s − c) D (p H ,β H ) with x H =1/p H (3.30) 

and Π 13 = −D 1 p 2 H > 0. Now, the optimal unilateral policy does not maximize 

the total profits of the domestic firm, but these profits net of the subsidy 

(notice that prices affect only foreign consumers). Therefore, the optimal 

policy must simply maximize the strategic impact on the domestic profits: it 

follows that, as long as entry in the international market is free, an export 

subsidy is always optimal. 

We can say something more than this: the optimal policy must implement 

nothing else than the Stackelberg equilibrium with endogenous entry in which 

the domestic firm is the leader, exactly the kind of equilibrium we have characterized 

in this chapter. Why this equilibrium? Simply because it is the best 

equilibrium that the domestic firm can aim for. It is now relatively simple 

to derive the subsidies that implement this equilibrium. For instance, with 

homogenous goods, increasing marginal costs and competition in quantities, 

the general expression for the optimal specific subsidy is (Etro, 2006,f): 33 

33 One can verify that the first order condition for the domestic subsidized firm:


s ∗ = p H 

> 0 (3.31) 

 

where p H is the equilibrium price of the domestic firm and = − (p H /x H ) 

(dx H /dp H ) the corresponding elasticity of demand. It is important to notice 

that this optimal subsidy rate is exactly the opposite of the optimal export 

tax rate in the neoclassical theory of trade policy. 

We can also derive the optimal specific subsidy under price competition. 

In our framework this is given by (Etro, 2006,f): 34 

s ∗ = (p H − c)D 2 (p H ,β H ) g 0 (p H ) 

> 0 (3.32) 

[−D 1 (p H ,β H )] 

It is important to notice that the traditional optimal policy in the same model 

with exogenous entry would have required, according to the result of Eaton 

and Grossman (1986), a negative subsidy, that is an export tax. 

At this point, the intuition for the general optimality of export promoting 

policies should be straightforward. While firms are playing some kind of Nash 

competition in the foreign market, a government can give a strategic advantage 

to its domestic firm with an appropriate trade policy. When entry is 

free, an incentive to be accommodating is always counterproductive, because 

it just promotes entry by other foreign firms and shifts profits away from the 

domestic firm. It is instead optimal to provide an incentive to be aggressive, 

to expand production or (equivalently) reduce the price, since this behavior 

limits entry increasing the market share of the domestic firm. This is only 

possible by subsidizing exports. 35 Of course, we need to remind the reader 

that we are here referring to the optimal unilateral policy: as well known, 

s + p(X)+x H p 0 (X) =c 0 (x H ) 

satisfies the equilibrium condition (3.16) when the subsidy is the one in the 

text. As it should be clear after the discussion in this chapter, in the case of 

constant or decreasing marginal costs, the optimal subsidy must implement an 

entry deterrence equilibrium. 

34 Again, one can verify that the first order condition for the domestic firm: 

(p H − c + s)D 1 (p H ,β H )+D(p H ,β H )=0 

corresponds to the pricing rule of a Stackelberg leader facing endogenous entry 

(3.20) when the subsidy is the one in the text. 

35 For related investigations on strategic trade policy see Kováč andŽigić (2006) 

and Boone et al. (2006). The first work analyzes strategic trade policy in markets 

where leaders choose the quality of their products before the followers. The 

second work shows that when domestic firmsareleadersinthedomesticmarket 

and invest in cost reducing innovations, but the protection of intellectual property 

rights on these innovation is limited abroad, positive tariffs can enhance 

consumer welfare (see also Žigić, 1998, 2000). The reason is that tariffs induce 

market leaders to be aggressive toward foreign imitators, whose entry is limited.

3.7 Privatizations 123 

if all countries were going to implement their optimal unilateral policies, an 

inefficient equilibrium would emerge. This may explain why international coordination 

tends to limit export subsidies. 

If we interpret globalization as the opening up of new markets to international 

competition we can restate the main result as follows: in a globalized 

word, there are strong strategic incentives to conquer market shares abroad 

by promoting exports. 

3.7 Privatizations 

A final application to privatizations deserves some comments. Recent decades 

have witnessed a huge sequence of privatizations, especially in Western European 

countries and in former communist countries. In many cases, public 

enterprises active in traditional markets were the subject of privatizations 

and an intense debate emerged on the conditions under which private or 

public property was better (see Boycko et al., 1997). In this section, following 

an important early contribution by Anderson et al. (1997) we provide an 

alternative way to approach this debate. 

Broadly speaking, a public firm is characterized by a different objective 

function, which we can (generously) identify with the welfare function, and 

by likely inefficiencies associated with the lack of an optimal allocation of 

incentives within public institutions. If this is the case, we can evaluate the 

behavior of the same firm when public and when privatized. A crucial issue 

in this case, is whether a process of liberalization, meaning of opening to 

endogenous entry of other private firms, occurs as well. 

As a benchmark case, consider the production of a homogenous good. A 

single public firm would maximize welfare by pricing at the marginal cost. If 

the same public firm faces a process of liberalization with entry of profit maximizing 

firms, it is immediate that the Marshall equilibrium will correspond 

exactly to the one under Stackelberg competition with endogenous entry. In 

such a case, the public firm would still price at marginal cost, 36 and the private 

firms will apply a markup to cover their fixed costs of production: the 

profits of the public firm would be positive only if its cost inefficiency is limited 

relative to the private firms. Consider privatization now. If the privatized 

firm is symmetric with respect to the other firms, it will end up obtaining 

zero profits as the others. If the privatized firm gains the role of the leader, 

it can keep pricing at its marginal cost while obtaining positive profits: the 

privatization does not affect the equilibrium price, but it increases profits 

for the privatized company. Overall, the privatization enhances welfare when 

36 The objective function of the public firm corresponds to π Publ = X 

 

p(j)dj − 

0 

i6=P c(x i) − c Publ (x P ) − nF where X is total production and the cost function 

of the public firm c Publ (·) can be different from that of the private firms because 

of some inefficiencies. Maximization of this function leads to p(X) =c 0 Publ(x P ).


the former public enterprise becomes the leader of a market with endogenous 

entry. 

Two remarks are in order. First, if products are differentiated or firms 

compete in prices (see Anderson et al., 1997) the gains from privatization 

may be larger because product variety flourishes. Second, if the privatization 

is not associated with a process of liberalization, it may lead to ambiguous 

results: for instance a privatized firm may increase its prices and induce other 

private firms to do the same. This cannot happen when entry is endogenous: 

liberalization is crucial to gain from privatizations. 


In this chapter we analyzed different forms of competition in the market 

where leaders can exploit a strategic advantage to increase their profits. We 

noticed that their behavior depends on the entry conditions in a crucial way. 

The difference is quite evident under competition in prices. In markets where 

entry is limited exogenously leaders tend to behave in an accommodating 

way choosing high prices, which leads the followers to chose high prices as 

well. All firms obtain large profits but a second mover advantage emerges: the 

followers obtain larger profits than the leader. When entry is endogenous (and 

determined by the opportunities to make profits in the market), new firms 

are attracted into the market from a similar accommodating strategy of both 

the leader and the followers. Since entry occurs until the net profits of the 

followers are driven to zero, the accommodating leader ends up with negative 

profits because of the second mover advantage (its profits must be lower than 

the profits of the followers, which in turn have been entirely dissipated by free 

entry). This implies that a leader can only gain from an aggressive pricing 

strategy: in equilibrium, the price of the leader is lower than the price of the 

followers and the first mover advantage is restored. 

With this chapter we have concluded our excursus on the different modes 

of competition in the market (in the choice of output or price variables). All 

sectors have such a component of competition. Nevertheless, in some sectors 

such a conponent plays a minor role in the interaction between firms and 

in the entry process: these are sectors in which competition is mainly for 

the market and entry of new products or new firms derives from successful 

innovations. These sectors are the subject of the next chapter.


3.9 Appendix 

ProofofProp3.2: The system (3.7)-(3.8) defines the impact on x and n 

to changes in x L . Totally differentiating the system we have: 

⎡ 

⎣ dx ⎤ ⎡ 

⎤ ⎡ 

⎦ = − 1 Π 2 h(x) 

−Π 12 h(x) 

⎣ 

⎦ ⎣ Π ⎤ 

12h 0 (x L )dx L 

⎦ 

∆ 

dn −(n − 2)Π 2 h 0 (x) Π 11 +(n − 2)Π 12 h 0 (x) Π 2 h 0 (x L )dx L 

where ∆ = Π 11 Π 2 h(x) and Π 11 +(n − 2)Π 12 h 0 (x)+Π 2 h(x) < 0 (under the 

contraction condition in case of SC), which implies stability. It follows that: 

dx 

dx L 

=0 

dn 

= −h0 (s) 

< 0 

dx L h(x) 

dβ 

dx L 

=0 

dβ L 

dx L 

= −h 0 (x L ) < 0 

which shows that the strategy of the followers is independent from the one 

of the leader. Since this holds also for x L = x, which replicates the Marshall 

equilibrium, in a Stackelberg equilbrium with endogenous entry any active 

follower adopts the same strategy as in the Marshall equilibrium. 

At the entry stage, entry of at least one follower takes place for any 

x L < ¯x L ,where¯x L is such that: 

Π [x(h(¯x L )),h(¯x L )] = F 

and the profit of the leader is: 

π L = ΠL [x L , (n − 1)h(x)] − Fifx L < ¯x L 

Π L (x L , 0) − F if x L > ¯x L 

hence, the optimal strategy is x ∗ L that satisfies the first order condition: 

Π L 1 [x ∗ L, (n − 1)h(x)] = Π L 2 [x ∗ L, (n − 1)h(x)] h 0 (x ∗ L) 

if it is smaller than ¯x L andsuchthat: 

Π L {x ∗ L, (n − 1) h(x)} >Π L (¯x L , 0) 

Otherwise the global optimum is the corner solution ¯x L . We will show that in 

equilibrium x L >xalways. In case of corner solution, this is trivial. Consider 

the case of an interior solution x ∗ L as defined above. Assume that x∗ L ≤ x;then 

it must be that β =(n − 2)h(x)+h(x ∗ L ) ≤ (n − 1)h(x) =β L, which implies 

Π(x ∗ L ,β L) ≤ Π(x ∗ L ,β) from the assumption Π 2 < 0. But the optimality of 

x and the free entry condition imply Π(x ∗ L ,β)


Proof of Proposition 3.3. Theeffect of a change in the fixed cost on 

the strategy and the number of firms are: 

dx 

dF = [−Π 12] 

[Π 11 Π 2 ] 

∙ 

dn 

dF = Π11 +(n − 2)Π 12 h 0 ¸ 

(x) 

+ ∂n ∂x L 

Π 11 Π 2 h(x) ∂x L ∂F 

The first derivative has the opposite sign of Π 12 . The second has a first negative 

term (under the contraction condition when Π 12 > 0) and a second ambiguous 

term. It follows that d[β + h(x)]/dF =[Π 11 − h 0 (x)Π 12 ]/Π 11 Π 2 h(x). 

Totally differentiating (3.12) we have: 

£ ¤ 

∂x L Π 

L 

∂F = − 12 − h 0 (x L )Π22 

L [Π11 − Π 12 h 0 (x)] 

D L Π 11 Π 2 h(x) 

where D L < 0 from the assumption that the second order condition is satisfied. 

It follows that: 

∙ 

dn 

dF ∝ Π 11 +(n − 2)Π 12 h 0 (x)+ h0 (x L ) 

h(x)D L [Π 11 − Π 12 h 0 (x)] £ ¤¸ 

Π12 L − h 0 (x L )Π22 

L 

The Proposition follows immediately after noticing from (3.12) that h 0 (x L )= 

Π L 1 /Π L 2 . Q.E.D. 

ProofofProp3.4: In a Marshall equilibrium, the number of firms is 

n m and each one produces x m ,withwelfare: 

W m = 

Z 

n m x m 

0 

p(j)dj − n m [c(x m )+F ]= 

Z 

n m x m 

0 

p(j)dj − p(n m x m )n m x m 

where we used the zero profit condition p(n m x m )x m = c(x m )+F . Under 

Stackelberg competition when there is endogenous entry by some followers, 

the strategy of each follower remains x m byProp.3.2,whilethenumberof 

firms n s satisfies the zero profit condition: 

p [x L +(n s − 1)x m ] x m = c(x m )+F 

which implies the same total production in the two cases x L +(n s − 1)x m = 

n m x m . Hence the welfare will be: 

W s = 

= 

Z 

x L+(n s −1)x m 

Z 

0 

n m x m 

0 

p(j)dj − (n m − 1)c(x m ) − c(x L ) − n s F = 

p(j)dj − p(n m x m )n m x m +[x L +(n s − 1)x m ] p(n m x m ) 

−(n s − 1)c(x m ) − c(x L ) − n s F 

= W m + x L p [x L +(n s − 1)x m ] − c(x L ) − F = W m + π L >W m


which proves the claim. Q.E.D. 

ProofofProp3.5: Adopt a generic cost function c(x) with c 00 (x) ≤ 0. 

Imagine an equilibrium without entry deterrence. The zero profit condition, 

stated in the proof of Prop. 3.4, sets total production and hence the inverse 

demand at the level: 

p[x m (n s − 1) + x L ]= F + c(xm ) 

x m 

where x m is always the equilibrium production of the followers, which corresponds 

to the equilibrium production in the Marshall equilibrium. Then, the 

profit function of the leader becomes: 

with: 

Π L (x L )=x L p[x m (n s − 1) + x L ] − c(x L )=x L 

∙ F + c(x m ) 

x m 

¸ 

− c(x L ) 

Π L0 (x L )= F + c(xm ) 

x m − c 0 (x L ) > 0 Π L00 (x L )=−c 00 (x L ) ≥ 0 

since p(·) >c 0 (x m ) >c 0 (x L ) for any x L >x m . Hence, the leader always 

gains from increasing its production all the way to the level at which entry 

is deterred. This level satisfies the zero profit condition for n s =2,thatis 

p (x m +¯x L )=[F + c(x m )] /x m . Since the right hand side is also equal to 

p(n m x m ) by the zero profit condition in the Marshall equilibrium (see the 

proof of Prop. 3.4), it follows that the entry deterrence strategy is exactly 

¯x L =(n m − 1)x m . Q.E.D. 

ProofofProp3.6: Total expenditure Ȳ for the representative agent is 

given by an exogenous part Y and the net profits of the firms P n 

i=1 π i,which 

is zero in the Marshall equilibria, but equal to the positive profits of the 

leader π L in the Stackelberg equilibrium with endogenous entry. The welfare 

comparison derives from the calculation of indirect utilities (2.22) for the 

Logit model and (2.23) for the Dixit-Stiglitz model in both cases. Labeling 

with W (Ȳ ) the indirect utility in function of total expenditure Ȳ , in the Logit 

case we have for both equilibria: 

W (Ȳ )=Ȳ + N µ 

λ ln 1+ N 

− N(1 + λc) − λF 

λF 

and in the Dixit-Stiglitz case we also have for both equilibria: 

W (Ȳ )= θ ¡ αȲ ¢ α £Ȳ 

− F (1 + α) 

¤ 

c (1 + α) 1+α 

∙ (1 − θ) Ȳ 

(1 + α)F 

1−θ 

θ 

+ θ¸


Since they are both increasing in total expenditure, the utility of the representative 

agent must be higher under Stackelberg competition with endogenous 

entry. Q.E.D. 

ProofofProp3.7: The analysis of the last stage is the same as before, 

andinparticulardx/dx L =0.Now,theleader’sfirst order condition becomes: 

Π L 1 [x L,β+ h(x) − h(x L ),k]=Π L 2 [x L,β+ h(x) − h(x L ),k] h 0 (x L ) 

which defines a continuous function x L = x L (k). It follows that: 

x 0 L(k) ∝ Π L 13 [x L ,β+ h(x) − h(x L ),k]−Π L 23 [x L ,β+ h(x) − h(x L ),k] h 0 (x L ) 

Clearly, when the condition in the proposition holds x 0 L (k) ≥ 0 and x L(k) ≥ 

x L (0) >xbyProp.3.2.Otherwise,sincex L (0) >x, continuity implies that 

there is a neighborhood of x L (0) for k small enough where x L (0) >x L (k) >x. 

Q.E.D. 

ProofofProp3.8: The analysis is similar to the basic one, but now 

we have: 

with: 

⎡ 

⎣ dx ⎤ ⎡ 

⎦ = − 1 

dn 

∆ Ω ⎣ Π ⎤ 

12h 0 (x L )dx L + [h(x L ) − h(x)]Π 12 dm 

⎦ 

Π 2 h 0 (x L )dx L + [h(x L ) − h(x)]Π 2 dm 

⎡ 

Π 2 h(x) 

−Π 12 h(x) 

⎤ 

Ω ≡ ⎣ 

⎦ 

−(n − m − 1)Π 2 h 0 (x) Π 11 +(n − m − 1)Π 12 h 0 (x) 

which again implies dx/dx L =0and dn/dx L = −h 0 (x L )/h 0 (x). Moreoverwe 

have: 

dx dn 

dm 

=0, 

dm =1− h(x L) 

h(x) 

< 0 

The first order conditions for each one of the leaders become: 

Π L 1 (x L ,β L )=Π L 2 (x L ,β L ) h 0 (x L ) 

where β L =(n−m)h(x)+(m−1)h(x L ). Totally differentiating this condition 

and using dn/dm it follows that dx L /dm =0.Theprofit ofeachleaderis 

not affected by the number of leaders since: 

dπ L 

dm = ΠL 2 

∙ 

h(x L ) − h(x)+h(x) dn 

dm 

¸ 

=0


which concludes the proof. Q.E.D. 

ProofofProp3.9:Denotewithx i =[x i1 ,x i2 , ..., x iK ] the strategies of 

a firm i. Assume again that a symmetric equilibrium in the strategies of the 

followers exist. The system of K +1 equilibrium conditions for the second 

stage: 

∂Π [x, (n − 2)h(x)+h(x L )] 

=0 for k =1, 2,..,K 

∂x k 

Π [x, (n − 2)h(x)+h(x L )] = F 

pins down the vector x and β =(n−2)h(x)+h(x L ). Consequently the profit 

of the leader is: 

π L = Π L [x L , (n − 1)h(x)] − F = Π L [x L ,β+ h(x) − h(x L )] − F 

which is maximized by the vector x L which satisfies the system of K first 

order conditions: 

∂Π L (x L ,β L ) 

∂x Lk 

= ∂h(x L) 

∂x Lk 

∂Π L (x L ,β L ) 

∂β L 

where clearly β L =(n − 1)h(x). Imagine that there is such an interior equilibrium 

with h(x L ) ≤ h(x). Then it must be that β ≤ β L , which implies 

Π(x L ,β L ) ≤ Π(x L ,β) from the assumption ∂Π/∂β < 0. But the optimality 

of x and the free entry condition imply Π(x L ,β)

4. Dynamic Competition and Endogenous 

Entry 

Static analysis of market structures as those studied in the previous two 

chapters are not particularly relevant for fast-moving markets of high-tech 

and New Economy industries (computer hardware and software, online businesses, 

mobile telephony and biotechnology). These industries are often characterized 

by massive R&D investments, strong reliance on IPRs and other 

intangible assets, network effects, high fixed sunk costs and low marginal 

costs. Competition in these markets is often dynamic in the sense that it 

takes place for the market in a winner-takes-all race. Leading firms in these 

markets might enjoy high market shares yet be subject to massive competitive 

pressure to constantly create better products at lower prices due to threats 

from innovative competitors and potential entrants. Companies that hold a 

significant share of the market at any given point of time may see this share 

decrease rapidly and significantly following the development and supply of a 

new and more attractive product by an actual or potential competitor (the 

launches of the iPod and the iPhone by Apple and their impact on the distribution 

of MP3 players and smart phones are good examples of such rapid 

and drastic market developments), or they may persist in their leading position 

thanks to heavy investments in R&D (think of Intel whose large and 

increasing investments induced sequential innovations in the development of 

chips). 1 

This chapter analyzes competition for the market through models where 

firms invest to obtain innovations and conquer a market. Since innovations 

often lead to patents or other forms of intellectual property rights that guarantee 

exploitation for a certain period, we often refer to this kind of competition 

as to a patent race. In Chapter 1 we analyzed a simple form of 

competition for the market, but here we augment it with a number of realistic 

additions: we introduce a time dimension, so that firms discount profits 

from future innovations, we allow for explicit forms of dynamic investment, 

we consider sequential innovations and endogenize expected profits in partial 

equilibrium, and finally we evaluate the impact of alternative forms of 

product market competition on the incentives to invest in R&D. 

1 The innovation process of Intel has been so systematic that the rule of thumb 

for which the number of transistors on an Intel chip doubles every two years has 

been labeled Moore’s Law from the intuition of Intel co-founder Gordon Moore.

132 4. Dynamic Competition and Endogenous Entry 

A central focus of this chapter will be on the role of incumbents in innovative 

sectors, and we will show under what conditions these firms invest in 

R&D and when their technological leadership persists. The first economist to 

forcefully emphasize the fundamental role of established large firms in driving 

technological progress has probably been Schumpeter: 

“As soon as we go into details and inquire into the individual 

items in which progress was most conspicuous, the trail leads not to 

the doors of those firms that work under conditions of comparatively 

free competition but precisely to the doors of the large concerns - 

which, as in the case of agricultural machinery, also account for much 

of the progress in the competitive sector - and a shocking suspicion 

dawns upon us that big business may have had more to do with creating 

that standard of life than with keeping it down” (Schumpeter, 

1943). 

Related analysis of modern capitalism as driven by the innovative and 

persistent leadership of large firms is also in the classic works of Galbraith 

(1952) and Chandler (1990). 

Recent evidence confirms that incumbents do a lot of research and their 

leadership persists through a number of innovations. One of the industry 

leaders investing more in innovation is Microsoft, the leading firm in operating 

systems: in 2000, its expenditure in R&D was $ 3.7 billion, corresponding 

to 16.4% of its total sales. High investments can also be found in many other 

major firms of high tech sectors. In the same year, the R&D/Sales ratio was 

15% for Pfizer and 5.8% for Merck, two leaders in the pharmaceutical sector, 

11.5% for Intel, leader in the chips market and 5.8% for IBM, and 5.4% for 

Hewlett-Packard, two leaders in computer technologies and services, 11.8% 

for Motorola and 8.5% for Nokia, leaders in wireless, broadband and automotive 

communications technologies, 10% for Johnson & Johnson, the world’s 

most comprehensive manufacturer of health care products and services, 6.6% 

for 3M and 6.3% for Du Pont, which are active in many fields with a leading 

role, 5.6% for Xerox and for Kodak, leaders in the markets for printers 

and photographs. Things did not change much since then. Today American 

corporations spend around $ 200 billion on R&D every year, much of it 

on computing and communications: in 2006 Microsoft spent around $ 6.6 billion, 

IBM and Intel about $6 billion each, Cisco Systems and Hewlett-Packard 

around $4 billion each (The Economist, 2007, “Out of the dusty labs”, March 

1). 

More systematic evidence on the R&D activity by market leaders comes 

from patented innovations and expenditure on licenses. The comprehensive 

study by Malerba and Orsenigo (1999) on EU patents provides clear evidence 

on this point. 2 For instance, they show that the percentage of patents granted 

to firms that had already innovated within their sectors is 70 % in Germany, 

2 See also Malerba et al. (1997).

4. Dynamic Competition and Endogenous Entry 133 

68 % in US, 62 % in Japan, 60 % in France, 57 % in UK and 39 % in Italy; 

moreover, they conclude that: 

“a large fraction of new innovators is composed by occasional innovators 

that exit soon from the innovative scene [...] Only a fraction 

of entrants survives and grows larger (in terms of patents) as times 

goes by: they become persistent innovators. Older firms who survive 

and continue to patent are few in number but represent an important 

contribution to total patenting activities in any period. Here, 

cumulativeness of knowledge and competencies play a major role in 

affecting the continuity of innovative activity of these firms.” 

Czarnitzki and Kraft (2007a) is the first study looking at who purchases 

licenses on patents: on the basis of German data they show that incumbents 

invest more in licensing expenditures than effective and potential entrants, 

and that the investment of these incumbents is higher when the entry threats 

are stronger. 3 

The literature on patent races has studied equilibrium outcomes in the 

market for innovations starting with Loury (1979) and Dasgupta and Stiglitz 

(1980). 4 The standard hypotheses of this literature are decreasing returns 

to scale, fixed costs of innovations and Nash competition between firms. The 

participants of the patent race are the current monopolists of the market, who 

have a patent on the leading-edge product, and a number of entrant firms 

trying to replace the patentholder. A main result is that the patentholder 

does less research than any other entrant and zero research under free entry 

because its incentives to invest in R&D are lower due to the Arrow (1962) 

effect: the expected gain of the patentholder is just the difference between 

expected profits obtained with the next technology and the current one, while 

the expected gain for each outsider is given by all the expected profits obtained 

with the next technology. In the presence of sequential innovations, the 

fact that patentholders do not invest in R&D implies a continuous leapfrogging 

and no persistence of monopolistic positions between one innovation and 

another, which is a quite counterintuitive picture of what is going on in the 

real world: that’s why the result is sometimes called the Arrow’s paradox. 

A number of solutions to the Arrow paradox have been proposed, most of 

which are based on some technological advantage of the patentholder, often 

derived from a gradual accumulation of knowledge. 5 Despite the fact that 

3 The empirical research on the reaction of the investment of incumbents to entry 

is limited. Scherer and Keun (1992) look at the increase in high-tech imports 

in US and find that incumbents in sectors without barriers to entry react more 

aggressively to endogenous entry, increasing R&D/sales more than other firms. 

4 See also Lee and Wilde (1980), Reinganum (1982, 1983, 1985a,b), Harris and 

Vickers (1985) and Beath et al. (1989). 

5 For a survey, see Tirole (1988, Ch.10). See also Reinganum (1982), Fudenberg et 

al. (1983), Harris and Vickers (1985) and Vickers (1986) for detailed analysis.


these are reasonable explanations for the puzzle, they do not seem to tell 

the whole story, as we see monopolists investing in R&D even if they do not 

have consistent technological advantage to the outsiders. Here we will study 

patent races where the patentholder has the opportunity to make a strategic 

precommitment to a flow of investment in R&D. This may happen through a 

specific investment in laboratories and related equipment for R&D, by hiring 

researchers or in a number of other ways. In the case of “contractual costs” 

of R&D, that is, when a fixed initial investment determines the arrival rate 

of the innovation, the interpretation of a strategic precommitment for the incumbent 

monopolist is very standard. The leader can choose to invest before 

the other firms, and since the leader is by definition the firm that has discovered 

the latest technology, it is reasonable to assume that such a discovery is 

associated with a first mover advantage in the following patent race. When 

the number of entrants is exogenous, the behavior of the incumbent is hard 

to predict: on one side the Arrow effect pushes toward a low investment, on 

the other side the strategic effect is ambiguous. Under reasonable conditions, 

however, a first mover advantage does not give strong incentives to invest for 

an incumbent monopolist, and the traditional view that monopolists stifle 

innovation is preserved: without competitive pressure, monopolists are not 

very innovative indeed. 6 

Under endogenous entry, the outcome is completely changed and generates 

a crucial result: the incumbent leader always invests in R&D and more 

so than any other firm, thus the Stackelberg assumption with endogenous 

entry delivers a new rationale for the persistence of a monopoly (Etro, 2004). 

The rationale for endogenous innovation by leaders is similar to the general 

rationale for aggressive strategies by leaders facing endogenous entry: competitive 

pressure determines the aggregate rate of innovation and the investment 

of the leader cannot affect this or the expected length of the current rent. 

Since the expected profits from the current technology are not affected by 

the leader’s strategy, the Arrow effect disappears and, as we also know from 

our general analysis in Chapter 3, the optimal behavior for a Stackelberg 

leader facing endogenous entry is always aggressive. The empirical results of 

Blundell et al. (1999) “are in line with models where high market share firms 

6 In the pre-industrial world, barriers to entry in the innovative sectors, monopolized 

for centuries by guilds, have represented a substantial limit to innovation. 

Dutch guilds opposed progress in shipbuilding, Swiss printers obtained laws to 

avoid improvements in printing press and French paper producers sabotaged 

machines that could speed up pulp production. Interesting historical evidence 

is described by Ogilvie (2004a,b) in a study on merchant guilds between the 

XVI and the XVIII century. These kinds of guilds, spread for centuries around 

Europe, were strongly restricting entry in many sectors and were detrimental to 

innovation activity. Finally, the English Luddites, organized in trade unions, had 

a similar role at the beginning of the Industrial Revolution.

4.1 A Simple Patent Race with Contractual Costs of R&D 135 

have greater incentives to preemptively innovate”. Their conclusion is rather 

explicit: 

“It is often asserted that the superior performance of large firms 

in innovating is because they have higher cash flows from which to 

finance investment in R&D. Our findings suggest that this is not the 

whole story - dominant firms innovate because they have a relatively 

greater incentive to do so. Firm with high market shares who innovate 

get a higher valuation on the stock market than those who do not.” 

However, notice that, contrary to purely-preemptive models of innovation, 

in our environment incumbents do not necessarily deter entry, but they typically 

invest more than other firms, so that their leadership is only partially 

persistent. 

When innovations are sequential, not only incumbent monopolists keep 

investing under the pressure of endogenous entry, but the same value of their 

leadership is enhanced, which in turn increases the aggregate incentives to 

invest in R&D. Contrary to a common belief for which monopolies would stifle 

innovation, the persistence of monopoly can be caused by innovative pressure 

and can enhance technological progress. This result appears in line with the 

original ideas of Schumpeter (1943) on the role of large established firms in 

fostering innovation, and we will use it to sketch a model of technological 

progress driven by market leaders. 

The chapter is organized as follows. Section 4.1 presents a simple model 

of patent races, Section 4.2 extends it in more realistic ways and Sections 

4.3 considers sequential innovations. Finally, Section 4.4. discusses the relation 

between competition in the market and competition for the market and 

Section 4.5 concludes. 

4.1 A Simple Patent Race with Contractual Costs of 

R&D 

In this chapter we will develop models of competition for the market. We 

already developed an example in Chapter 1, but in that case we assumed a 

very simple technology of investment in innovations. Investment could be just 

successful or not (and by investing enough a firm could even innovate with 

certainty), while in the real world it takes time and risk to innovate, and future 

gains are properly discounted taking into account alternative investment 

opportunities. In this section we will introduce a time dimension developing 

a simple patent race in which investment can only increase the chances of 

innovating early on. Of course this is crucial in a competition where the first 

to innovate wins a patent and the associated profits, while all the others get 

nothing. Nevertheless, we still assume that an initial investment determines 

the future chances to innovate, therefore we are still dealing with a form of


competition which is partially static (in the next section we will augment the 

model with a genuinely dynamic investment). 

Following the pathbreaking contribution of Loury (1979) and Dasgupta 

and Stiglitz (1980) we will adopt a particular R&D technology, assuming 

that, given the investment choices of the firms, innovations arrive according 

to a stochastic Poisson process in the continuum. According to this process, 

the probability that a single firm i will obtain the innovation before a certain 

amount of time t ∈ [0, ∞) is independent across firms, memoryless and given 

by: 

G(t, i) =1− e −h it 

where h i is a firm specific parameter. Notice that this probability does not 

depend on the corresponding probability of other firms and does not depend 

on the probability of innovation of the same firm i before time t. The density 

function is g(t, i) =h i e −hit . Another property of a Poisson process is that 

the so-called hazard rate, the instantaneous probability of innovation in t 

conditioned to previous failure, corresponds to the firm specific parameter 

h i > 0. Indeed, we have: 

Pr(i innovates in t) = 

g(t, i) 

1 − G(t, i) = h i 

The simplest kind of investment we can consider is a fixed investments, 

usually called a contractual cost of innovation. In this case, at the beginning 

of the race, each firm i invests a fixed amount F to participate to the contest, 

and decides a variable amount, x i , so that the arrival rate of an innovation 

is: 

h i = h(x i ) with h(0) = 0, h 0 (x) > 0 and h 00 (x) R 0 for x S ˆx 

If we look at h(x) as to a stochastic production function of innovation, loosely 

speaking we are allowing for increasing returns to scale for low investment, 

but we assume decreasing returns for investment greater than a cut off ˆx ≥ 0. 

Using basic properties of probability theory, we can calculate the probability 

that firm i winstheraceattimet as: 7 

Pr(i wins in t) =g(t, i) Y j6=i 

[1 − G(t, j)] = h i e − n 

j=1 hj 

The exogenous value of the innovation is V . In most of our discussion, for 

simplicity, we will refer to this as to the value of a patent. More generally, 

we may think of this as the expected value of the profits obtained by the 

innovation. For instance, the innovation could be kept secret and exploited 

7 Since we work in the continuum, the probability that two firms innovate at the 

same time is zero: there will always be a unique winner in these contests.


until other innovations will replace it, or it could be disclosed with the innovator 

enjoying a first mover advantage in the marketing of the invention 

(even when facing free entry of imitators, as we have seen in the models of 

the previous chapters). Nevertheless, it should be clear that a strengthening 

of the protection of IPRs will increase the value of the innovation V .Since 

we have introduced a time dimension, we need to take in consideration the 

present discounted value of the expected profits. Given the exogenous interest 

rate r, expectedprofits from the patent race are: 

π i = 

Z ∞ 

t=0 

e −rt V Pr(i wins in t)dt − x i − F = 

= h(x i)V 

r + p 

− x i − F 

wherewedefined with p = P n 

j=1 h(x j) the aggregate instantaneous probability 

of innovation. Also this profit function is nested in the general version 

(2.1) employed in the previous chapters. Rearranging and defining 

β i = P n 

k=1,k6=i h(x k), wehave: 

Π (x i ,β i )= 

h(x i )V 

r + h(x i )+β i 

− x i 

Here it can be verified that expected profits for firm i areaninvertedU 

function of the investment of the same firm x i and are decreasing in the investment 

of each other firm, since the relative probability of winning the race 

is what matters. However, in this case the cross derivative (Π 12 ) has an ambiguous 

sign. When another competitor invests more, the relative probability 

of winning is reduced, which makes a marginal investment less profitable, 

but at the same time the aggregate probability of innovation in the market 

is increased and this creates an effect in the opposite direction. If the first 

effect prevails R&D investments are strategic substitutes, as in our simple 

example of Chapter 1. In such a case, we would expect that a firm with a 

first mover advantage over a rival would invest more because of what we 

called the Stackelberg effect: a higher investment reduces the incentives of 

the competitor to invest and increases the relative probability of winning the 

contest. 

We can also easily incorporate an asymmetric position for the incumbent 

monopolist. Assume that this monopolist has a flow of profits K from its 

own leading edge technology. Assume also that the innovation is drastic, so 

the incumbent obtains nothing in case of innovation by another firm: this 

characterizes a situation where the “winner takes all”. The expected profits 

of the monopolist are now: 

Π (x M ,β M ,K)= 

h(x M)V + K 

− x M 

r + h(x M )+β M 

What in Chapter 1 we called the Arrow’s effect is again at work: this 

effect tells us that current profits reduce the marginal profitability of R&D


investment (Π 13 < 0), and consequently they reduce the incentives of the 

incumbent monopolist to invest in innovation. Therefore, in any Nash equilibrium 

with an exogenous number of firms, the incumbent monopolist will 

invest less than any other firm. 8 The behavior of the incumbent monopolist 

acting as a leader in this model is complex because the Arrow effect and the 

Stackelberg effect may work in opposite directions. If the fixed costs of entry 

are high enough, an entry deterring strategy can be optimal, but when this 

is not the case, the optimal strategy for the incumbent monopolist will be 

biased toward a lower investment if the Arrow effect prevails. 

4.1.1 Endogenous Entry 

As shown in Etro (2004, 2008), any ambiguity of the results disappears in 

equilibria with endogenous entry. Consider first a Marshall equilibrium, where 

all firms compete in Nash strategies and entry takes place as long as there are 

profitable opportunities. In this environment, as we noticed, the incumbent 

monopolist is always investing less than the rivals because of the Arrow effect. 

When entry has dissipated all profitable opportunities for the other firms, the 

optimality condition for the outsiders and the free entry condition are: 

h 0 (x)V 

r + p 

= h0 (x)h(x)V 

(r + p) 2 +1, 

h(x)V 

r + p = x + F (4.1) 

These conditions determine the equilibrium investment of each outsider and 

the aggregate probability of innovation independently from the equilibrium 

strategy of the monopolist. In particular, the investment of each outsider can 

be implicitly expressed as: 

h 0 (x) 

µ 

1 − x + F 

V 

 

= h(x) 

x + F 

(4.2) 

and it can be verified to increase in the value of innovation. 9 

Let us now look at the equilibrium behavior of the incumbent monopolist, 

and in particular at its incentives to invest in this competition. First of all, 

notice that the aggregate probability of innovation is going to be independent 

from the investment of the incumbent monopolist. Therefore, the expected 

profits from the leading edge technology will be the same whether the monopolist 

invests or not to innovate. Consider now its expected profits from the 

8 This can be easily seen comparing the respective first order conditions in a Nash 

equilibrium where the fixed costs are assumed low enough that all firms invest: 

the marginal cost of investment is higher for the monopolist because an increase 

in the aggregate probability of innovation reduces the expected lenght of exploitation 

of the current technology. 

9 A simple example with linear technology, h(x) =x, can be solved analytically. 

In this case the Marshall equilibrium implies x = √ VF − F .


actual patent race. Because of the Arrow effect, the monopolist is going to 

invest less than the outsiders. On the other side, the outsiders are investing to 

maximize the expected profits from the actual patent race. Nevertheless, endogenous 

entry reduces to zero these expected profits. Consequently, it must 

be that the alternative strategy of the monopolist can only reach negative 

expected profits in the actual patent race. In conclusion, it is better for the 

monopolist to withdraw from the competition and retain the current flow of 

profits until some other firms will innovate. 

Finally, we will study the case in which the incumbent monopolist is 

the leader of the patent race. In a Stackelberg equilibrium with endogenous 

entry, as long as entry takes place, the first order condition and the free entry 

condition at the second stage are the same as before, and they generate the 

same investment for the outsiders (4.2), and the same aggregate probability 

of innovation implicit in the free entry condition in (4.1). As a consequence 

of the usual neutrality result emerging under endogenous entry, the strategy 

of the leader is not going to affect the strategy of the active followers, but 

just their number. Using (4.1), we can now re-express the expected profits of 

the incumbent monopolist as: 

π M = h(x M)V + K 

− x M − F = 

r + p 

= h(x M)(x + F ) 

h(x) 

+ K(x + F ) 

h(x)V 

− x M − F 

where the investment of the outsiders x is now taken as given according to 

the equilibrium condition (4.2). The incumbent monopolist can now exploit 

its first mover advantage choosing its investment according to the optimality 

condition: 

h 0 (x M )= h(x) 

(4.3) 

x + F 

which defines a local maximum when h 00 (x M ) < 0, aswewillassume,andit 

is associated with a higher investment than the one of the outsiders defined 

in (4.2). Since the monopolist could still invest as much as the outsiders 

and obtain zero expected profits from the actual patent race, the optimality 

condition above, which differs from that of the outsiders, implies that the 

monopolist can do even better and obtain positive profits from the patent 

race. This also implies that the strategy defined by (4.3) is always preferred 

to the corner strategy of not participating to the race. However, it may not 

be preferred to the corner strategy that deters entry. Such an entry deterring 

strategy would require an investment high enough to deter entry, that is 

h(x M )=(V − F − x)h(x)/(x + F ) − r. 10 The possibility of entry deterrence 

10 For instance, this is what happens in the case of a linear technology, h(x) = 

x. Given the expected behavior of the outsiders, the expected profits of the


by the monopolist was pointed out by Gilbert and Newbery (1982) in a 

different duopolistic framework. 11 . 

Notice that the level of current profits does not affect the equilibrium 

outcome, 12 which confirms two results. First, the Arrow’s paradox disappears: 

the monopolist that is leader in a patent race with free entry takes as given 

the expected value of the current monopoly and simply exploits its strategic 

advantage to increase the relative probability of success in the patent race. 

Second, the escape competition effect associated with Aghion and Griffith 

(2005) disappears: an increase in the intensity of product market competition 

associated with a decrease in the profits before a drastic innovation does not 

affect the aggregate level of innovation. In this model, effective competition 

for the market leads the incentives to innovate, and competition in the market 

cannot enhance further these incentives. 

In conclusion, our extension of the simple model of competition for the 

market analyzed in Chapter 1 allows to generalize the result obtained in that 

simpler environment: incumbent monopolists facing a competitive pressure 

in the competition for future markets behave in an aggressive way and invest 

more than each other rival, but they do not necessarily deter entry. We can 

summarize our findings as follows: 

Proposition 4.1. In a competition for the market with contractual 

costs of R&D, the incumbent monopolist invests more than 

any other firm and independently from its current profits when 

has a leadership and entry is endogenous. 

As intuitive, entry deterrence can be optimal when investment is not too 

costly or its marginal productivity is constant (or not too much decreasing). 

However, when the marginal productivity of investment diminishes strongly 

with the same investment, entry deterrence requires a very large and costly 

monopolist turn out to be linearly increasing in its investment. The monopolist 

is better off deterring entry with the limit investment ¯x M = V + F − 2 √ VF− r. 

11 Gilbert and Newbery (1982) obtained entry deterrence by the monopolist in a 

deterministic contest, where investment reduces the waiting time for innovation 

in a deterministic way. They also suggested that a similar result could occur in 

stochastic patent races, providing an early insight for our result (see also Gilbert 

and Newbery, 1984). However, they did not move one step further and show that 

even when entry deterrence is not optimal, the monopolist with a first mover 

advantage invests more than any outsider as long as entry is free. For this reason, 

their result was forced to suggest a rationale for “sleeping patents” without 

innovative purposes and used by monopolists to preempt entry. Our point here is 

the exact opposite: under competitive pressure incumbent monopolists are led to 

invest a lot in R&D to conquer useful patents and generally without exclusionary 

purposes. 

12 This is a consequence of Prop. 3.7 since in equilibrium we have Π13 L = −(r + 

p) −2 = Π23h L 0 (x M).


investment and becomes suboptimal. As noticed by Kortum (1993), Griliches 

(1994), Cohen and Klepper (1996) and other empirical works, investments in 

R&D are characterized by decreasing marginal productivity at the firm level. 

Cohen and Klepper (1996) show that “the assumption of diminishing returns 

to R&D is well grounded empirically” for a broad sample of industries. 13 Even 

Aghion and Howitt (1998, Ch.12) accept this as a stylized fact. Therefore, 

it is reasonable to focus on this case where the marginal productivity of 

investment is decreasing and, accordingly, both the monopolist and some 

outsiders invest in R&D. 

4.1.2 Welfare Analysis 

Before, moving on in our discussion, we want to analyze our equilibria from 

a welfare point of view. Assuming that V ∗ is the social value of innovations, 

potentially higher than its private value, a social planner would maximize a 

welfare function based on the discounted expected social value of the innovation 

net of the total investment costs: 

P n 

i=1 

W = 

h(x i)V ∗ n 

r + P n 

i=1 h(x i) − X 

(x i + F ) 

i=1 

The social planner problem amounts to choosing n ∗ firms and an investment 

x ∗ for each firm to solve: 

max W = nh(x)V ∗ 

x,n r + nh(x) − n(x + F ) 

Combining the optimality conditions, one obtains the optimal investment as 

satisfying: 

h(x ∗ ) 

x ∗ + F = h0 (x ∗ ) 

which implies that the investment of each firm is too low in Marshall equilibrium. 

Moreover, the number of firms is too high when the social value of 

the innovation is small, for instance when it coincides with its private value 

(W n < 0 at the number of firmswhichmakesnetprofits equal to zero), and 

it is too low when the social value of the innovation is large enough. In Stackelberg 

equilibrium with endogenous entry the incumbent monopolist invests 

more than the outsiders, reducing the number of firms but not the aggregate 

13 From a theoretical point of view, notice that, while in most of the productive 

sectors there are good reasons to believe that doubling the amount of input total 

production will double (constant returns to scale hold), there are no reasons to 

believe that doubling the amount of inputs in the R&D activity will double the 

expected amount of innovations.


probability of innovation, which remains the same. This leads to a simple 

welfare comparison (Etro, 2008): 

Proposition 4.2. In the competition for the market with contractual 

costs of R&D and endogenous entry, the allocation of resources 

in the Stackelberg equilibrium with endogenous entry is 

Pareto superior compared to the Marshall equilibrium. 

4.2 Dynamic Competition for the Market 

Competition for the market is an intrinsically dynamic phenomenon and not 

a static one, as we often remarked. Nevertheless, until now we considered 

simple forms of this competition where an initial investment by each firm 

was exhausting the research activity. In reality, firms invest over time and 

keep investing until one of them innovates: just at that point the race is over 

and all firms stop spending for that innovation. In the rest of this chapter we 

will study patent races where firms continuously invest a flow of resources in 

R&D and their probability of innovation depends on this flow. 

Following Lee and Wilde (1980), if x i is now the flow of investment of 

firm i determining an instantaneous probability of innovation h(x i ) assumed 

positive, increasing and strictly concave, the expected profits of a generic 

outsider are given by: 

π i = 

Z ∞ 

t=0 

e −rt [V Pr(i wins in t)dt − x i Pr(no one wins in t)] − F = 

= h(x i)V − x i 

− F 

r + p 

which again can be rewritten as a particular case of our general formulation 

(2.1) employed in the previous chapters, with: 

Π(x i ,β i )= 

h(x i)V − x i 

[r + h(x i )+β i ] 

(4.4) 

An interesting feature of this model is that now we can determine unambiguously 

the sign of the cross derivative. In particular, when firm i maximizes 

its expected profits, the impact of a change in the strategy of the other firms 

on its marginal profit is: 

Π 12 ≡ [h0 (x i )V − 1] 

[r + h(x i )+β i ] 2 > 0 

Contrary to the simple example of Chapter 1, where investments of the firms 

were strategic substitutes, and to the ambiguous case of the previous section, 

we now realize that under more realistic conditions, investment strategies

4.2 Dynamic Competition for the Market 143 

are strategic complements. When a firm invests more in R&D, the aggregate 

probability of innovation in the sector increases and this reduces expected 

profits of the other firms, but it also increases their expected marginal profits, 

and therefore their incentives to invest. 

Finally, we can derive the objective function of the incumbent monopolist 

with a flow of current profits K as follows: 

Π (x M ,β M ,K)= h(x M)V + K − x M 

r + h(x M )+β M 

(4.5) 

which is again characterized by Π 13 < 0: an increase in current profits reduces 

the marginal profitability of investment. In what follows, we will describe in 

detail the equilibrium of the competition for the market under alternative 

forms of strategic interaction. 

4.2.1 Nash Equilibrium 

Under Nash competition the equilibrium symmetric optimality condition for 

the investment of each entrant is: 

[h 0 (x)V − 1] (r + p) =h 0 (x)[h(x)V − x] (4.6) 

where p = h(x M )+(n − 1)h(x) is the aggregate probability of innovation. 

Straightforward differentiation shows that the investment of each entrant is 

increasing in the expected value of innovation, in the interest rate and in the 

number of firms (since SC holds). If the incumbent invests, its choice x M 

satisfies the first order condition: 

[h 0 (x M )V − 1] (r + p) =h 0 (x M )[h(x M )V + K − x M ] (4.7) 

which differs from the previous one just because the flow of current profits 

increases the marginal cost of investment: this is a consequence of the Arrow 

effect and it implies that, ceteris paribus, the incumbent invests less than 

each entrant and has lower expected profits from participating to the patent 

race (Reinganum, 1983). Because of SC, a change in K affects all firms in the 

same way: for instance if we interpret an increase in the intensity of product 

market competition as a reduction in current profits K, allfirms invest more 

in R&D according to the escape competition effect. Summarizing we have: 

Proposition 4.3. A Nash equilibrium in the competition for the 

market implies a lower investment by the incumbent monopolist 

than any other firm and an investment for each firm which is decreasing 

in the current profits.


4.2.2 Marshall Equilibrium 

Let us assume free entry now. Since the expected profit functions of all firms 

derived in the Nash equilibrium are decreasing in the number of firms, and the 

incumbent expects lower profits from the R&D investment than the others, 

we can conclude that the incumbent will stop researching if the number of 

firms is great enough: the Arrow effect induces the incumbent to withdraw 

from the competition for the market. Moreover, the entrants will break even 

if the number of firms achieves a still higher bound. This bound is defined by 

the free entry condition: 

r + p = h(x)V − x 

(4.8) 

F 

Rearranging the equilibrium first order condition for the outsiders and this 

free entry condition, we can re-express the equilibrium flow of investment in 

the following implicit way: 

h 0 (x) = 1 

(4.9) 

V − F 

which is increasing in the difference between the expected value of the innovation 

and the fixed cost, but independent from the interest rate. Moreover, 

the equilibrium number of firms is increasing in the value of innovation and 

decreasing in the fixed cost of entry and in the interest rate, while it is independent 

from the current profits of the incumbent monopolist. Summing up, 

we have: 

Proposition 4.4. A Marshall equilibrium in the competition for 

the market implies that the incumbent monopolist does not invest 

and the investment of the outsiders and the aggregate probability 

of innovation do not depend on the current profits. 

In general, if the social value of innovation is higher enough than its 

private value, equilibrium investment is too low and there are too few firms. 

Nevertheless, if the social value of innovation is close enough to its private 

value, the equilibrium number of firms can be excessive. 

4.2.3 Stackelberg Equilibrium 

We will now assume that the patentholder has the opportunity to make a 

strategic precommitment to a level of investment in R&D. This may happen 

through a specific investment in R&D laboratories, by hiring researchers or 

in a number of other ways. Our strategic assumption seems a natural one 

since the patentholder can be easily seen in a different perspective from all 

the other entrants in the patent race. 

Assume that the fixed costs are low enough that the entry deterrence 

strategy is not optimal. Then, the incumbent leader will commit to a low


level of investment because such a strategy will induce a reduction in the 

investment of the other firms and a longer expected lifespan of the current 

patent (Reinganum, 1985,b). The reason of this unambiguous result is that 

now the Stackelberg effect and the Arrow effect work in the same direction. 

The first pushes toward a low investment by the monopolist because it reduces 

the incentives of the followers to invest as well. The second pushes in the same 

direction because a lower investment by the monopolist reduces the aggregate 

probability of innovation so as to increase the length of time in which the 

monopolist enjoys the profit flow from the current patent. 

More formally, each entrant chooses its own investment according to the 

optimality condition (4.6). In the initial stage, the choice of the leader x M 

satisfies the optimality condition: 

[h 0 (x M )V − 1] (r + p) = 

∙ 

h 0 (x M )+(n − 1) ∂h(x) ¸ 

[h(x M )V + K − x M ] 

∂x M 

(4.10) 

unless current profits are so high that the incumbent leader prefers to withdraw 

from the race. The system (4.6)-(4.10) defines the interior equilibrium. 

The effect of SC is now strengthened by the Arrow effect and leads to a low 

investment of the incumbent monopolist compared to the entrants. In the 

Appendix we show that the investment by each firm is increasing in the interest 

rate r and decreasing in the flow of current profits, but ambiguously 

dependent on the value of the innovation V and the number of firms n. Summarizing: 

Proposition 4.5. A Stackelberg equilibrium in the competition 

for the market implies a lower investment for the incumbent monopolist 

than for the other firmsaslongasentryisaccommodated; 

investment by each firm is decreasing in the current profits. 

An immediate corollary of this result is that a Stackelberg equilibrium 

implies an aggregate investment in R&D which is increasing in the interest 

rate and decreasing in the current profits of the incumbent, and an expected 

lifespan of the current patent which is affected in the opposite way. Compared 

to the Nash equilibrium, both the incumbent and each entrant invest less, 

and, since the number of firms is exogenous, the aggregate investment must 

be lower. In conclusion, a Stackelberg leadership with a fixed number of firms 

does not give a rationale for incumbents’ investment in R&D. 

Finally, notice that the escape competition effect is now working: if we 

imagine that an increase in product market competition decreases current 

profits K but not the value of the innovation (because this is a drastic innovation), 

then a more intense competition increases individual and aggregate 

investment in R&D.


4.2.4 Stackelberg Equilibrium with Endogenous Entry 

Let us now consider the endogenous entry case, in which the leader has to 

foresee the effects of its investment choice on the equilibrium number of entrants. 

In this case, as shown by Etro (2004), the results of the previous three 

market structures are radically modified: the incumbent monopolist has incentives 

to invest more than any other firm, the Arrow’s paradox disappears 

and the escape competition effect disappears as well. 

Once again, we focus on the realistic case in which entry of followers 

occurs in equilibrium. In the last stage all the entrants choose the same flow 

of investment x determined by the symmetric optimality condition: 

[h 0 (x)V − 1] [r +(n − 1)h(x)+h(x M )] = h 0 (x)[h(x)V − x] (4.11) 

Using symmetry, the zero profit condition becomes: 

h(x)V − x 

r +(n − 1)h(x)+h(x M ) = F (4.12) 

Substituting this in (4.11) we obtain the same implicit expression for the 

entrant’s investment as under Marshall competition (4.9): 

h 0 (x) = 1 

V − F 

which does not depend on the leader’s decision. However, the equilibrium 

number of firms does depend on the leader’s choice as predicted by the free 

entry condition. Totally differentiating the latter, using the fact that x does 

not depend on x M , delivers the expected change of investment in R&D of 

each entrant for a change in the leader’s investment: 

∂ [(n − 1)h(x)] 

= −h 0 (x M ) 

∂x M 

which shows that a higher investment of the incumbent reduces the aggregate 

investment of the other firms through a reduction in the number of entrants. 

In the initial stage, the incumbent monopolist maximizes profits according 

to the optimality condition: 

[h 0 (x M )V − 1] (r + p) = 

∙ 

h 0 (x M )+ 

¸ 

∂ [(n − 1)h(x)] 

[h(x M )V + K − x M ] 

∂x M 

and, substituting our expression for the indirect impact ∂ [(n − 1)h(x)] /∂x M 

we obtain a simple equilibrium expression: 

h 0 (x M )= 1 V 

(4.13)


which shows a larger investment than the one of the entrants. This also 

implies that the equilibrium number of firms is lower than in the Marshall 

equilibrium. 14 Summarizing, we have: 

Proposition 4.6. A Stackelberg equilibrium with endogenous 

entry in the competition for the market implies a) the same investment 

as in Marshall equilibrium for the entrants with a lower 

number of entrants, b) a higher investment for the incumbent monopolist 

than for each of the other firms, and c) a higher total 

investment than in Marshall equilibrium. 

Once again, Stackelberg competition with endogenous entry induces the 

aggressive behavior of the incumbent. The intuition is related to the perception 

the leader has of the entry process. It is understood that any profitable 

opportunity for doing R&D left open by the leader will be seized by new 

entrants until their expected profits are zero. The aggregate probability of 

innovation is determined by the free entry constraint independently from the 

investment of the leader and is thus taken as given by the latter. So, the monopolist 

looses the strategic incentive to keep its investment low: the latter 

is not going to affect the expected lifespan of the current patent. The Arrow 

effect disappears. Therefore, the only purpose of investing in R&D for the 

leader is to actually win the patent race, and the incentives to do it are now 

higher than those of any other entrant. 

An intuitive way to see this asymmetry relies on the fact that the leader 

maximizes its profits taking as given the aggregate probability of innovation, 

which is equivalent to maximize h(x M )V − x M , without taking into account 

the impact on the aggregate arrival rate of innovation. This impact, instead, 

is taken into account by each entrant and reduces the marginal profits of each 

entrant, explaining why the entrants invest less than the leader. 15 We finally 

derive some comparative statics in the following proposition: 

Proposition 4.7. A Stackelberg equilibrium with endogenous entry 

in the competition for the market implies an investment for each 

entrant firm which is increasing in the value of the innovation and 

decreasing in the fixedcost,andaninvestmentfortheincumbent 

monopolist which is increasing in the value of innovation while none 

of them is affected by changes in the current profits. 

An immediate corollary of this result is that a Stackelberg equilibrium 

with endogenous entry implies an aggregate investment in R&D which is decreasing 

in the interest rate and independent from current profits. We confirm 

14 Also in this model we have entry deterrence when the marginal productivity of 

investment is not too decreasing. In this case, the equilibrium investment of the 

monopolist satisfies h(¯x M)=(V −F )h(x)/F −x/F −r. In the rest of the chapter 

we will focus on the case in which there is entry of outsiders in equilibrium. 

15 The result holds even when the leader has a lower gain from innovation than the 

outsidersaslongthisgainishigherthanV − F (Lee and Sung, 2004).


that the escape competition effectemphasizedbyAghionandGriffith (2005) 

disappears when there is endogenous innovation by leaders: here competition 

for the market eliminates the impact of product market competition on the 

incentives to innovate. We will discuss later on the implications of this result. 

Finally, from a welfare point of view, a leadership reduces the number 

of firms and hence the expenditure in fixed costs, but it increases the total 

flow of investment, maintaining the aggregate probability of innovation at the 

same level. This makes ambiguous a welfare comparison between the Marshall 

outcome and the Stackelberg outcome with endogenous entry. 

4.2.5 Non-drastic Innovations 

Until now we confined our analysis to drastic innovations.Oftentimes,once 

an outsider has introduced an innovation, the previous leader is not completely 

replaced, and both firms can still obtain positive profits; in these 

cases we have non-drastic innovations. Imagine that if the incumbent loses 

the patent race a duopoly between the winner and the incumbent sets in. Let 

us denote the value of winning the patent race for the incumbent with V W . 

When an outsider wins, the previous incumbent obtains V L and the entrant 

obtains V ≤ V W . The standard assumption is that, even if the innovation 

is drastic and the duopoly is characterized by perfect collusion, the sum of 

the discounted profits obtained by the two duopolists cannot be greater than 

the discounted profits obtained by the incumbent who wins the patent race 

V W ≥ V + V L . Notice that the case of drastic innovations is a particular 

case for V W = V and V L =0. Using the properties of Poisson processes 

in a standard fashion, the objective function of each outsider is the same as 

before, (4.4), with a value of innovation V , while the gross expected profits 

of the incumbent monopolist are now: 

Π (x M ,β M ,K)= h(x M)V W + K + β M V L − x M 

r + h(x M )+β M 

(4.14) 

In Nash and Stackelberg equilibria the comparison between the incentives 

of the incumbent monopolist and the outsiders to invest are ambiguous because, 

beyond the usual Arrow and Stackelberg effects, we now have two new 

effects. On one side the gain from innovating for the incumbent is larger than 

for an outsider (V W >V), which increases the relative marginal benefit of 

innovating for the incumbent. On the other side the gain from the duopolistic 

profits of the incumbent in the case in which another firm innovates (V L > 0) 

increases the marginal cost of innovating for the incumbent. Of course, if the 

first effect is strong enough, the incumbent may be the only firm to invest. 16 

16 Gilbert and Newbery (1982) studied an auction for a non drastic innovation between 

an incumbent and an entrant and noticed that the incumbent is willing 

to pay more for the innovation than an outsider. In theory, their deterministic


However, in what follows we will not deal with entry deterring strategies, 

but we will focus on the more realistic case where both the leader and the 

followers invest in R&D. 

Consider equilibria with endogenous entry. In a Marshall equilibrium, 

as long as entry of outsiders drives expected profits to zero, we can obtain 

the same equilibrium condition for the investment of each outsider (4.9) as 

obtained earlier, h 0 (x) =1/ (V − F ). In a Stackelberg equilibrium with endogenous 

entry, when the incumbent monopolist is the leader, the equilibrium 

is characterized by this same investment for the outsiders and by an aggregate 

probability of innovation p = h(x M )+β M which is again independent 

from the strategy of the incumbent. Accordingly, the incumbent monopolist 

maximizes: 

π M = h(x M)V W + K +[p − h(x M )] V L − x M 

r + p 

− F 

which is equivalent to maximize h(x M )V W − h(x M )V L − x M , and implies 

the optimal investment: 

h 0 1 

(x M )= 

V W − V L (4.15) 

Clearly, condition V W ≥ V + V L always implies that that the monopolist 

invests more than each outsider. The investment of the leader is directly 

related to the net perspective value of innovating V W − V L ,which 

is strictly higher than the one of the entrant V E . Assuming for simplicity 

that a symmetric duopoly takes place in caseofinnovationbyanoutsider, 

V = V L ∈ (F, V W /2), wecanconcludewith: 

Proposition 4.8. With non-drastic innovations, a Stackelberg 

equilibrium with endogenous entry in the competition for the market 

implies that the incumbent monopolist invests more than any 

other firm, all investments are not affected by changes in current 

profits, and the investment of the monopolist (outsiders) is decreasing 

(increasing) in the value of the duopolistic competition. 

Also in this case, the basic escape competition effect disappears: an increase 

in product market competition leading to lower current profits for 

the incumbent does not affect the investment in R&D of any firm, including 

the same incumbent. However, in this case, we can extend our analysis 

to another interesting experiment. When tougher product market competition 

reduces the duopolistic profits expected by an innovative outsider and 

model would apply to cases in which firms can license existing innovations, however 

Salant (1984) has shown that the result collapses if any firm can license 

the patented innovation, and Czarnitzki and Kraft (2007b) have extended the 

model to entry of challengers (endogenizing the number of licenses) obtaining 

ambiguous results.


the incumbent (V ), the investment of the former is always reduced and the 

one of the latter is always increased: a standard Schumpeterian effect impacts 

on the outsider, and an escape competition effect àlaAghion et al. 

(2005) impacts on the incumbent monopolist. As we have seen, this happens 

also when entry in the competition for the market is endogenous. However, 

the aggregate impact of a higher intensity of product market competition is 

unambiguously in favor of the Schumpeterian effect. Formally, remembering 

that p = h(x M )+(n − 1)h(x), wehave: 

∂p 

∂V = h(x) 

F − h00 (x)(V − F ) 2 > 0 

Once again, we realize that when competition for the market is free, product 

market competition cannot increase the aggregate incentives to innovate 

through the escape competition effect. In a sense, when leaders are endogenously 

innovating to escape from the innovative pressure of the outsiders, 

they cannot escape also from product market competition. 

4.2.6 Strategic Commitments 

The model can also be extended to the case in which the size of innovations 

is actually endogenous. A widespread view claims that the innovations of 

the outsiders are more radical since patentholders may have a technological 

advantage in obtaining small improvements on their technologies, so as to 

induce entrants to try replacing the patentholder with radical innovations. 

Etro (2004) questions such a view showing that in this model the incumbent 

monopolist invests also in more radical innovations than the other firms as 

long as it is the leader in the competition for the market. 

Before moving on, we should notice that in this chapter we focus on a 

purely strategic advantage for the incumbent monopolist. As we know from 

Chapter 2, however, similar results would emerge if we allowed the incumbent 

to engage in preliminary investments that could induce an aggressive 

behavior. For instance, the incumbent could commit to invest in R&D more 

than its rivals through a strategic investment that reduces the variable costs 

of R&D (Section 2.6), or one that increases the value of innovation (Section 

2.7): examples include research efforts aimed at obtaining more radical innovations, 

entry in related sectors where the same innovation could be fruitfully 

exploited in the future, or expansion of the market for the future innovation. 

According to our general analysis of debt financing in Section 2.8, competition 

for the market is the typical case in which a bias toward debt financing 

in the financial structure (for instance through venture capital financing) 

would lead to aggressive investment in a risky activity as R&D: this would 

endogenously reduce the cost of innovation, since in case of failure, debtholders 

would bear those costs. 

Finally, a recent interesting work by Erkal and Piccinin (2007,b) has studied 

R&D cartels, which are aimed at coordinating R&D investments, and

4.3 Sequential Innovations 151 

research joint ventures (RJV) cartels which are aimed at sharing the results 

of cooperative R&D investment, in the presence of endogenous entry. 17 As 

we have seen in the more general case of Section 2.13, R&D cartels are ineffective 

as any other form of horizontal collusion, because they induce less 

investment for the members of the cartel than for the outsiders, which leads 

to lower profits under endogenous entry. On the contrary, RJV cartels between 

a small number of members can manage to increase their profits by 

coordinating on a larger investment level than the other firms. This happens 

because RJV cartels increase the expected value of innovation: as long as 

one of the members wins the race, the right of exploiting the innovation is 

awarded to all of them. Under endogenous entry, these cartels do not affect 

the aggregate arrival rate of innovations: therefore, when RJV cartels take 

place, they can increase welfare if an increase of the number of firms with the 

new technology is expected to create gains for the consumers. In other words, 

antitrust authorities evaluating RJV cartels should focus their attention on 

the foreseen impact on the product market. 

4.3 Sequential Innovations 

Many innovative markets are characterized by a continuous development 

through sequential innovations. It has been sometimes argued that, in the 

presence of sequential technological advances, patents may stifle innovation 

because they may refrain outsiders from improving the existing technologies 

leaving the burden of innovation to slacker monopolists. 18 On the contrary, we 

will show that in an environment where innovations are sequential, patents 

and intellectual property rights play a crucial role in fostering innovation 

because they can start a virtuous circle of incentives to innovate, and this 

happens exactly when incumbent monopolists are the leaders in the patent 

races. The idea, fully developed in Etro (2001, 2007,a), is quite simple. 

In a one shot patent race the value of the expected monopolistic profits 

provides the incentives to invest in R&D, and, when entry is endogenous, 

the aggregate incentives are unchanged when the outsiders or the incumbent 

monopolist invest. However, in a sequential patent race, the value of becoming 

a monopolist patentholder is what provides the incentives to invest, and 

that value is crucially affected by the role of the incumbent monopolist. If 

17 In a related work, De Bondt and Vandekerckhove (2007) have extended the 

model of Etro (2004) to the case where the players may commit to share their 

rewards. The larger investment by the leaders is confirmed when sharing may 

occur among all entrants, but not necessarily when the leader shares with all the 

entrants (“winner does not take all”). 

18 For instance, see Bessen and Maskin (2002). On this issue, see also Erkal (2005), 

Etro (2005d), Denicolò (2007), and Scotchmer (2004, Ch. 5) for a survey.


the latter does not invest, the market is characterized by systematic replacement 

of the monopolist with a new one and the value of being a patentholder 

coincides with the expected profit flow of a single patent. If the incumbent 

monopolist is the leader in the patent race and hence, as we know by now, 

invests in R&D more than any other firm, there is a chance that its monopolistic 

position will be preserved at the time of the new innovation, and then 

at the time of the following one, and so on. This possibility of a persistent 

innovation dramatically increases the value of being a patentholder, which in 

turn enhances the incentives to invest by all firms, the incumbent and the 

outsiders. In this case, we will have to associate a (partial) persistence of 

monopolies with stronger incentives to invest in R&D and therefore with a 

faster technological progress. 

This process is at the source of technologically driven growth in the global 

economy. In this section we will examine this mechanism, dividing it in two 

separate steps: the first is to endogenize the value of a patent as function 

of the related innovation and all the subsequent innovations, and the second 

is to endogenize the value of technological progress in a partial equilibrium 

production economy. One could also take a third step and endogenize the 

interest rate in a general equilibrium framework, but this is beyond the scope 

of this book, whose analysis is limited to a partial equilibrium context. 

4.3.1 Endogenous Value of Innovations 

Consider a sequence of drastic innovations τ =1, 2, ...T − 1,T, each one associated 

with the exogenous profit flow K τ . Every innovation can be obtained 

after winning a patent race as the one we studied in the previous section. 

Participation to the patent race for the innovation τ requires a fixed cost F τ 

andaninvestmentx τ , which induces an instantaneous probability of innovation 

h τ (x τ ) with the same properties as before, but potentially changing for 

different innovations. The interest rate is always exogenous and constant at 

the level r. The value of conquering the patent on innovation τ is defined V τ 

and for now will be taken as given. This is natural since it does not depend 

on investment choices during the regime of innovation τ − 1, andallfirms 

will consider it as exogenous while choosing their investments to conquer it. 

Accordingly, the expected profit ofanoutsiderfirm i participating to the 

patent race for the innovation τ is: 

π iτ = h τ (x iτ )V τ − x iτ 

r + p τ 

− F τ (4.16) 

where p τ = P h τ (x jτ ) is the aggregate probability of innovation in this patent 

race. Of course, while this patent race takes place, the current monopolist 

has a patent on the previous innovation τ − 1, which is associated with a 

flow of profits K τ−1 . The expected profit of this incumbent monopolist can 

be expressed analogously, taking into account the flow of profits from the 

current patent:


π Mτ−1 = h τ (x Mτ )V τ + K τ−1 − x Mτ 

− F τ · I[x Mτ > 0] (4.17) 

r + p τ 

where I[x Mτ > 0] is an indicator function with value 1 if x Mτ > 0 and 0 

otherwise. 

While the value of the innovation, the current flow of profits and the fixed 

cost of production may change over time, each patent race can be characterized 

exactly as in our previous analysis. In equilibrium, the investment of each 

firm and, in case of endogenous entry, the number of firms investing in R&D 

will depend (positively) on the value of the innovation in ways that we have 

examined earlier and that change with the kind of competition. In particular, 

the incumbent monopolist will not invest in a Marshall equilibrium, but will 

invest more than any other outsider when is leader in the patent race, as we 

have seen for the Stackelberg equilibrium with endogenous entry. 

However, following Reinganum (1985a) and Etro (2004), we can now endogenize 

the value of these innovations, because the value of holding patent τ 

must correspond to the equilibrium expected profit of the incumbent monopolist 

with the patent on the innovation τ, and the value of patent τ − 1 must 

correspond to the equilibrium expected profit of the incumbent monopolist 

with the patent on innovation τ − 1, and so on. Accordingly, V s = π Ms for 

any s = τ − 1,τ,... 

For instance, if Marshall competition takes place in every patent race, 

we know that the incumbent monopolist will not participate, each outsider 

will invest in the patent race for innovation τ an amount x τ (V τ ) satisfying 

the condition h 0 τ (x τ )(V τ − F τ )=1, and the aggregate probability of innovation 

will be determined by the zero profit condition for the outsiders. Using 

these equilibrium conditions, the dynamic relation that links the value of 

subsequent innovations becomes simply: 

K τ−1 F τ 

V τ−1 = 

(4.18) 

h τ [x τ (V τ )]V τ − x τ (V τ ) 

whose right hand side is decreasing in V τ . Given the value of the last innovation 

(say V T = K T /r at time T ), one can recursively obtain the value of all 

the previous innovations. 19 

Something analogous emerges with Stackelberg competition and endogenous 

entry. In this case the incumbent monopolist participates always to 

the patent race and, assuming that entry deterrence is not optimal (which 

19 Notice that this implies a negative relation between the value of subsequent innovations. 

The intuition is straightforward: if the value of innovation τ is expected 

to be large, there will be more investment in the patent race to obtain this innovation, 

which reduces the expected length of the monopoly associated with the 

previous patent τ − 1, whose value will be smaller as a consequence. This may 

lead to innovation cycles (see Etro, 2004).


requires the h τ function to be concave enough), 20 its investment x Mτ (V τ ) 

satisfies h 0 τ (x Mτ ) V τ =1, while the equilibrium investment of the outsiders 

and the aggregate probability of innovation are given by the same conditions 

as before. The relation between subsequent values of innovations becomes: 

½ ¾ 

hτ [x Mτ (V τ )]V τ + K τ−1 − x Mτ (V τ ) 

V τ−1 = 

− 1 F τ (4.19) 

h τ [x τ (V τ )]V τ − x τ (V τ ) 

which implies an important consequence. Since the first mover advantage 

represents a strategic advantage for the incumbent monopolist and increases 

its expected profits compared to the outcome without such an advantage, the 

value of being the incumbent monopolist is endogenously increased. 21 But, 

since the value of being the current monopolist is what provides the incentives 

to invest in R&D, also the total investment and the aggregate probability 

of innovation must endogenously increase. More precisely, for every innovation 

except the last one, the value of becoming the incumbent monopolist is 

higher under Stackelberg competition with endogenous entry rather than under 

Marshallian competition. This induces a larger investment by each firm 

and a larger aggregate investment when the incumbent monopolist has a first 

mover advantage. Summarizing, we have: 

Proposition 4.9. With sequential innovations, competition for 

the market with endogenous entry implies that the aggregate probability 

of innovation is higher when the incumbent monopolist has 

a leadership in the patent races. 

The bottom line is that, far from stifling innovation, incumbent monopolists 

facing endogenous entry of competitors enhance aggregate investment 

in R&D. Of course, the first mover advantage of these monopolists is a precondition 

for both a larger investment in R&D and a more likely persistence 

of technological leadership. Therefore, we obtain the paradoxical result for 

which endogenous entry in the competition for the market is associated with 

persistent monopolies. 

Notice that our theory suggests a way to discriminate between different 

degrees of persistence of leadership in innovative sectors. As we have seen, 

when entry of firms in the competition for the market is endogenous we should 

expect that technological leaders invest a lot and their persistence is more 

likely. Of course, when there is no competition for the market we would also 

expect that the leadership is persistent. However, when the degree of competition 

for the market is intermediate, we expect that the incumbent does not 

20 The analysis of sequential patent races in case of entry deterrence can be found in 

Denicolò (2001) in a related framework with linear technology, and an additional 

externality from aggregate investment, and in Etro (2001) within our framework. 

See also Cozzi (2007) for further discussion. 

21 The right hand side of (4.19) is always larger than the right hand side of (4.18).


invest much in R&D and its leadership is more likely to be replaced. This suggests 

an inverted U curve between the degree of persistence of technological 

leadership and the degree of competition for the market. This may explain 

why it is so difficult to find empirical support for the dynamic view of competition 

which suggests that a leadership position should rapidly vanish. 22 In 

the last part of the chapter, we will discuss the relation between competition 

in the market and for the market, and draw some policy implications. 

4.3.2 Endogenous Technological Progress 

In all our static and dynamic description of patent races we have kept exogenous 

the flow of profits obtained by the incumbent monopolists. It is now 

time to endogenize it and, for this purpose, we need to describe explicitly the 

market through which firms exploit their innovations, employ their patents 

and derive their profits. We will do it in a framework where innovations improve 

the productivity of intermediate goods that are used in the production 

of final goods. This implies that the incentives to invest to improve the quality 

of these intermediate goods derive from the profits obtained from sales to 

the market for final goods. 

Following the pathbreaking analysis of Romer (1990), Segerstrom et al. 

(1990) and Aghion and Howitt (1992, 1998), consider a competitive market 

for final goods with a production function as: 23 

Z 

Y = (q τ j 

X j ) α dj (4.20) 

j∈J 

where output Y is produced employing intermediate goods of different kinds 

(from a set J). Each one of these intermediate goods is produced by a monopolist 

with a patent on its leading technology at a constant and unitary 

marginal cost. An infinite sequence of product innovations characterizes these 

intermediate goods: an innovation τ j for the intermediate good j implies that 

X j units of this input are equivalent to qX j units produced with the preexisting 

technology τ j − 1, withq>1/α, which guarantees that the innovation 

is drastic. Demand for an input sold at a price 1+µ j , that is with a mark up 

µ j > 0, canbederivedasD τj = £ αq ατ j /(1 + µ j ) ¤ 1/(1−α) 

.Thisimpliesthat 

the profit maximizing price of a monopolist producing this input would be 

1+µ j =1/α, however, we will maintain a general expression for the equilibrium 

price to encompass alternative assumptions. 24 Since each sector works 

22 See Cable and Mueller (2006). 

23 Other inputs are held constant and normalized to unity for simplicity. As long 

as their markets are perfectly competitive the analysis is not affected by them. 

See Barro and Sala i Martin (1995) for a discussion. 

24 Our result generalizes to non-drastic innovations if Bertrand competition with 

free entry takes place. In such a case, the equilibrium implies limit pricing by


in the same way, in what follows we will disregard the sector index j. Hence, 

each patent τ for any intermediate good gives the right to a flow of profits: 

µ 1 

αq 

ατ 1−α 

K τ = µD τ = µ 

1+µ 

(4.21) 

Suppose that the probability of innovation is given by: 

h τ (x τ )=(φ τ x τ ) (4.22) 

where ∈ (0, 1). To have an idea of the realistic shape of this function, notice 

that the first estimate of the elasticity of the number of innovations with 

respect to investment in R&D by Pakes an Griliches (1980) was 0.6, while 

the time series study of Hausman et al. (1984) estimated an elasticity of 0.87 

using the Poisson distribution, decreased to 0.5 with the larger sample used 

by Hall et al. (1986). More recently, Kortum (1993) suggests a range between 

0.1 and 0.6 and Blundell et al. (2002) find a long-run elasticity close to 0.5. 

Most of these estimates are based on the relation between investment and 

the number of patented innovations, which is not necessarily a good measure 

of innovation (since only a small percentage of patents are really valuable). 25 

Acemoglu and Linn (2004) have focused on the new drugs obtained in the 

pharmaceutical industry (rather than the new patents) obtaining an implicit 

estimate of the elasticity of the innovations with respect to R&D investment 

around 0.8. 

Finally, assume that new ideas are more difficult to obtain when there 

is an increase in the scale of the sector, as represented by expected production 

with the new technology. Furthermore, assume that the fixed cost is a 

constant fraction of the expected cost of production with the new technology. 

Summarizing, assume φ τ =1/ζD τ and F τ = ηD τ /(r + p τ+1 ),where 

ζ>0 and η ∈ (0,µ) parametrize how costly are innovations. With these last 

assumptions we want to capture the idea that the larger is the scale of expected 

production of a firm, the larger are the costs necessary to discover and 

the last innovator (1+µ j = q for any j) and no other firms active in the market. 

Cournot competition with free entry would imply that more than one firm would 

produce intermediate goods, but Stackelberg competition in quantities with free 

entry would result again in having only the last innovator producing for the 

market and obtaining positive profits (something quite similar to the idea of the 

first mover avantage of the innovators in a world without patents advanced by 

Boldrin and Levine, 2005). 

25 Moreover, as Scotchmer (2004) notices, “these estimates should be interpreted 

with caution, due to the noisiness of the data. It is not clear that the estimated 

coefficients address the experiment of increasing the R&D spending in firms, 

since other circumstances of the invention environment change.” See also the 

discussion in Denicolò (2007). Notice that Segerstrom (2007) assumes =0.3 in 

his model.


develop the associated technology (construction of prototypes and samples, 

new assembly lines and training of workers). 26 These ingredients allow us to 

fully characterize the equilibria of the sequential patent races in function of 

the interest rate r. 27 

Under Marshall competition in the patent races the incumbent monopolist 

never invests in R&D and is systematically replaced by a new firm when the 

subsequent innovation is obtained: this process of continuous “leapfrogging” 

between firms implies that monopolies are not persistent and technological 

progress is driven by outsider firms. This is the standard result in the literature 

on Schumpeterian growth (Barro and Sala-i-Martin, 1995; Aghion and 

Howitt, 1998), even if it has little to do with the original ideas of the late 

Schumpeter (1943), for which large established firms are the main drivers of 

innovation and technological progress. The original Schumpeterian characterization 

of the innovation process emerges when Stackelberg competition with 

endogenous entry takes place in the competition for the market: when the 

incumbent monopolist has a first mover advantage in the patent races and 

invests in R&D more than any other firm, its leadership is partially persistent 

and technological progress is driven by both the outsiders and the incumbent 

monopolists. 28 Moreover, as we have seen in the previous section, the partial 

persistence of monopoly associated with this leadership must increase the 

incentives to invest for all firms. 

As long as entry in the competition for the market is free, under both 

forms of competition, the aggregate probability of innovation is positively 

correlated to the mark up and negatively correlated to the interest rate. 

In particular, as shown in the Appendix, in steady state the probability of 

innovation for each patent race is: 

∙ (µ ∗ ¸ ∙ 

− η) (1 − )(µ ∗ − η) 

p = 

+1¸1− 

− r (4.23) 

ζ 

η 

where µ ∗ can be interpreted as the effective gross return on a patent. Under 

Marshall competition this is simply equal to the mark up µ, since this is the 

only gain expected by a patentholder. Under Stackelberg competition, µ ∗ is 

26 See Peretto and Connolly (2005) on the role of these kinds of fixed costs in 

endogenous growth models, and Peretto (2007) for further applications. 

27 Full fledged patent races with decreasing marginal productivity have been introduced 

in the Schumpeterian growth model in Etro (2004). The previous literature, 

starting with the pathbreaking contribution of Aghion and Howitt (1992) 

assumed linear technology of innovation so that a no-arbitrage condition was 

able to pin down the aggregate investment in R&D without any insights on the 

industrial organization of the patent races. For a related treatment of patent 

races in growth models see Zeira (2004). 

28 Here we focus on the case where is realistically low. When is high enough, 

the incumbent monopolist deters entry.


higher and includes the value of a partially persistent leadership, which is 

also increasing in the size of innovations. Summarizing, we have: 

Proposition 4.10. With sequential innovations, competition for 

the market with endogenous entry implies a steady state aggregate 

probability of innovation that is increasing in the mark up on 

patented products and that is higher when the incumbent monopolist 

has a leadership in the patent races. 

The relation (4.23) provides an implicit equilibrium relation between the 

interest rate and the investment in innovation, which is expressed in terms 

of the aggregate probability of innovation that the firms can support. Of 

course, a higher interest rate reduces the incentives to invest in R&D since it 

increases the return on alternative investments. To evaluate the consequences 

for growth, one could endogenize savings of the consumers as a (decreasing) 

function of the interest rate, and determine the equilibrium interest rate that 

clears the credit market (equating investments and savings) and consequently 

the growth rate of the economy. 29 

This framework can be used for a number of macroeconomic experiments, 

that are however beyond the scope of this book. 30 Here,wewillsummarize 

a few results that are relevant for our purposes. First, one can show that the 

decentralized equilibrium is always characterized by dynamic inefficiency becauseofabiasintheR&Dsectortowardfirms 

investing too little - essentially 

because, for a given total investment in R&D, too many firms do research, 

since they do not consider the negative externality induced by their entry on 

the expected profits of the other firms. The presence of incumbent monopolists 

doing a lot of research limits this inefficiency, but does not eliminate it. 

Dynamic inefficiency means that a reallocation of resources in the innovation 

sector (inducing larger research units) could increase both current and future 

consumption, and a consequence of this is that the optimal innovation policy 

29 If the final good is consumed by a representative agent with logarithmic utility, 

the Euler condition for utility maximization implies the growth rate of consumption 

g C = r − ρ, whereρ is the time preference rate. Since the equilibrium 

α 

α 1−α 

production of the final good must amount to Y = 

1+µ 

j∈J q κ j α 

1−α dj,its 

growth rate can be approximated as g Y =(pα ln q) /(1 − α). Equating these two 

expressions for the unique steady state growth rate, one obtains an implicit expression 

for the savings that the agent is willing to provide at a given interest 

rate, expressed in terms of the aggregate probability of innovation that these 

savings can support p =(1− α)(r − ρ) /α ln q. Equating this with (4.23) one 

obtains the equilibrium interest rate, and consequently the general equilibrium 

growth rate of the economy. 

30 On macroeconomic policy and the effect of aggregate demand shocks in this 

framework see Etro (2001).

4.4 Competition in the Market and Competition for the Market 159 

requires always R&D subsidies. 31 Nevertheless, the equilibrium growth rate 

may well be below its socially optimal level (essentially because the private 

value of innovations can be lower than their social value), therefore the optimal 

innovation policy may require also subsidies to entry in the competition 

for the market. 

Segerstrom (2007) has introduced the possibility of imitation by the followers 

(which drives industry profits to zero), showing that an increase in 

the probability of imitation can increase the incentives to invest of the leader 

whose innovation has been copied (through a sort of escape competition effect), 

but it reduces the value of the endogenous leadership and hence the 

aggregate incentives to invest (that are always determined by the free entry 

condition for the outsiders in the competition for the market). 

One can also explore in more details the markets for inputs, which we assumed 

to be perfectly competitive in our discussion, 32 and introduce other 

forms of productivity growth to study their impact on the innovation activity 

in general equilibrium. 33 Finally, one could also extend the analysis to a 

multicountry framework to study global growth and the difference between 

strategic (unilateral) innovation policy and optimal international coordination 

of the same policy (in terms of R&D subsidies and protection of IPRs 

as well). 34 

4.4 Competition in the Market and Competition for the 


The basic theories of innovation, as those described until now, suggest that 

competition in the patent races increases investment in R&D, but also the 

31 See Etro (2007a). The interesting work of Minniti (2006) has introduced the 

first complete analysis of multiproduct firms in the Schumpeterian framework, 

showing that the equilibrium is characterized by too many firms (too much interfirm 

diversity) and too few products per firm (too little intra-firm diversity). On 

the effectiveness of R&D subsidies in promoting investment in innovation see the 

empirical work of Aerts and Schmidt (2007). 

32 See Koulovatianos (2005) and Grieben (2005). 

33 In general, an increase in an exogenous growth rate of total factor productivity 

has a positive direct effect (since directly enhances the value of innovations) and a 

negative general equilibrium effect due to the increase in the interest rate (needed 

to increase savings to sustain a higher growth). This implies that an increase in 

total factor productivity growth increases the growth rate of the economy, but 

has an ambiguous impact on the percentage of income spent in R&D activity. 

This may explain the lack of a clear correlation between R&D per capita and 

growth over time and across countries (see Scotchmer, 2004, Ch. 9). For related 

investigations see Kornprobsty (2006). 

34 See Etro (2007a), and Impullitti (2006 a,b, 2007).


market power of the innovators in the product market is positively related 

with investment in R&D. While the firstresultisconsistentwiththeevidence, 

the second one is, to some extent, at odd with empirical evidence. This shows 

a positive relation between competition and technological progress (Blundell 

et al., 1999), or at most a non monotone relation, positive for low levels of 

competition and negative for high levels (Aghion et al., 2005). 

Aghion and Griffith (2005) have provided a possible explanation for this 

relation in a model of Schumpeterian growth with exogenous innovation by 

leaders. They consider step by step innovations, that is they assume that 

frontier technologies can be used by their developers while other firms have 

to develop them before trying to expand the frontier. In this set up, tougher 

competition may increase the incentives of the leaders to innovate with the 

aim of escaping competition. The intuition of this “escape competition effect” 

is simple because, as usual, the incentives to invest for the leaders depend on 

the difference between the profits with innovation and those without innovation: 

competition reduces both, but tends to reduce more the profits of a 

leader that does not innovate, since a leader that obtains a drastic innovation 

is less constrained by competition. 35 

While this theory is fascinating, it is not entirely convincing. In particular, 

Aghion and Griffith (2005) do not derive innovation by leaders endogenously, 

but assume that the technological leaders invest in innovation and 

there is not entry of outsiders in the competition for the market. 36 Since we 

have seen that innovation by incumbent monopolists emerges endogenously 

exactly when there is free entry in the competition for the market and the incumbents 

are leaders in this competition, leaving entry aside does not appear 

neutral: the escape competition effect heavily depends on the hypothesis that 

the leaders undertake the research activity, since standard incentives would 

drive the investment of the outsiders (namely less investment when competition 

is tougher). As we have noticed in a number of models, the escape 

competition effect works when competition for the market is exogenously 

limited, but when competition for the market is free we noticed that the behavior 

of outsiders determines the rate of innovation (constraining in a way 

or another the strategy of the leaders), and the escape competition effect 

vanishes. Finally, Aghion and Griffith (2005) do not associate the intensity 

of competition with more competitive structures in the product market, but 

with a lower price of the competitive fringe of firms, with a higher probability 

of entry (see also Aghion et al., 2006) or with other exogenous elements. The 

crucial interaction between competition in the market and for the market 

35 This does not happen always but just when firms are neck-and-neck, that is 

when the technology of the leader is similar to that of the other firms and the 

leader has strong incentives to escape competition. The result is strengthened 

when competition increases the fraction of neck-and-neck sectors. 

36 Aghion et al. (2005) augment the model with a single follower, but still without 

free entry in the competition for the market.

4.4 Competition in the Market and Competition for the Market 161 

remains to be studied for the escape competition effecttobeconvincingfrom 

a theoretical point of view. 

Denicolò and Zanchettin (2006) adopt an alternative approach and compare 

alternative forms of competition in the market for intermediate goods 

when innovations are non drastic. They describe a sort of “Darwinian selection 

effect” induced by competition. When this is weak many inefficient firms 

can be active in the product market, while tough competition is consistent 

with just few efficient firms. In other words, when the intensity of competition 

increases, inefficient firms have to exit the market leaving the most efficient 

ones in it. Moreover, this process gradually shifts profits from less efficient 

to more efficient firms (“front-loading effect”), that are the most recent innovators. 

As a result of these effects, industry profits for the efficient firms 

may increase in such a way that also the incentives to invest in R&D are 

strengthened. 

More formally, let us extend our model of section 4.3.2 with different 

forms of competition in the market for intermediate products. In case of 

innovations of limited size (q 1, and it is easy to verify that with our demand function this leads to the 

equilibrium price 1+µ =(1+q)/(1+α). This price is always higher than the 

limit price under Bertrand competition 1+µ = q, but may generate lower 

industry profits and lower profits for the technological leader, because part 

of the production of the latest innovator is replaced by the production of a 

less efficient firm.Thisalwayshappenswhenq is close to the monopolistic 

price 1/α, since industry profits under Bertrand competition remain close to 

their monopolistic level, while industry profits (and the profits of the latest 

37 As we know by now, a leadership for the latest innovator also in the product 

market competition would lead to limit pricing as well, leaving our analysis 

unchanged again.


innovator) under Cournot competition have a first order reduction due to the 

entry of a less efficient firm. 38 

More in general, whenever industry profits are lower with Cournot competition 

than with Bertrand competition, and they are shifted toward the less 

efficient firms, the incentives to innovate are lower as well - even if Cournot 

competition generates higher prices than Bertrand competition. In particular, 

in our duopolistic example, the value of becoming the last innovator is a 

weighted discounted average of the profits expected as a producer with the 

leading technology and with the second best technology (once a better one is 

invented), and under Marshall competition in the patent races, this value is 

what drives the investment of the outsiders (current producers do not invest 

because of the Arrow effect once again). 

Denicolò and Zanchettin (2006) show that the same positive relation between 

the intensity of competition and growth can emerge when there is 

endogenous persistence of technological leadership due to Stackelberg competition 

with endogenous entry in the patent races. As we have seen before, 

non drastic innovations that give raise to duopolies between the last two 

innovators do not affect the general principle for which the leader invests 

more than any other firm. Denicolò and Zanchettin focus on the extreme 

case where only the last innovator invests ( =1) and the persistence of 

technological leadership is complete. Notice that the incentives to invest of 

the outsiders determine the entry deterrence investment of the technological 

leader and those incentives depend again on a weighted discounted average 

of the expected profits in the potential duopoly. This implies that, under the 

same circumstances as before, Cournot competition in the product market 

leads to lower industry profitsandlowerinvestmentsinR&DthanBertrand 

competition. Nevertheless, in this case duopolistic competition in the market 

for intermediate goods does not take place in equilibrium since all innovations 

are due to a single leading firm with eternal leadership. Similar results 

are likely to emerge in the more realistic case where investment by outsiders 

takes place and the persistence of technological leadership is only partial. 


In their Epilogue, Aghion and Griffith (2005) address some policy issues and 

emphasize two contrasting views: 

“some commentators have argued there is a specificity of innovative 

markets with respect to competition. They see the role of 

antitrust action in innovative sectors as one of counteracting incumbent 

firms that try to prevent innovation by new entrants by issuing 

38 Denicolò and Zanchettin (2006) prove that this outcome emerges under more 

general conditions.


and accumulating (unjustified) patents. In other words, antitrust action 

should focus on fostering competition for the market, but not 

so much on increasing competition in the market, since this would 

reduce innovation incentives by reducing rents. In innovative markets 

where incumbents innovate, antitrust action should be restrained so 

as not to stamp out monopoly power in such markets. Instead, our 

analysis suggests that stimulating competition in the market, especially 

in sectors that are close to the corresponding world frontier 

and/or where incumbent innovators are neck-and-neck, can also foster 

competition for the market through the escape competition effect. 

Incumbent firms innovate precisely as a response to increased product 

market competition or to increased entry threat, at least up to 

some level.” 39 

We are not sure that this distinction is properly motivated. First, we 

do believe that there is a specificity of innovative markets with respect to 

competition, because firms in high-tech markets compete mainly with investments 

to create better products rather than with standard price strategies, 

and this should be taken into account. Second, we do not see any contradiction 

between the claim of the theory of market leaders and endogenous entry 

for which strong competition for the market enhances technological progress 

and the fact that competition in the market may enhance it as well under 

certain conditions: when this is the case, antitrust policy should be aimed at 

promoting both forms of competition in innovative markets. Nevertheless, we 

have shown that when competition for the market is characterized by endogenous 

entry (and by a leadership position), the incentives to invest in R&D 

are maximized and there is a limited space for competition in the market to 

enhance investment: to a large extent, competition for the market is a good 

substitute for competition in the market in dynamic sectors. 

An interesting exception to this principle derives from the Darwinian selection 

effect, which implies that tougher product market competition can endogenously 

exclude inefficient firms from production and constrain the price 

of the efficient ones, while still promoting innovation (of the most efficient 

firms) through the gains in production efficiency. 40 

Finally, it is clear, and in no way contradicted by the results of Aghion and 

Griffith (2005), that the ultimate engine of market-driven innovations is associated 

with the possibility of exploiting the fruits of uncertain investments 

through intellectual property rights. Therefore, we believe that a main policy 

implication of this research is that antitrust policy should promote competi- 

39 Aghion and Griffith (2005, p. 91) associate the two positions respectively with 

Etro (2004) and Vickers (2001). 

40 This is another case in which competition leads to exit of the competitors of the 

leader, but it enhances consumer welfare as well.


tion both for and in the market, 41 but should never interfere with the legal 

protection of patents and trade secrets, which drive the private incentives to 

invest in R&D. 

With this chapter we have concluded the theoretical part of the book. 

In the following chapters we will move on to the policy implications of the 

theories we have examined. 

41 For a policy analysis on the benefits of product market reform taking in considerations 

the effects on innovation see Faini et al. (2006), Parascandolo and 

Sgarra (2006), Barone and Cingano (2007) and Leiner-Killinger et al. (2007).


4.6 Appendix 

ProofofProp.4.2.Imagine that the social value of the innovation is V ∗ . 

Under Marshall competition with n firms investing x each, welfare is: 

W N = nh(x)V ∗ 

− nx − nF 

r + nh(x) 

Under Stackelberg competition with a leader investing x M and n s −1 followers 

investing x, usingthefactthatnh(x) =h(x M )+(n s − 1)h(x), wehavean 

increase in welfare: 

W S = [h(x M)+(n s − 1)h(x)] V ∗ 

r + h(x M )+(n s − 1)h(x) − x M +(n s − 1)x − n s F 

= W N + (x + F )(x ∙ 

M + F ) h(xM ) 

h(x) x M + F − h(x) ¸ 

>W N 

x + F 

since the second term is positive because x M >x. Notice that this second 

term corresponds to the expected profit of the leader from the patent race. 

Q.E.D. 

ProofofProp4.5.Symmetry between the entrants in the second stage 

implies the equilibrium system: 

f(·) ≡ [h 0 (x)V − 1] [r +(n − 1)h(x)+h(x M )] − h 0 (x)[h(x)V − x] =0 

g(·) ≡ [h 0 (x M )V − 1] [r +(n − 1)h(x)+h(x M )]+ 

∙ 

− h 0 (x M )+ ∂nh(x) ¸ 

[h(x M )V + K − x M ]=0 

∂x M 

with ∂nh(x)/∂x M = nh 0 (x)φ 0 (x M ) where x = φ(x M ) is the common reaction 

function for x as a function of x M and increasing in it: 

φ 0 (x M )= 

− [h 0 (x M )V − 1] h 0 (x M ) 

h ” (x) {V [r +(n − 1)h(x)+h(x M )] + x} 

Since ∂φ 0 (x M )/∂r < 0, ∂φ 0 (x M )/∂K =0and ∂φ 0 (x M )/∂n > 0 , while 

the sign of ∂φ 0 (x M )/∂V is ambiguous, by totally differentiating the system 

above we obtain the comparative statics for y = r, n, K, V : 

" # 

dx 

dy 

dx M 

= − 1 ∙ 

gxM 

dy 

∆ 

¸ ∙ ¸ 

−f xM fy 

−g x f x g y 

where ∆ ≡ f x g xM − f xM g x > 0 by assumption of stability, and assuming 

f x < 0 and noting that f xM > 0, f r > 0, f K =0, f n > 0, f V > 0, g x > 0, 

g xM < 0, g r > 0, g K < 0 while g n and g V have the only ambiguous signs. It 

follows that comparative statics for n and V is ambiguous, but dx M /dr > 0, 

dx/dr > 0, dx M /dK < 0, anddx/dK < 0. Q.E.D.


ProofofProp.4.6: To complete the proof we need to rigorously show 

that the choice of the leader is indeed a global maximum, or, in other words, 

that the option of zero investment is dominated by that choice. If we use the 

equilibrium free entry condition of the second stage to rewrite the objective 

function of the leader as: 

Π L h(x M )V + K − x M 

= 

[r +(n − 1) h(x)+h(x M )] − F = h(x M)V + K − x M 

F − F 

h(x)V − x 

we notice that the local maximum satisfying the first order equilibrium condition 

h 0 (x M ) V =1is a global maximum if: 

h(x M )V +K−x M 

h(x)V −x 

F − F> 

K 

h(x)V −x F ⇔ 

h(x M )V −x M 

h(x)V −x 

> 1 

but this is always true since we know that h(x M )V − x M >h(x)V − x. The 

last part follows noticing that nh(x) =h(x M )+(n s − 1)h(x) implies: 

nx − [x M +(n s − 1)x] = h(x M)x 

− x M = x ∙ 

Mx h(xM ) 

− h(x) ¸ 

< 0 

h(x) 

h(x) x M x 

since h 00 (x) < 0. Q.E.D. 

ProofofProp.4.9.Consider first the case of Marshall competition 

in each patent race, so that incumbent monopolists do not invest and are 

replaced at each innovation. Under our functional form assumptions every 

patent race will be characterized by an investment for each outsider: 

x τ = 1 

τ (V τ − F τ ) 1− 

1 

and by a zero profit condition: 

(φ τ x τ ) V τ − x τ 

= F τ 

r + p τ 

The value of innovation is simply: 

V τ = 

µD τ 

r + p τ+1 

 

1− φ 

1− 

where D τ is the demand of the corresponding intermediate good sold to the 

final good sector as in (4.21). Solving the endogenous entry condition we 

have: 

r + p τ = (φ τ x τ ) V τ − x τ 

F τ 

= 

= [(φ 

1− 

τ )(V τ − F τ )] V τ − 1 1− 

τ (V τ − F τ ) 1 

1− 

= 

F τ 

1− φ 

 

= (/ζ) 

1− 

(µ − η) 

1− [µ − (µ − η)] 

η (r + p τ+1 ) 

1−


which shows a negative relation between probabilities of innovation of subsequent 

patent races, exactly as in the model of sequential patent races with 

an exogenous flow of profits for each innovation. Focusing on the steady state 

with a constant probability of innovation p, wecansolvetheaboverelation 

for the effective discount factor in steady state, r + p, thatsatisfies: 

(r + p) = (/ζ) 

1− 

(µ − η) 

1− [µ − (µ − η)] 

η (r + p) 

1− 

from which we obtain: 

∙ ¸ ∙ (µ − η) µ(1 − )+η 

r + p = 

ζ 

η 

¸1− 

This is increasing in the mark up, and it allows to derive explicitly the investment 

for each firm: 

µ ∙ ¸ 1 

x τ = 1 

1− 

1 

1− 1− 

(µ − η) D τ = 

ζD τ r + p τ+1 

= η (µ − η) D τ 

µ − (µ − η) 

that is increasing in the mark up and also in the size of demand for the 

corresponding product. The explicit equilibrium expression for the value of 

innovations is: 

V τ = 

µ (ζ/) η 1− D τ 

(µ − η) [µ(1 − )+η] 1− 

Consider now the case of Stackelberg competition with endogenous entry. 

In each patent race we still have the same general rules for the investment of 

the outsiders in function of the value of innovation, and the same free entry 

condition as before. However, also the incumbent monopolist participates to 

the patent race, investing according to the following rule: 

x Mτ = 1 

 

1 

1− φ 

1− 

τ V τ 

1− 

and the value of being a monopolist with the patent τ − 1 is now given by 

the following recursive relation: 

V τ−1 = (φ τx Mτ ) V τ + K τ−1 − x Mτ 

r + p τ 

− F τ 

While this is general a complex relation, our modeling assumptions on technological 

progress allow us to derive a complete solution. First of all, notice 

that free entry by the outsiders determines the aggregate probability of innovation 

in each patent race independently from the behavior of the incumbent, 

while the value of innovation depends on the behavior of the leader as well.


The profit function of the producers of intermediate goods implies that 

demand increases in a deterministic way through subsequent innovations: 

D τ = q α/(1−α) D τ−1 . Because of this, it turns out that also the value of 

innovation increases at the same rate between subsequent innovations. We 

can solve for this using the method of undetermined coefficients. Guessing a 

functional form V τ = ψD τ /(r + p τ+1 ) we have also: 

1−α α 

Dτ 

V τ−1 = ψq− 

r + p τ 

Substituting the equilibrium investment of the incumbent monopolist in the 

recursive relation above, we obtain: 

i h(φ τ ) 1 1 

1− 

V τ 

1− Vτ + K τ−1 − 1 

1 

1− φ 

1− 

τ V τ 

1− 

V τ−1 = 

− ηD τ 

r + p τ r + p τ+1 

Equating the two expressions for V τ−1 and solving in steady state we have: 

µ " 

p = 

ζ 

(1 − ) q α 

1−α 

ψ − µ + ηq α 

1−α 

# 1− 

ψ − r 

which provides a negative relation between the aggregate probability of innovation 

p and the rate of return from the leadership ψ (for ψ small enough): 

the higher is the probability of innovation, the shorter is the lifetime of an 

innovation, and, consequently, the lower is the value of being a leader. 

Moreover, using again our guess, we can solve for the free entry condition 

fortheoutsidersasbefore: 

∙ ¸ ∙ ¸1− (ψ − η) ψ(1 − )+η 

p = 

− r 

ζ 

η 

This is a positive relation between the aggregate probability of innovation p 

and the rate of return from leadership ψ: the higher is the value of being a 

leader, the larger will be the investment in R&D and hence the probability 

of innovation. 

Finally, putting together these last two relations we can derive an implicit 

expression for the equilibrium value of ψ: 

ψ(µ) =µ + 

(1 − ) ηq 1−α α 1 

ψ 

1− 

(ψ − η) 

1− 

[ψ(1 − )+η] − ηq α 

which must be larger than µ for our guess to be consistent (otherwise the 

incumbent monopolist would not find it convenient to invest), which can be 

verified to be the case for a wide set of parameter values. 

To close our equilibrium description, the investments of the incumbent 

monopolists and of each outsider for any patent race are: 

1−α


x Mτ = 

ηψD τ 

ψ − (ψ − η) 

x τ = η (ψ − η) D τ 

ψ − (ψ − η) 

where the first is 1/(1 − η/ψ) times the second. The expression for the aggregate 

probability of innovation can be obtained with µ ∗ = µ in case of 

Marshall equilibrium and µ ∗ = ψ in case of Stackelberg equilibrium with 

endogenous entry. Q.E.D.

5. Antitrust and Abuse of Dominance 

The scope of antitrust policy is to avoid distortions of competition that may 

negatively affect consumers, like collusive arrangements aimed at fixing prices 

above their competitive level, mergers aimed at creating a dominant position, 

and abuse of dominance by market leaders against the interests of consumers. 

Given the particular focus on market leaders in this book, our attention in 

this chapter will be mainly on the last aspect of antitrust policy: abuse of 

dominance with anticompetitive purposes. 1 

In the United States the main federal antitrust statute is the Sherman Act 

of 1890, which was developed in reaction to the widespread growth of large 

scale business cartels and trusts. Section 1 of the Sherman Act prohibits restraints 

of trade in general, while Section 2 deals with monopolization stating 

that: 

“Every person who shall monopolize, or attempt to monopolize, or 

combine or conspire with any other person or persons, to monopolize 

any part of trade or commerce among the several States, or with 

foreign nations, shall be deemed guilty of a felony”. 

Enforcement at the federal level is shared by the Antitrust Division of the 

Department of Justice and by the Federal Trade Commission. The current 

interpretation of US antitrust law associates abusive conduct with predatory 

or anticompetitive actions having the specific intent to acquire, preserve or 

enhance monopoly power distinguished from acquisition through a superior 

product, business acumen or historical accident (hence monopoly per se is 

not illegal). It is generally accepted that an action is anticompetitive when it 

harms consumers. 

In Europe, competition policy has a more recent history which is mostly 

associated with the creation of the European Union and its coordination of 

policies for the promotion of free competition in the internal market. The 

main provisions of European Competition Law concerning abuse of domi- 

1 On the first two aspects of antitrust, see Motta (2004, Ch. 4-5) for a wide survey 

of the economic literature, and Sections 2.13 and 3.5 for some implications of 

the endogenous entry approach. Recently, Rhee (2006) has applied aspects of the 

theory of market leaders to merger policy for the New Economy.

172 5. Antitrust and Abuse of Dominance 

nance are contained in the Article 82 of the Treaty of the European Communities 

which states that: 

“Any abuse by one or more undertakings of a dominant position 

withinthecommonmarketorinasubstantialpartofitshallbeprohibited 

as incompatible with the common market in so far as it may 

affect trade between Member States. Such abuse may, in particular, 

consist in: (a) directly or indirectly imposing unfair purchase or selling 

prices or other unfair trading conditions; (b) limiting production, 

markets or technical development to the prejudice of consumers; (c) 

applying dissimilar conditions to equivalent transactions with other 

trading parties, thereby placing them at competitive disadvantage; (d) 

making the conclusion of contracts subject to acceptance by other parties 

of supplementary obligations which, by their nature or according 

to commercial usage, have no connection with the subject of such 

contracts.” 

This article on abuse of dominance is part of the law of each member 

state and is enforced by the European Commission and by all the National 

Competition Authorities (as Article 81 on horizontal and vertical agreements 

and the Merger Regulation). 2 The application of EU competition law on 

abuse of dominance involves the finding of a dominant position and of an 

abusive behavior of the dominant firm, usually associated with exploitative 

practices such as excessive pricing, 3 and with exclusionary practices such 

as predatory pricing, rebates, tying or bundling, exclusive dealing or refusal 

to supply. However, the analysis of both dominance and abusive behaviors 

entails complex economic considerations and its reform in the EU is the 

subject of an ongoing debate. 

Many economists have pointed out the necessity of a closer focus on consumer 

welfare in the implementation of competition policy with specific reference 

to abuses of dominance. While antitrust legislation was written with this 

objective in mind, its concrete application has sometimes been biased against 

market leaders and in defense of their competitors rather than toward the 

defense of competition and of the interests of consumers. The two objectives 

do not necessarily overlap. The development of the New Economy, characterized 

by very dynamic and innovative markets, has increased the pressure 

for a new approach, already somewhat developed in the United States, and 

in progress in Europe. An important EU Report by Rey et al. (2005), has 

2 TheCommissionactsbothasaprosecutorandjudgeatafirst level. The Court 

of First Instance has jurisdiction in all actions brought against the decisions of 

the Commission, while the European Court of Justice decides on appeal actions 

brought against the judgments of the Court of First Instance. Motta (2004) 

provides a careful treatment of competition policy in the EU. For a non-technical 

treatment see Riela (2005). 

3 On this point see Katsoulacos (2006).

5. Antitrust and Abuse of Dominance 173 

recently argued in favor of an effects-based approach to competition policy, 

which associates abuses of dominant positions with anti-competitive strategies 

that harm consumers. 

In line with this proposal, we believe that a new approach to competition 

policy should be based on rigorous economic analysis, from both a theoretical 

and an empirical point of view. Rey et al. (2005) emphasize this element in 

the antitrust procedure: 

“a natural process would consist of asking the competition authority 

to first identify a consistent story of competitive harm, identifying 

the economic theory or theories on which the story is based, as 

well as the facts which support the theory as opposed to competing 

theories. Next, the firm should have the opportunity to present its 

defence, presumably to provide a counter-story indicating that the 

practice in question is not anticompetitive, but is in fact a legitimate, 

perhaps even pro-competitive business practice.” 

Moreover, any theory of the market structure able to provide guidance 

in detecting abuses of dominant positions should take into account the role 

and the strategies of market leaders, describe the equilibrium outcomes as a 

function of the entry conditions and of the demand and supply conditions, 

and provide welfare comparisons under alternative set-ups. 

In this chapter we will try to argue that, while the Chicago school and 

the post-Chicago approach had problems in providing a unified framework 

which matches these requirements, the theory of market leaders formalized 

in the previous chapters has provided alternative insights that may be useful 

for this purpose. The general principle derived until now is that market 

leaders may behave in an anti-competitive way, accommodating or predatory, 

in markets where the number of firms is exogenous (meaning that outsiders 

cannot overcome barriers to entry even when there are profitable opportunities), 

while they always behave in an aggressive way when entry into the 

market is endogenous (meaning that it depends on the profit opportunities). 

In the first situation a large market share of the leader can be the fruit of 

anti-competitive strategies, but in the second situation a large market share 

of the leader is a consequence of its aggressive strategies and of the entry conditions, 

and not of market power. Therefore, there should be no presumption 

of a positive association between market shares and market power unless the 

lack of free entry conditions has been established. 

This has a main implication: while the old approach to abuses of dominant 

positions needs to verify dominance through structural indicators and 

the existence of a certain abusive behavior, a new economic approach would 

simply need to verify the existence of harm to consumers. As Rey et al. (2005) 

correctly point out, “the case law tradition of having separate assessments 

of dominance and of abusiveness of behavior simplifies procedures, but this 

simplification involves a loss of precision in the implementation of the legal


norm. The structural indicators which traditionally serve as proxies for ‘dominance’ 

provide an appropriate measure of power in some markets, but not 

in others”, in particular not in markets where entry is an important factor 

(a concentration index is uniquely concerned with actual competition and 

ignores potential competition) and when innovation is important (a concentration 

index can deal with competition in the market, not for the market). 

In this chapter we review the traditional approaches to antitrust analysis 

in Section 5.1 and the market leaders approach in Section 5.2, while Section 

5.3 contains a digression on the protection of IPRs. We apply our results to 

a profound policy oriented discussion in Section 5.4 and conclude in Section 

5.5. 

5.1 The Traditional Approaches to Abuse of Dominance 

In this section, we review some aspects of the traditional approaches to antitrust 

policy on abuse of dominance and start comparing them with the 

insights of the recent theoretical attempts to build a comprehensive theory 

of market leadership and competition policy. 

5.1.1 The Chicago School 

The so-called pre-Chicago approach was mostly based on the simplistic insights 

of the early studies on imperfect competition, which associated monopolistic 

behavior and abusive conduct with firms having large market shares. 

Such a naïve view has been challenged since the 50s- 60s by what we now call 

the “Chicago school”, led by Aaron Director and other exponents of the Law 

School of the University of Chicago, whose main merit has been to introduce a 

systematic economic approach to antitrust - as opposed to what Posner (2001) 

calls the “populist” approach and Bork (1993) associates with a “farrago of 

amorphous and leftist political and sociological propositions”. 4 While the 

Chicago school was seriously attacking collusive agreements as conducive to 

large welfare losses, it was less critical of mergers and exclusionary practices. 

Many scholars were (and still are) convinced that, when there are potential 

entrants in a given sector, mergers are mostly aimed at creating beneficial 

4 Bork (1993) cites the following two primary characteristics of the early Chicago 

school. “The first is the insistence that the exclusive goal of antitrust adjudication, 

the sole consideration the judge must bear in mind, is the maximization of 

consumer welfare. The judge must not weigh against consumer welfare any other 

goal, such as the supposed social benefits of preserving small businesses against 

superior efficiency. Second, the Chicagoans applied economic analysis more rigorously 

than was common at the time to test the propositions of the law and to 

understand the impact of business behavior on consumer welfare” (p. xi).

5.1 The Traditional Approaches to Abuse of Dominance 175 

cost efficiencies, while aggressive strategies such as bundling, price discrimination 

and exclusive dealing, are not necessarily anti-competitive but may 

instead have a strong efficiency rationale behind them. For instance, bundling 

is typically used for price discrimination purposes and not for exclusionary 

purposes. Moreover, according to a widespread view in the Chicago school, 

there is no such a thing as predatory pricing, which is a reduction of the 

price below cost to induce exit by the competitors in order to compensate for 

the initial losses with future monopolistic profits. The main reason is that, if 

the predator can sustain such initial losses, any other prey can also sustain 

the induced losses (which are smaller since its output is lower) as long as 

credit markets are properly working, therefore predatory pricing would not 

be effective to start with. 5 

More recently, Posner (2001) has taken a less extreme position, claiming 

that: 

“there is an economic basis for concern with at least some exclusionary 

practices, in at least some circumstances; and a few practices 

that are not exclusionary (though so classified in the law), like 

persistent price discrimination, may still be undesirable on strictly 

economic grounds” (Posner, 2001, p. 4) 

Accordingly, Posner proposes a moderate standard for judging practices 

claimed to be exclusionary: 

“in every case in which such a practice is alleged, the plaintiff 

must prove first that the defendant has monopoly power and second 

that the challenged practice is likely in the circumstances to exclude 

from the defendant’s market an equally or more efficient competitor. 

The defendant can rebut by proving that although it is a monopolist 

and the challenged practice exclusionary, the practice is, on balance, 

efficient” (ibidem, pp. 194-5). 

This efficiency defense is at the basis of the rule of reason approach, for 

which a business practice is not per se illegal, but can be justified if it does 

not harm consumers or creates efficiencies. 

In the modern economic debate, the Chicago school has been criticized for 

failing to provide results that were robust enough to withstand full-fledged 

game theoretic analysis of dynamic competition between incumbents and 

5 See McGee (1958) on the Standard Oil Trust (1911), a famous US case of predatory 

pricing which led to the break up of the Rockefeller’s oil refining company 

into thirty four small companies. Beyond what pointed out in the text, another 

reason why firms should not engage in predatory pricing is that a merger would 

be a better solution. Of course this alternative is not viable if the merger is prohibited 

by the same antitrust law (but in the US, mergers capable of reducing 

competition became the subject of antitrust investigations only after the Clayton 

Act of 1914).


entrants. The so-called “post-Chicago” approach has shown that in the presence 

of strategic asymmetries between incumbents and entrants and pervasive 

market imperfections, strategies such as price-cuts, bundling or vertical restraints 

can be anti-competitive because they can successfully deter entry 

in the short run and protect monopolistic rents in the long run. Broadly 

speaking, US antitrust authorities have been highly influenced by all of these 

approaches over time, while it is hard to claim that the same is true of 

the EU antitrust authorities. It has recently been pointed out by Ahlborn 

et al. (2004) that “in Europe it has taken longer for new developments in 

economic theory to affect competition policy. While U.S. antitrust has been 

influenced by Chicago school and post-Chicago school theories, pre-Chicago 

school considerations still play a role in Europe, albeit at times dressed up 

in post-Chicago clothing”. 6 

We believe that the Chicago school provided fundamental insights into 

many antitrust issues, but it failed to provide a complete understanding of 

the behavior of market leaders. In particular, it limited most of its analysis 

to the understanding of how monopolistic and perfectly competitive markets 

work, and in a few cases it focused on markets characterized by a monopolist 

facing a competitive fringe of potential entrants. 7 Dismissing the useful 

progress in the applications of game theory, the Chicago school ignored the 

important role of the strategic interactions between incumbents and entrants. 

Consequently, its approach to exclusionary practices has often been biased 

toward a competitive role of the incumbents without an updated theoretical 

support. 

5.1.2 The Post-Chicago Approach 

In the 80s, while the Chicago school was succeeding in reducing the enforcement 

attitudes of US antitrust law, especially under the Reagan Administration, 

a new school of thought started to expand its influence between economists 

and, in the following decade, also between antitrust scholars. The socalled 

post-Chicago approach introduced new game theoretic tools to study 

complex market structures and derive sound normative implications, which 

6 A symptom of the pervasive European approach, which is more against market 

leaders than in favor of free entry, emerges in basic business and industrial 

regulation. For instance, in many European countries the development of large 

chains of supermarkets is condemned as an unfair threat to small retail businesses. 

Similarly, it is hard to liberalize entry in the markets for taxicabs even if 

the efficiency gains for the consumers would be quite clear. 

7 Somewhatrelatedtothisliteratureisthe theory of contestable markets by Baumol 

et al. (1982), which, however, was mostly limited to simple forms of price 

competition with homogenous goods. The theory of Stackelberg competition with 

endogenous entry generalizes that theory to product differentiation and other 

forms of competition.

5.1 The Traditional Approaches to Abuse of Dominance 177 

represents one of the main contributions of this line of research. With reference 

to exclusionary practices, the post-Chicago approach has shown that in 

thepresenceofstrategiccommitmentsto undertake preliminary investments, 

of asymmetric information between firms, of credit market imperfections or 

in the presence of limited forms of irrationality, predatory pricing can be 

an equilibrium strategy for the incumbent, can deter entry and it can harm 

consumers. Similarly, it has shown that bundling can be used to strengthen 

price competition and exclude a rival from a secondary market. Analogously, 

many other strategies can have an exclusionary purpose. 

One should keep in mind that many of the results of the post-Chicago 

approach (summarized in the early but still unsurpassed work of Tirole, 

1988) are quite weak, and they largely depend on a number of restrictive 

assumptions. For example, predatory pricing has been shown to be exclusionary 

under extreme circumstances, including forms of irrational behavior 

(in reputation models) or pervasive market imperfections, and, even when 

exclusion emerges under more plausible conditions, it is not necessarily associated 

with a pricing below cost or even with reductions in consumer welfare 

(in signalling models), which is what should matter in drawing antitrust implications. 

Nevertheless, the intellectual achievements of the post-Chicago 

approach, especially the introduction of game theory as the ultimate tool of 

industrial organization and the proof of the possibility of profitable exclusionary 

strategies, are remarkable. 

Our critique of the post-Chicago approach is not focused on its game theoretic 

foundation or on its specific results, but on the general applicability of 

these results for policy purposes. In most cases, the modern game theoretic 

literature in industrial organization has studied the behavior of incumbent 

monopolists facing a single potential entrant. To cite the most known theoretical 

works with strong relevance for antitrust issues, this was the case of the 

Dixit (1980) model of entry deterrence, of the models by Kreps and Wilson 

(1982) and Milgrom and Roberts (1982) of predatory pricing, by Fudenberg 

and Tirole (1984) and by Bulow et al. (1985) on strategic investment, by 

Brander and Lewis (1986) on strategic debt financing, by Rey and Stiglitz 

(1988) and Bonanno and Vickers (1988) on vertical restraints, by Whinston 

(1990) on bundling for entry deterrence purposes, and many other subsequent 

works based on the analysis of duopolies with an incumbent and an 

entrant. 8 Most of the standard results on the behavior of incumbents in terms 

of pricing, R&D investments, mergers, quality choices and vertical and horizontal 

differentiation are derived in duopolistic models, where the incumbent 

chooses its own strategies in competition with a single entrant. While this 

analysis simplifies the interaction between incumbents and competitors, it 

can be highly misleading, since it assumes away the possibility of endogenous 

entry, and hence limits its relevance to situations where the incumbent 

already has an exogenous amount of market power. 

8 See Motta (2004) and Whinston (2006) on the post-Chicago approach.


It is not surprising that the results of the post-Chicago approach are 

often biased toward an anti-competitive role of the incumbents: these incumbents 

engage in predatory pricing, threaten or undertake overinvestments in 

complementary markets and patent new technologies only to preempt entry, 

impose exclusive dealing contracts, or bundle their goods with the sole 

purpose of deterring the entry of the competitor. Otherwise they are accommodating, 

engaging in excessive pricing or in anticompetitive mergers aimed 

at increasing prices, or stifling innovation to preserve their power. In such a 

simple scenario, what antitrust authorities should do is unambiguously fight 

against incumbents: punish their aggressive pricing strategies as predatory, 

and their accommodating pricing strategies as exploitative, punish investments 

in complementary markets as attempts to monopolize them, weaken 

their intellectual property rights, forbid bundling strategies, prohibit mergers 

and so on. The bottom line is that, according to this view, antitrust authorities 

should sanction virtually any behavior of the incumbents which does not 

conform to that of their competitors. 

The fallacy of this line of thought, in our view, derives from a simple fact: 

it is based on a partial theory of oligopoly limited to the analysis of duopolies 

with an incumbent and an entrant which does not take into account that, 

at least in most cases, entry by competitors is not an exogenous fact, but 

an endogenous choice. Whether entry is more or less costly, it is typically 

the fruit of an endogenous decision by the potential competitors. Of course, 

entry can be regarded as an exogenous phenomenon in the case of a natural 

monopoly or when there are legal barriers to entry, but these cases should not 

be a subject of antitrust analysis, but of regulatory analysis. When entry can 

be regarded as an endogenous element which depends on the technological 

conditions that constrain the profitability of the firms, we need a complete 

understanding of the behavior of leaders facing endogenous entry. 

5.2 The Theory of Market Leaders and Endogenous 

Entry 

The theory of market leaders studied in the previous chapters clarifies the role 

of market leaders and of the entry conditions in a game theoretic framework 

that is more general than most analysis within the post-Chicago approach. 

In this section we will review its results and compare its implications for 

antitrust with those of the traditional approaches, but before doing that, 

we need to clarify a few concepts concerning the determinants of entry in a 

market. 9 

The industrial organization literature has emphasized different kinds of 

constraints on entry. The definition of barriers to entry has been quite debated 

in the literature. Bain (1956) associated them with the situation in 

9 This section is partly derived from Etro (2006b).

5.2 The Theory of Market Leaders and Endogenous Entry 179 

which established firms can elevate their selling prices above minimal average 

costs of production without inducing entry in the long run. Broadly 

speaking, such a situation corresponds to what we define as competition between 

an exogenous number of firms: even if profits can be obtained in the 

market, entry is not possible. Stigler (1968) has proposed a different definition 

of barriers to entry, associating them with costs of production which 

must be borne by firms seeking to enter an industry but not borne by the 

incumbents; a similar approach has prevailed more recently (Baumol et al., 

1982), so that we can talk of barriers to entry as sunk costs of entry for the 

competitors which are above the corresponding costs of the incumbent (or 

have been already paid by the incumbent). According to this definition, sunk 

costs can be binding on the entry decision of the followers, therefore, they 

can be a crucial determinant of the endogeneity of entry in a market. 10 A 

final category is that of the fixed costs of entry: these are equally faced by 

the incumbent and the followers to produce in the market, but they can also 

represent a binding constraint on entry. While there is a fundamental difference 

in the concepts of sunk costs and fixed costs of entry, their role in 

endogenizing entry is virtually the same, and we will not stress the difference 

in what follows. 11 

5.2.1 Competition in the Market and Policy Implications 

The main point emerging from our analysis of the behavior of market leaders 

facing or not facing endogenous entry is that standard measures of the concentration 

of a market have no relation to the market power of the leaders of 

a market, and may lead to misleading welfare comparisons. 

10 There is a relation between the theory of market leaders and the “bounds approach” 

by Sutton (1998, 2005). His approach is largely based on the concept of 

endogenous sunk costs as strategic investments - see Etro (2006,b) and Chapter 1 

for an attempt to endogenize sunk costs in the theory of market leaders. However, 

his focus is more on explaining market concentration rather than the strategies 

of market leaders. The two approaches could be seen as complementary. 

11 Another important aspect is about the source of these barriers and costs. As 

we noticed before, they can constitute a source of antitrust examination if they 

have been artificially created or enlarged by the incumbent; they cannot if their 

source is purely technological. Nevertheless, it is hard to imagine how artificial 

barriers could be erected under normal circumstances. The Chicago school is 

quite clear on this point, as we can conclude from the following position of Bork 

(1993): “If everything that makes entry more difficult is viewed as a barrier, and 

if barriers are bad, then efficiency is evil. That conclusion is inconsistent with 

consumer-oriented policy. What must be proved to exist, therefore, is a class of 

barriers that do not reflect superior efficiency and can be erected by firms to 

inhibit rivals. I think it clear that no such class of artificial barriers exists.”


Competition in Quantities. Theirrelevanceofmarketsharesfortheevaluation 

of the market power of leaders emerges quite clearly in the simplest 

environment we studied, that of competition in quantities with homogenous 

goods, constant marginal costs and a fixed cost of production. Such a simple 

structure approximates the situation of many sectors where product differentiation 

is not very important but there are high costs to starting production 

(as in many high-tech sectors). In such markets the characterization of the 

equilibrium structure is drastically different when entry conditions change. 

First of all, as long as the number of firms is exogenously given and the fixed 

costs of production are not too high, the leader is aggressive but leaves space 

for the followers to be active in the market. As external observers, we would 

look at this as a market characterized by an incumbent with a market share 

typically larger than its rivals, but with a certain number of competitors 

whose supply of goods reduces the equilibrium market price. The higher the 

number of these competitors, the lower the price will be: in such a case, lower 

concentration would be correctly associated with higher welfare. 

Radical changes occur when entry in the market is endogenous, and is determined 

by the existence of profitableopportunitiesinthesamemarket.In 

such a case (as we have seen in Section 1.1) the leader would expand production 

until no one of the potential entrants has incentives to supply its goods 

in the market. The intuition for this extremely aggressive behavior of the 

market leader is simple. When entry is endogenous, the leader understands 

that a low production creates a large space for entry in the market while a 

high production reduces entry opportunities. More precisely, knowing how 

technological constraints govern the incentives to enter in the industry, the 

leader is aware that its output exactly crowds out the output of the competitors 

leaving unchanged the aggregate supply and hence the equilibrium price. 

However, taking this equilibrium price for the market as given, the leader can 

increase its profits by increasing its output and reducing the average costs 

of production. Here the fixed costs of production (associated with constant 

marginal costs) are crucial: on one side they constrain the profitability of 

entry, while on the other side they create scale economies in the production 

process that can be exploited by the leader through an expansion of its output. 

Actually, it is always optimal for the leader to produce enough to crowd 

out all output by the competitors: exploiting the economies of scale over the 

entire market allows the leader to enjoy positive profits even if no entrant 

couldobtainpositiveprofits in this market. As external observers, in this 

case, we would simply see a single firm obtaining positive profits in a market 

where no one else enters, and, following traditional paradigms, we would 

associate this situation with a monopolistic environment, or at least with a 

dominant position derived by some barriers to entry. But this association is 

not correct, since entry is indeed free in this market: it is the competitive 

pressure of the potential entrants that induces the leader to produce so much 

to drive down the equilibrium price until no other firm can enter. We are


referring to firms that are as efficient as the leader (assuming identical cost 

technologies). Finally, in Chapter 1, we even noticed that this equilibrium 

with only the leader in the market is associated with a higher welfare than 

the free entry equilibrium without a leadership - the Marshall equilibrium, 

which involves many firms active in the market and earning zero profits. 

Let us now consider a related situation with a different cost pattern for 

the firms (see Section 1.2.1). When marginal costs are substantially increasing 

in the production level or, more generally, when the average costs have a U- 

shape, a market leader facing endogenous entry of competitors may not have 

incentives to deter entry, but would still behave in an aggressive way. In such 

a case, given the strategy of the leader, all the entrants maximize their own 

profits and therefore they price above the marginal cost. However, endogenous 

entry reduces the equilibrium price to a level that is just high enough to 

cover the fixed costs of production. Notice that this equilibrium generates 

a production below the efficient scale (which should equate marginal and 

average costs). Also in this case, the leader takes into account these elements 

and, in particular, takes as given the equilibrium price emerging from the 

endogenous entry of the competitors. Accordingly, the leader finds it optimal 

to produce as much to equate its marginal cost to the price, which requires 

a production above the efficient scale. Since marginal costs are increasing for 

such a high production level, the leader is pricing above its average cost, and 

hence obtains positive profits. In this case the strategy of the leader does not 

even affect the market price, which is fully determined by endogenous entry 

of firms. Nevertheless, the leader obtains a larger market share than its rivals 

and positive profits. Moreover, we have shown that the aggressive behavior 

of the leader, that adopts a price equal to the marginal cost, improves the 

allocation of resources compared to the same market with free entry and no 

leadership. 12 

A similar situation emerges when goods are not homogeneous but differ in 

quality (see Section 1.2.2). This happens when consumer needs or tastes are 

quite differentiated, as is the case in many sectors where the design and the 

inner quality of products play an important role. Under these circumstances, 

firms often compete in prices by choosing different mark-ups for different 

products. When quality differs, it is important to have a number of firms 

producing different varieties of goods. A competitive market typically satisfies 

12 As we saw in the general model of Chapter 3, under Stackelberg competition 

with endogenous entry, the followers equate the price to their average total cost 

following the standard mark-up rule, and the leader equates the price to its own 

marginal cost: 

p = 

c0 (q) 

1 − 1/ = c(q)+F 

q 

= c 0 (q L) 

where is the elasticity of demand. It follows that the equilibrium output of the 

leader, q L , is always higher than the one of the followers, q.


this requirement, but it tends to induce excessive proliferation of products. 

The presence of market leaders is again beneficial: they will not conquer the 

entire market, but they will expand production and consequently reduce their 

prices below the prices of their competitors, some of which will be driven 

out of the market. Consumers will then face a lower variety of alternative 

products, but pay less for some of them. 13 

The crucial lesson from this analysis is that we should be careful in drawing 

any conclusion from indexes of concentration or from the market shares. 

We have seen examples in which the equilibrium outcome of a market with 

free entry was characterized by a single active firm enjoying positive profits, 

and other examples where the outcome was less drastic, but not too different. 

Notice that in all these cases, the market leader was adopting aggressive 

strategies which were reducing entry but increasing welfare nevertheless. It 

is important to emphasize that strategies that are aimed at reducing entry 

are not necessarily negative for consumers, especially when entry is not fully 

deterred, but simply limited due to a low level of the prices, so that some 

competitors are still active in the market and able to exert a competitive 

pressure on the leader. As a matter of fact, this is a good example of how 

real competition works. 

Of course, a predatory behavior can still be associated with aggressive 

strategies aimed at foreclosure and with negative consequences on consumers. 

This can be the case under two circumstances: 1) when these strategies are 

implemented by leaders with genuine market power which is not constrained 

by effective entry, and 2) when the same leader has built barriers to artificially 

constrain entry without efficiency reasons (see the Appendix in Chapter 1). 14 

Finally, notice that a complete analysis of the consequences of entry deterrence 

would require a dynamic model taking into account the behavior of the 

13 Consider a generalization of the examples of Chapter 1 with both product differentiation 

and U-shaped costs. Under the profit function: 

π i = q i (a − q i − b j6=i q j) − cq i − dq 2 i /2 − F 

a Stackelberg equilibrium with endogenous entry is characterized by followers 

producing: 

 

2F 

q = 

2+d 

and a leader producing: 

q L = 2 − b + d 

 

2F 

2 − 2b + d 2+d 

14 Artifical barriers associated with bureaucracy and lobbying activity on government 

processes are emphasized by the Chicago school as well (see Bork, 1993, 

Ch. 18).


leader before and after deterrence, which is beyond the scope of this book. 

However, simple models can reveal a lot. Our point here is simply to warn 

against the risk of directly associating aggressive price strategies that reduce 

entry with strategies that harm consumers. 

CompetitioninPrices.Another important implication of the theory of 

market leaders emerges quite clearly under competition in prices. In this typical 

situation, the traditional analysis of Stackelberg oligopolies shows that 

dominant firms are either accommodating (setting high prices) or trying to 

exclude rivals by setting low enough prices: the first case happens when the 

fixed costs of entry are small (and predation would be too costly), the second 

when they are high enough. 15 Such an outcome implies the risk of erroneously 

associating an aggressive price strategy with an entry deterring strategy in 

a systematic fashion. As we have seen (in Section 1.3), when we endogenize 

entry in the market, leaders never adopt accommodating pricing strategies 

while they are always aggressive. Again, in equilibrium with endogenous entry, 

leaders increase their market shares and obtain positive profits. Of course 

an aggressive pricing strategy will still reduce entry, even if it will not exclude 

all rivals. Nevertheless, we must be more careful in associating aggressive 

pricing with predatory purposes. The reason why predatory strategies are 

anti-competitive is that they exclude competition in the future allowing the 

dominant firm to behave in a monopolistic fashion once competitors are out 

of the market. Clearly, if an aggressive pricing strategy is aimed at excluding 

some but not all competitors, this anti-competitive element is more limited. 

Notice that competition in prices is quite typical of markets where product 

differentiation is relevant and firms have more autonomy in choosing their 

prices directly. The results are also relevant in oligopolistic markets in which 

prices determine the volume of business, as in the banking sector, where the 

interest rates on loans determine how much firms borrow from a bank, and the 

interest rates on deposits determine how much households lend to a bank. 16 

15 Accommodating high prices are chosen by the leader when fixed costs of entry 

are small. The problem is that this is exactly when there are incentives for other 

firms to enter, hence the duopolistic equilibrium is quite weak, and the study of 

endogenous entry becomes crucial. 

16 Price competition is typical of the banking sector, where banks choose both the 

interest rates on loans, ι, and on deposits, r (see Freixas and Rochet, 1997). When 

entry in the sector is exogenous we would expect leaders to offer worse terms 

to their customers, when it is endogenous we would expect the opposite. For 

instance, imagine that banks compete only on the deposit side, and the supply 

of deposit for firm i is S(r i, 

j6=i 

h(rj)) with S1 > 0 and S2 < 0. Adopting the 

usual notation, profits for bank i are: 

π i =(ι − r i − c)S (r i,β i ) − F 

where c is the marginal cost of intermediation. A Stackelberg equilibrium with 

endogenous entry is characterized by the optimality and free entry conditions for


Strategic Commitments. In general, as we have seen in Chapter 2, the 

spirit of our result on the aggressive behavior of leaders goes through when 

leaders cannot commit to output or price strategies, but can undertake preliminary 

investments that change their incentives in the market. For instance, 

a market leader facing an exogenous number of competitors may want to 

underinvest or overinvest strategically in cost reducing R&D according to 

the kind of competition (in prices or in quantities), because it may want to 

commit through these investments to adopt an accommodating or an aggressive 

strategy in the market: in particular, underinvesting is optimal before 

price competition, while overinvesting is optimal before quantity competition. 

However, this ambiguity collapses if the leader is facing endogenous entry of 

competitors. In such a case, it is always optimal to adopt the strategy that 

allows one to be aggressive in the market: strategic overinvestment in cost 

reducing R&D is optimal independently from the form of competition, because 

it allows one to be aggressive against competitors (see Section 2.6). 17 

A similar role is attached to investment in production capacity, to debt as a 

financing tool issued to commit management to produce higher output, and 

to many other strategic investments. 

An interesting situation for antitrust purposes emerges when demand is 

characterized by network effects. In such a case, market leaders tend to underprice 

their products initially to attract customers in the future. As known, 

these strategies may induce pricing below marginal cost without entry deterrence 

purposes. Moreover, in Section 2.9 we have seen that leaders facing 

endogenous entry may have further strategic incentives to reduce initial prices 

(or expand initial production): by doing so, they enhance network externalities 

and are able to reduce their prices also in the future. Therefore, antitrust 

authorities should be careful in evaluating aggressive pricing in the presence 

the followers: 

ι − r − c = 

S(r, β) 

S 1 (r, β) = F 

S(r, β) 

and by the optimality condition for the leader: 

ι − r L − c = 

S(r L ,β L ) 

S 1 (r L ,β L ) − S 2 (r L ,β L )h 0 (r L ) 

which implies r L >r. Only under the pressure of free entry, the leader affords 

to compensate deposits with a high rate than its followers. 

17 Both effective and potential competition are crucial here. On this point, we are 

close to early informal insights of the Chicago school. For instance, Posner (2001, 

p. 145) notices that “notions of potential competition cannot and should not be 

banished entirely from antitrust law... a monopolist who creates excess capacity 

inordertoreducehismarginalcost,sothatentrants(whohavetobeableto 

cover their average total cost if they are to make a go of entry) are deterred, is 

reacting to potential competition.”


of network effects. Finally, this point applies in particular to multi-sided markets, 

where network effects take place between different kinds of customers, 

and firms can charge their different customers differently. In such an environment 

market leaders tend to price quite aggressively one of the sides, but 

again without exclusionary purposes. We will return to this point with more 

details in the next chapter. 

The same care in judging aggressive strategies is needed in cases of complementary 

strategies that virtually induce aggressive behaviors. One of these 

is bundling. In an influential paper, Whinston (1990) has studied bundling 

in a market with two goods. The primary good is monopolized by one firm, 

which competes with a single rival in the market for the secondary good. Under 

price competition in the secondary market, the monopolist becomes more 

aggressive in its price choice in the case of bundling of its two goods. Since a 

more aggressive strategy leads to lower prices for both firmsaslongasboth 

are producing, the only reason why the monopolist may want to bundle its 

two goods is to deter entry of the rival in the secondary market. This conclusion 

can be highly misleading because it neglects the possibility of further 

entry in the market. As we have seen in Section 2.10, if the secondary market 

is characterized by endogenous entry, the monopolist would always like to be 

aggressive in this market and bundling may be the right way to commit to an 

aggressive strategy. Bundling would not necessarily deter entry in this case, 

especially if there is a high degree of product differentiation in the secondary 

market, but may increase competition in this market and reduce prices with 

positive effects on the consumers. 18 

Another application of the theory of market leaders concerns vertical restraints 

affecting inter-brand competition (Bonanno and Vickers, 1988; Rey 

and Stiglitz, 1988). Also in this case, the behavior of the market leader can be 

anticompetitive depending on the entry conditions. In particular, under price 

competition, a contract delegating distribution to a downstream firm tends 

to soften price competition when entry in the market is exogenous (because 

the upstream firm imposes high prices through direct or indirect contractual 

restraints), but it strengthens price competition when entry is endogenous 

(in which case the upstream firm can only gain by inducing an aggressive 

behavior of the downstream firm): the consequences on consumers tend to be 

negative in the former case and positive in the latter case (Section 2.11). 

We encounter a more complex situation when we consider price discrimination 

versus uniform pricing, since they can both soften or strengthen price 

competition in different markets. However, we have shown an example where, 

when price discrimination emerges between two groups of customers, it is also 

likely to soften price competition compared to uniform pricing (Section 2.12). 

If this is the case, price discrimination is adopted by a firm competing with 

18 Notice that the same limit of the analysis of Whinston, namely the exogenous 

assumption that there are just two firms and further endogenous entry is not 

taken into account, applies to many other duopolistic models of bundling.


an exogenous number of competitors, but not when entry is endogenous. Accordingly, 

when it takes place price discrimination is likely to harm at least 

some consumers. 

Conclusion. Our final remark is about the presence of high and sustained 

profits (sometimes called supernormal profits) of the market leaders. These 

high profits are frequently, but sometimes erroneously, associated by the traditional 

approaches with a situation of market dominance and barriers to 

entry that prevents competition from driving down the rate of return to its 

competitive level. As we have seen repeatedly, even in the presence of free 

entry market leaders with a first mover advantage or with a more reasonable 

chance to undertake preliminary investments are able to obtain positive 

profits, or, in other words, they are able to preserve a rate of return above 

the opportunity cost of capital. Evidently, these sustained profits in a market 

where entry is free are not a symptom of dominance per se. Notice that there 

are other important reasons why sustained profits may persist in innovative 

markets, but we will look at them in the next section on the competition for 

the market and its implications. 

The bottom line of this discussion on competition in the market is that in 

evaluating market structures and the behavior of market leaders we should 

give special attention to the entry conditions. Standard results on aggressive 

price and non-price strategies with exclusionary purposes emerging for markets 

with an incumbent and an entrant can change in radical ways when we 

take in consideration the possibility of endogenous entry by other firms. After 

all, antitrust policy in an uncertain world should derive from a comparison of 

the expected losses from incorrectly challenging a practice that benefits consumers 

(a Type I error ) versus the expected losses from incorrectly failing to 

challenge a practice that harms consumers (a Type II error ). We believe that 

while the Chicago School has been extremely biased to reduce the first kind 

of losses (exactly because it largely ignored strategic interactions), the post- 

Chicago approach has been excessively biased in the opposite sense (exactly 

because it often neglected endogenous entry). 19 

5.2.2 Competition for the Market and Policy Implications 

Competition in high-tech markets is dynamic in the Schumpeterian sense that 

it takes place as competition for the market in a so-called winner-takes-allrace, 

and such an element requires a deeper evaluation of competition policy 

than that suggested in the analysis of the previous section, which was mostly 

focused on a static concept of competition in the market. 20 

19 On the design of optimal procedures for competition policy see Katsoulacos and 

Ulph (2007). 

20 In the terminology of the famous growth-share matrix popularized by the Boston 

Consulting Group, new products in the growing high-tech markets are Stars (for


Economic research has emphasized the positive relationship linking patents 

to investments in innovation and these investments to technological progress 

and growth. In high-tech sectors (hardware, software, pharmaceuticals, biotechnology) 

firms compete mainly by innovating. This is possible as long as there 

are well defined intellectual property rights (IPRs), and especially patents, 

protecting their innovations and investments, which is ultimately what leads 

to technological progress in our economies. In Section 1.4 we have even suggested 

that this form of dynamic competition can be a valid substitute for 

the competition in the market: when entry in the competition for the market 

is free, an increase in the degree of competition in the market cannot provide 

further incentives to invest in innovation (because any escape competition 

effect disappears). 

Moreover, even if most economists are used to thinking about market 

leaders as firms with weaker incentives to invest in R&D, recent theoretical 

and empirical research has also found support for an old idea associated with 

the institutional work of Schumpeter (1943), Galbraith (1952) and Chandler 

(1990), according to which market leaders play a crucial role in the innovative 

activity. The theory of market leaders has clarified the mechanics of 

these results. IPRs drive competition through innovation in these markets 

and induce technological progress led by incumbent monopolists under two 

conditions: their leadership in the contest to innovate and free entry of outsiders 

in this same contest. In particular, in Chapter 4 we contrasted two 

scenarios. According to traditional theories, in the absence of strategic advantages, 

a technological leader that is also an incumbent monopolist in its 

market, would have less incentives to invest in R&D compared to other firms, 

since its relative gain from improving its own technology is smaller than the 

gain of the outsiders from replacing the incumbent monopolist. This result, 

sometimes called the Arrow’s paradox, has often been used to suggest that 

incumbent patent-holders invest less than other firms and stifle innovation. 

However, we have also seen that when an incumbent monopolist is the leader 

in the contest for innovating, the pressureofacompetitivefringeofpotential 

innovators leads this monopolist to invest more than any other firm. The 

competitive environment spurs investment by leaders and consequently induces 

a chance that their leadership persists. Finally, we have also suggested 

that when the leadership persists because of the endogenous investment in 

R&D by the leaders, the same value of becoming a leader is increased, which 

strengthens even further the incentives for any other firm to invest, and so 

on. Paradoxically, the persistence of a leadership in high-tech sectors can be a 

sign of effective dynamic competition for the market, which leads to a faster 

rate of technological progress in the interest of consumers. 

market leaders) or Question Marks (for the followers), as opposed to the mature 

markets typical of the traditional sectors that can be characterized by products 

with high market shares (Cash Cows) or low market shares (Dogs).


Notice that our results on the relation between entry in the competition 

for the market and investment by the incumbent monopolists can be seen as 

strengthening our initial claim that standard indices of market concentration 

or market shares should not be related to the degree of competition in a 

market. In high-tech markets where competition is mostly for the market, it 

is natural that better products conquer large shares and, exactly when entry 

is free, incumbent patent-holders have more incentives to invest and their 

leadership is more likely to persist. There is no basis to relate in a significant 

way market shares and market power in dynamic sectors. 

This mechanism is even more radical in markets with network effects, 

where the natural outcome is a sequence of dominant paradigms associated 

with market leaders whose behavior is still constrained by innovative competitive 

pressure. Scotchmer (2004, p. 296), in her discussion of network effects, 

emphasizes this point neatly: 

“All this calls into question whether an incumbent’s share of a 

network market is a good test of market power for antitrust purposes. 

With tippy markets, any snapshot of the market will find some firm 

with a dominant market share. But sequential monopoly is only a 

problem for competition policy if the price charged by each sequential 

monopolist is high [...] the price is constrained at first by the 

proprietor’s need to attract users of the previous product, and later 

by a fear of scaring users into embracing a successor. The same fears 

will cause the incumbent to keep innovating.” 

Of course, we do not want to give the message that persistent monopolies 

are necessarily the fruit of effective competition for the market, but rather 

that they can be the fruit of effective competition. What we would like to 

emphasize is the importance of entry conditions in the market for innovations. 

This is in line with an old Chicago-style position associated with Demsetz 

(1973), who pointed out that: 21 

“Under the pressure of competitive rivalry, and in the apparent 

absence of effective barriers to entry, it would seem that the concentration 

of an industry’s output in a few firms could only derive from 

their superiority in producing and marketing products ... an industry 

will become more concentrated under competitive conditions only if a 

differential advantage in expanding output develops in some firms ... 

The cost advantage that gives rise to increased concentration may be 

reflected in scale economies or in downward shifts in positively sloped 

marginal cost curves, or it may be reflected in better products which 

satisfy demand at a lower cost” (Demsetz, 1973). 

Consequently, industrial policy, including antitrust policy, should primarily 

promote, and possibly subsidize, investment in R&D, and it should be less 

21 See Hughes (2007) for a recent and successful test of the Demsetz hypothesis.

5.3 A Digression on IPRs Protection 189 

relevant whether the incumbent monopolist or new comers invest in R&D and 

innovate once entry is free. On the other side, the protection of IPRs should 

be established at a legislative level (possibly even coordinated at an international 

level) because its stability is essential to foster investments, while 

the discretionary activity of antitrust authorities should not affect the basic 

principles of IPRs protection. 

The credibility of innovation policy is crucial to give incentives to firms to 

innovate, because investment in R&D depends mainly on the expectations on 

the protection of IPRs. This point is quite similar to standard results in monetary 

and fiscal policy. A commitment to low inflation is essential because price 

setting decisions are based on the expectations of inflation: surprise inflation 

may push the economy in the short run, but will just increase inflationinthe 

long run. A commitment to a capital income tax is essential because savings 

decisions are based on the expectations of capital income taxes: unexpected 

higher capital taxation can raise more tax revenue in the short run, but it 

will mainly reduce savings and tax revenue in the long run. Analogously, a 

commitment to a level of protection of IPRs is essential because investment 

decisions are based on the expectation of this protection: forcing disclosure 

of IPRs can have some positive effects for outsider firms in the short run, but 

will have devastating effects on innovation and growth in the long run. 

This leads us to another important aspect of industrial policy, the protection 

of IPRs, which has an old and well recognized tradition in developed 

market economies. 22 

5.3 A Digression on IPRs Protection 

To understand the crucial role of IPRs and patents in promoting technological 

progress and growth we rely on an old important theory developed 

by Nordhaus (1969). In general, patents assign a temporary monopolistic 

power for the innovators which creates price distortions and hence carries a 

social cost, but also constitutes an incentive for many firms to invest and 

try to gain market leadership through innovations. This effect leads to social 

benefits because innovations have a social value that can be higher than the 

22 Patent protection was recognized in Renaissance Italy. In 1474 the Republic of 

Venice issued a decree by which new and inventive devices, once they had been 

put into practice, had to be communicated to the Republic in order to obtain 

legal protection against potential infringers. Galileo applied for a patent on an 

hydraulic system in 1593 noticing that “it does not suit me that the invention, 

which is my property and was created by me with great effort and cost, should 

become the common property of just anyone.” The Venetian Senate assigned 

him a patent valid for twenty years. For more on the history of innovations and 

IPRs see Scotchmer (2004).


private value (and that cannot be fully appropriated by the innovators) 23 and 

because they drive technological progress and growth. Clearly social benefits 

and costs can be different for different inventions and generally for different 

fields of technology, so, in theory, the optimal length and breadth of patents 

should depend on the field it applies to. For simplicity, and to avoid discriminations 

between fields of technology, patents typically have a uniform 

length and common principles on infringement regulation. Nevertheless, from 

a strictly economic point of view, one may question this uniformity and consider 

the advantages of providing different terms of protection in different 

sectors (at least this could avoid the inefficient choice of radically excluding 

certain innovations from patentability rather than allowing a more limited 

protection). More importantly, an evaluation of the social benefits and costs 

of patents for different fields is essential in judging the net benefit ofapatent 

system. 24 

5.3.1 Patents in Dynamic Sectors and Innovations 

Consider the pharmaceutical sector, where the role of patents on new drugs 

is, to say the least, at the basis of competition in the market and of scientific 

progress in the world. These kinds of patents have been often criticized 

for jeopardizing health defense around the world and especially in developing 

countries, where western drugs are very important but very expensive. 

Nevertheless, one should not forget that those same patents induced many 

firms to invest and some of them to invent new drugs which are now available, 

something which would have hardly happened or would have happened 

later without patent protection: in other words the social benefit ofpatents 

on drugs is very high. Fortunately, there are ways to reduce the problems 

related with the pricing of drugs and their adoption depends mostly on the 

public sector. For instance, governments could buy drugs and distribute them 

at lower prices through the medical system, or just pay part of the prices. 

They may even directly buy the same patents from the innovators and produce 

the drugs (or outsource their production) and sell them at lower prices. 

Finally, western governments could redirect their international aid toward 

similar initiatives in favor of developing countries. These solutions, widely 

discussed between economists, may preserve the proper incentives to invest 

and discover new drugs while spreading their effects globally. Ultimately, this 

suggests that patents in the pharmaceutical sectors are a crucial determinant 

of innovation and progress and should be protected while finding alternative 

solutions to guarantee health defense for poor classes and poor countries. 

23 For a “public choice” perspective on this and the relation with the theory of 

market leaders see Reksulak et al. (2006). 

24 When the social value of patents is very high, public sponsorship of R&D activities 

and public-private partnership can be useful (on the latter experience see 

the empirical works by Baarsma et al., 2004, and Ambrosanio et al., 2004).


Another field in which patents are particularly valuable and induce high 

investments in R&D is the New Economy. In the last few years the European 

Union tried (without success) to complete a process of harmonization 

of the patent system for computer-implemented inventions (CIIs). 25 We believe 

that the rationale for these patents is strong: while their main social 

gain is to promote innovation in the most dynamic sectors, the social cost 

is smaller than for other patents since in these sectors competition mainly 

works through frequent price-reducing and quality-improving innovations, 

therefore price distortions are less relevant and do not last long anyway. 

Neglecting these traditional economic insights, opponents of the patent system 

have often claimed that patents stifle innovation. There is not, however, 

consistent theory or empirical evidence behind these claims. In US, the extension 

of patent protection to CIIs started in 1980 (the firstpatentofthis 

kind was granted by the US Patent and Trademark Office in 1981), and it 

was associated with a clear increase in R&D investment during the eighties. 

The R&D/sales ratio for US firms innovating on computer, telecommunications 

and electronic components (the relevant field here) increased from 5.5% 

to above 8% in 1989 (see Etro, 2007c). In a careful empirical study Mann 

(2005) has shown that patents bestow significant benefits, especially for start 

up companies, in terms of traditional appropriability, information signalling 

and cross-licensing revenue, while Merges (2006), looking at patent data in 

the US software market, finds out that “new firms entry remains robust, despite 

the presence of patents (and, in some cases, perhaps because of them). 

Successful incumbent firms have adjusted to the advent of patents by learning 

to put a reasonable amount of effort into the acquisition of patents and the 

building of patent portfolios. Patent data on incumbent firms shows that several 

well-accepted measures of ‘patent effort’ correlate closely with indicators 

of market success such as revenue and employee growth.” 26 

5.3.2 Open-Source Innovations 

While IPRs are fundamental drivers of innovation in all sectors, software development 

has recently been characterized by a large amount of innovation 

25 After a long procedure, the Common Position adopted by the European Council 

in March 2005 proposed the patentability of CIIs when they provide a technical 

contribution to a field of technology. While this positive proposal simply reaffirmed 

the requirements already adopted in Europefortheprevioustwodecades 

and it excluded from patentability any pure software, business methods and consulting 

practices (which are patentable in US), the European Parliament ended 

up rejecting the Directive in July 2005. See Etro (2005a,b). 

26 See Bessen and Maskin (2002) for a theoretical and empirical position against 

software patents, and Etro (2007c) for a critical view of their theoretical and 

empirical results.


obtained in a decentralized, voluntary and uncompensated way by programmers 

within the so-called open source movement. 27 While many private corporations 

support it because they supply products that are complementary 

to open source software (IBM first of all, but also Hewlett-Packard, Intel, 

Sun, Oracle,...), it remains surprising that such a large innovative process 

can take place, at least in part, through directly unrewarded efforts. 28 Lerner 

and Tirole (2002, 2006) have provided a few explanations for the incentives 

of these individual programmers: career concern, ego gratification and signalling 

activity are quite powerful and effective in this field. Unfortunately, 

the same nature of these incentives shows the possible limitations of the innovative 

activity in the open source community: it is limited by the usual 

free riding problems emerging in the private provision of public goods, it 

requires a complementary activity in the for-profit sector (to motivate the 

career concern and the signalling activity), it may be biased by research efforts 

that are different from general consumer needs and by adverse selection 

of the contributors, and it may be effective to solve a number of small and 

short term problems, but less effective to solve multi-sided challenges and 

approach long term projects. 29 While the development of this new form of 

user-driven innovation is a symptom of high competitive pressure in the sec- 

27 Open source software is made available for direct use and modification (through 

direct access to the source code) under limited protection. For instance, the GPL 

(General Public License, first used in 1981 by Richard Stallman, the leader of the 

Free Software Movement) grants unlimited right to use, modify and distribute 

software as long as its redistribution makes available the modified source code 

and does not impose further restrictions on the rights granted by the GPL. 

These enforcement mechanisms make cooperative innovation quite effective and 

immune from free riding, but can create problems when an innovation includes 

both open source software and licensed proprietary software. 

28 Major results of the open source movement are Linux, an operating system based 

on Unix (an old OS first created at Bell Labs) and developed in 1991 by Linus 

Torvalds, Apache, a world wide web (HTTP) server, and Mozilla Firefox, a web 

browser. Besides software that is freely distributed, there is an increasing number 

of companies, like Red Hat and Novell, that profit from collateral services supplied 

jointly with free software. In theory, any rival could resell Red Hat software 

at a lower price because it is under GPL (and some firmsactuallydoit),butRed 

Hat managed to sidestep this problem protecting its products with trademark 

law. In this sense, the difference between proprietary software and open source 

software appears much less relevant: the former earns from licenses to end-users, 

the latter mainly licenses software free of charge and earns from selling support 

description needed by end-users to install and run the software. For empirical 

evidence on the open source development see Koski (2007). 

29 It is often claimed that open source software is more effective than proprietary 

software in debugging activity (since many programmers find and solve many 

defects within a software and make the solutions freely available), but may have


tor, it does not provide any evidence against the fundamental role of IPRs in 

driving core innovations. 30 Actually, we believe that the current coexistence 

of open source software and proprietary software exerts a positive impact on 

innovation on both sides. 31 

In a fascinating work, Boldrin and Levine (2005) adopted open source software 

as a main example of innovation created without commercialization of 

IPRs, and collected some anecdotal evidence suggesting that innovations can 

perfectly take place in the absence of what they call “intellectual monopoly”. 

Their idea is that the first mover advantage of the innovator in the competition 

in the market preserves a certain amount of profits even when entry 

of imitators is free, and this Stackelberg advantage can be sufficient to probig 

problems confronting issues as synchronization of upgrades and efficient levels 

of backward compatibility. 

30 In a debate on the Financial Times, the author of this book expressed a related 

point: “It is true that the competitive pressure from open source software has 

led technological leaders to continue investing in research and development, but 

major advances such as the iPhone or Microsoft Surface keep arriving from the 

commercial software world. Moreover, restrictive open source software creates a 

fundamental asymmetry. On one side, open source software companies (allied 

with big business, such as IBM) can use proprietary software within their products 

and freely distribute them while covering licence expenditures through customer 

support services. On the other side, commercial companies cannot pursue 

their business model when including open source within their software, because 

they would infringe the "copyleft" if they apply a price to the licence. This asymmetry 

can create substantial problems for the conventional business model, and 

may inhibit or bias consumer-driven innovation. Finally, the notion that European 

competitiveness vis a vis China will be enhanced by the promotion of the 

open source software model is preposterous. The general public licence is built 

on the proposition that anything you do and distribute can be freely appropriated 

by anyone within or outside Europe, in fact handing over the result of your 

investment to China on a silver platter. Rather than democratising innovation, 

we should protect it.” (Etro, 2007,e). 

31 To see why, think of a different sort of open source activity: Wikipedia is a famous 

and successful online encyclopedia where anybody can post a new voice or edit 

an old one (www.wikipedia.org). While it contains a lot of useful and constantly 

updated information (especially in certain fields, like those related to the online 

community), it often includes unmotivated and misleading references or mistakes 

that are the normal consequences of overlapping additions by heterogeneous 

contributors whose preparation is not properly controlled and whose effort is not 

rewarded. Traditional encyclopedias based on rewarded contributions by selected 

experts are not constantly updated like Wikipedia, but they provide a standard 

of quality and a balanced unifying structure that Wikipedia lacks. The tradeoff 

for the end users is clear, and coexistence appears natural. See Aghion and 

Modica (2006).


mote innovation. Since a main leitmotif of our book has been showing that 

market leaders with a first mover advantage can obtain positive profits even 

in markets where entry is free by adopting aggressive strategies (Chapters 

2-3), and since our formalization of competition for the market was perfectly 

compatible with incentives deriving from the profits of a market leader facing 

free entry, rather than deriving from a monopolistic position (Chapter 4), 

we certainly do not dislike the idea of Boldrin and Levine. But the point is: 

how much innovation can be promoted by the simple first mover advantage? 

Without an analysis of the industrial organization of the competition for the 

market it is quite hard to answer this question, and the general equilibrium 

analysis of Boldrin and Levine (1998) concluding that perfectly competitive 

innovations can achieve the first best amount of innovation neglects, to a 

large extent, the industrial organization of the market for innovations. Unfortunately, 

whether the incentives to invest are efficient or not is more an 

empirical question than a theoretical one, and we still do not see a consistent 

piece of evidence showing that current patent systems provide excessive 

incentives in a systematic way, or that we should totally eliminate IPRs legalizing 

“intellectual expropriation”- as Boldrin and Levine (2005) actually 

suggest. As a matter of fact, the opposite may be true. Recently, Denicolò 

(2007) analyzed a general model of the organization of innovations and obtainedasimplerulefortheoptimallevel 

of patent protection: his empirical 

estimates suggest that current patent systems do not over-compensate innovators, 

while they may actually induce too limited incentives to invest in 

R&D. 32 

5.3.3 Conclusions on IPRs Protection 

Before returning to the core discussion on antitrust issues, we list a number 

of implications of the economic debate on IPR protection that in our opinion 

are quite relevant: 

1) the optimal patent system should trade-off the social benefits of the 

incentives to innovate and the social costs due to temporary price distortions, 

and the protection of IPRs is crucial in those fields, such as in the New 

Economy, where the net benefits of patents are higher or in those fields, like 

the pharmaceutical sector, where social benefits are higher and there are 

proper policies which can reduce the social costs; 

2) restrictions to the patentability of innovations in high-tech sectors for 

one country or a group of countries could severely jeopardize investment in 

innovation and technological progress in the leading high-tech sectors with 

negative consequences on growth and competition in the global economy 

and would shift investments toward other countries where IPRs are better 

protected without regard for comparative advantage; 

32 On the same point see Erkal (2005) and Cozzi and Galli (2007).

5.4 Reforming Antitrust 195 

3) improvements of the effectiveness of the current patent systems should 

rather promote access to patents, especially for small and medium size enterprises 

which are traditionally less able to exploit this opportunity, and 

enhance the spillovers created by the patent system on the diffusion of knowledge 

through further requirements on a disclosure of the patented inventions 

whichshouldbesufficiently clear and complete to be carried out by a person 

skilled in the art; 

4) a proper industrial policy promoting competition for the market should 

adequately protect and subsidize R&D investments, and at the same time 

guarantee open access to the markets for innovations. 

5.4 Reforming Antitrust 

In the last few years there has been a lot of academic and political debate 

on how to reform the EU approach to antitrust, and in particular on issues 

concerning abuse of dominance, moving toward an economic based approach 

more similar to the US approach. European Commission (2005) proposed a 

new approach to exclusionary abuses under Article 82 which is the subject of 

an open debate and gives an important indication as to how the Commission 

may approach antitrust cases of abuse of dominance in the future. We will 

comment on this debate focusing on the general principles of EU antitrust 

policy, but our discussion tries to provide principles for antitrust policy that 

could be applied to any national antitrust authority. 

The EU approach appears to move toward a purpose of competition policy 

associated with the protection of competition in the market as a means of enhancing 

consumer welfare and of ensuring an efficient allocation of resources. 

This implies that antitrust should protect competition and not competitors, 

and be based on an economic analysis aimed at the maximization of consumer 

welfare and allocative efficiency rather than based on a legalistic analysis, a 

new direction which appears much more in line with the consolidated US 

approach. 

While the aim is to enhance consumer welfare and to protect competition 

and not competitors, we have some concern that these principles are not fully 

carried through into certain aspects of the current EU competition policy and 

of the proposal of European Commission (2005). 33 As a matter of fact, until 

now the approach of the European Commission has often been in line with 

outdated views, for instance when stressing an excessive reliance on market 

33 This section is partly derived by Etro (2006c). See International Chamber of 

Commerce (2006,2007) for a more extensive and related treatment. Here we 

will focus on issues related to our previous theoretical analysis, namely market 

dominance, predatory pricing, bundling and protection of IPRs. I am grateful to 

Martti Virtanen of the Finnish Competition authority for precious comments on 

this section.


shares in determining dominance. The analysis of whether an undertaking has 

engaged in abusive conduct under Article 82 should ultimately turn on the 

conduct’s actual effects on efficiency and consumer welfare. Thus, we believe 

that, if the pro-consumer benefits of a dominant undertaking’s conduct are 

significant, it should be immune from liability even if it disadvantages certain 

competitors. Inventing better products or more efficient methods of distribution, 

reducing prices or offering better terms of trade, and more quickly 

adapting to changes in the market can disadvantage rivals and maybe even 

cause them to exit the market. Yet, these forms of conduct often also enhance 

efficiency and consumer welfare. 

Thefocusontheeffects for consumers is particularly important with respect 

to fast-moving markets such as those commonly found in high-tech 

and New Economy industries which are often characterized by massive R&D 

investments, strong reliance on IPRs and other intangible assets, network effects, 

high sunk costs and low marginal costs. As we already noticed, under 

competition for the market, leading firms might enjoy high market shares 

yet be subject to massive competitive pressure to constantly create better 

products at lower prices due to threats from innovative competitors and potential 

entrants. Undertakings that hold a significant share of the market at 

any given point in time may see this share decrease rapidly and significantly 

following the development and supply of a new and more attractive product 

by an actual or potential competitor. Nevertheless, the current EU approach 

is still characterized by a close association between market shares and market 

dominance without any reference to the kind of market that is under 

consideration. 

5.4.1 Efficiency Defense 

Since the main purpose of antitrust policy should be the protection of consumers 

and of the efficient allocation of resources within sectors, it is important 

that strategies that create efficiency gains remain outside the realm of 

abusive strategies. 

The proposal on the efficiency defenses for dominant firms contained in 

European Commission (2005) appears to be going in the right direction since 

it allows otherwise abusive strategies if they create a net efficiency gain (which 

benefits consumers). 34 In our view, conduct that generates efficiencies should 

not be deemed abusive unless it is demonstrated that the impact of this conduct 

on competition will result in consumer harm outweighing these efficien- 

34 This can happen in two ways: through an objective necessity defense “where the 

dominant company is able to show that the otherwise abusive conduct is actually 

necessary conduct on the basis of objective factors external to the parties involved 

and in particular external to the dominant company”, or a meeting competition 

defense “where the dominant company is able to show that the otherwise abusive 

conduct is actually a loss-minimising reaction to competition from others”.


cies. Nevertheless, the proposal of the European Commission (2005) provides 

relatively limited scope for taking efficiencies into account. First, according 

to the proposed approach, it will fall on dominant undertakings to prove the 

extent to which their conduct was justified on grounds of efficiency. However, 

such a system would send the wrong signal to the business community: investigations 

would often move quite far along before efficiency considerations 

fully come into play. Placing the burden of proof on competition authorities, 

by contrast, would make more sense as they are likely to be in a better 

position to obtain relevant evidence from the dominant undertaking as well 

as other market participants (such as consumer organizations) on whether 

challenged conduct promotes efficiency. 

Second, to assert a successful efficiency defense under the proposed framework, 

dominant undertakings will be required to show that there are no other 

economically practicable and less anticompetitive alternatives to achieve the 

claimed efficiencies. This condition means that liability could be imposed even 

on conduct whose efficiency and consumer benefits far outweigh its adverse 

effect on competitors simply because there exists an alternative that would 

have disadvantaged rivals less. We doubt that such a rule would have any 

economic justification and any basis in commercial reality. 

Finally, the effectiveness of these rules in safeguarding consumer welfare 

would be weakened under the proposal of European Commission (2005) for 

which some firms are virtually excluded from the possibility of an efficiency 

defense: according to this proposal, the protection of competitors would be 

given priority over efficiency when the dominant undertaking holds a market 

share above seventy-five per cent. In our view, efficiencies should be assessed 

in the same manner in all cases, regardless of the defendant’s market 

share: undertakings that generate pro-competitive efficiencies that benefit 

consumers should not be penalized regardless of the level of market share or 

potential impact on less efficient competitors. 

5.4.2 Predatory Pricing 

Predatory pricing is defined by European Commission (2005) as “the practice 

where a dominant company lowers its prices and thereby deliberately incurs 

losses or foregoes profits in the short run so as to eliminate or discipline one 

or more rivals or to prevent entry by one or more potential rivals thereby 

hindering the maintenance or the degree of competition still existing in the 

market or the growth of that competition”. The standard antitrust approach 

uses a number of cost benchmarks in order to assess whether “predatory pricing” 

by a dominant undertaking has actually taken place, and in particular 

it sets a cut-off such that pricing below this cut-off gives rise to a rebuttable 

presumption that the pricing is predatory. This strategy is supported by the 

traditional idea that pricing below marginal cost should have an exclusionary 

purpose in standard markets, while pricing above marginal cost should not.


The theory of market leaders emphasizes some limits of this way of thinking: 

pricing at or below marginal cost by the market leader does not need to 

exclude (equally efficient) competitors and it does not even need to induce 

short run losses for the same leader. To see why, let us remember that, as 

we noticed in Chapter 3 and in Section 5.2.1, a leader in a standard market 

with quantity competition and endogenous entry can generally choose 

between two alternative strategies. The first one is to price below the rivals 

and allow their entry with a price equal to their average cost but above the 

marginal cost. The second strategy is to choose a limit price such that entry 

is not profitable for any firm. The former strategy is optimal when marginal 

costs are increasing enough in the production level and/or products are differentiated, 

while the latter strategy is optimal in the case of decreasing or 

constant marginal costs and/or homogenous goods. 

Let us focus on the first situation. When goods are homogenous, the 

equilibrium strategy of the leader is simply to price at marginal cost, and its 

profits are positive because production is in the region where average total 

costs are increasing. When goods are differentiated, the equilibrium price of 

the leader is above its marginal cost, and profits are again positive. As we have 

seen, in this equilibrium entry occurs, and is not deterred. Moreover, if the 

leader can obtain positive profits in equilibrium by pricing at marginal cost, 

positive profits could be preserved even by pricing slightly below marginal 

cost as long as the scale of production is large enough. 

Let us focus on the second situation now. The leader can deter entry when 

marginal costs are constant or decreasing and/or goods are homogenous, and 

this happens with a price of the leader above the marginal cost. Nevertheless, 

when entry is endogenous this is a normal competitive strategy of a firm able 

to exploit scale economies and reduce average costs of production (and, as 

we have seen in Section 1.1, this strategy does not even reduce welfare). 

Finally, in Section 2.9 we saw that in dynamic (and multi-sided) markets 

where demand is characterized by network externalities or supply is characterized 

by learning by doing, leaders may want to price below the marginal 

cost without entry deterrence purposes. The purpose of pricing below marginal 

cost would be to develop network effects or decrease costs for the future 

and to be more aggressive in the future competition. 

In conclusion, it is highly questionable that the marginal cost should be 

the right theoretical cut-off below which predation can be presumed, and we 

do believe that a rule of reason should be applied also in this case, because 

different sectors and different cost and demand structures require different 

approaches to the definition of predatory pricing. 

For the sake of argument, suppose we could agree that marginal cost 

pricing represents a crucial cut-off under some circumstances. The problem 

is that it is quite difficult to measure such a figure. Therefore, many antitrust 

scholars, notably Areeda and Turner (1974), have proposed to substitute it 

with the average variable cost:


“the incremental cost of making and selling the last unit cannot 

readily be inferred from conventional business accounts, which 

typically go no further than showing observed average variable cost. 

Consequently it may well be necessary to use the latter as an indicator 

of marginal cost” 

This rule has influenced antitrust policy worldwide, but one should always 

keep in mind that there are (demand and technological) conditions 

under which its premise, the marginal cost as a cut-off below which pricing 

is predatory, is not valid. 

On the basis of our theoretical discussion, we can now try to draw our 

conclusions on the proper approach to predatory pricing. As we have noticed 

repeatedly in this book, one can not judge the pricing behavior of a market 

leader in a correct way without taking the entry conditions into account. 

When entry is endogenous, in the practical sense that entry is driven by 

profitable opportunities and it is rapid, no firm can manipulate the market 

at its will. As McGee (1958) noticed in his pioneering work on predatory 

pricing, a necessary condition for the success, and therefore the viability, of 

a predatory strategy is that entry must be exogenously blocked: 

“Obstacles to entry are necessary conditions for success. Entry is 

the nemesis of monopoly. It is foolish to monopolize an area or market 

into which entry is quick and easy. Moreover, monopolization that 

produces a firm of greater than optimum size is in for trouble if entry 

can occur even over a longer period. In general, monopolization will 

not pay if there is no special qualification for entry, or no relatively 

long gestation period for the facilities that must be committed for 

successful entry.” 

Only when entry is not feasible (even when it could be profitable), a leader 

can hope to exclude the current rivals and monopolize the market. 

On the basis of these considerations, we propose the following rule based 

on two steps: 

1) the Antitrust Authority should evaluate whether the undertaking is 

effectively constrained by endogenous entry of competitors in his strategic 

choices: if entry is endogenous dismiss the case, otherwise proceed. 

2) the Antitrust Authority should evaluate the relation between price, average 

total cost (ATC) and average variable cost (AVC): 

a) a price above ATC should be lawful without exceptions; 

b) a price below ATC but above AVC should be presumed lawful with the 

burden of proving the contrary on the Antitrust Authority, and on the basis 

of the consequences on consumers and allocative efficiency; 

c) a price below AVC should be presumed unlawful with the burden of 

proving the contrary on the undertaking, through an efficiency defense or 

proving that demand or technological conditions reduce the relevant cut-off 

below the AVC.


Notice that the first step we propose is different from the traditional one, 

which simply evaluates whether there is a dominant position in the relevant 

market. 35 The traditional step is based on the idea that after excluding the 

rivals, a dominant firm can monopolize the market and recoup its initial losses 

with higher prices. But, this is impossible when entry in the competition in 

the market is endogenous (there is no way to recoup losses by increasing 

future prices if a price increase attracts entry), and it is extremely unlikely 

when entry in the competition for the market is endogenous (there is a low 

probability to recoup losses by increasing future prices of goods that may 

be soon replaced by innovations of other firms). The traditional definition 

of dominance (associated with the market share and the related indexes of 

concentration) should not be the relevant element to establish the likelihood 

of recoupment, particularly in high-tech markets. We believe that the focus 

should not be on the market leader in the first step of an antitrust investigation 

for abuse of dominance, but on the followers and on the chances that 

these followers have to exploit profitable opportunities in the market. 

Concerning the second step in the evaluation of predatory strategies, EU 

antitrust has also adopted a similar approach (but an efficiency defense still 

needs to be formally introduced). However, the recent proposal by European 

Commission (2005) has suggested to substitute the AVC with an average 

avoidable cost (AAC), the average of the costs that could have been avoided 

if the undertaking had not produced a discrete amount of extra output (this 

extra output is usually the amount allegedly subject to abusive conduct), a 

sort of average marginal (or incremental) cost of the extra output to serve 

the predatory sales. Unfortunately, the AAC can be quite higher than the 

right theoretical concept whenever it accounts for fixed costs. Moreover, the 

AAC can be much more difficult to measure than the AVC, since it is almost 

always impossible to precisely define which costs are sustained for a given 

output and isolate the extra output (supposedly the predatory output) from 

the total one. Finally, there are well known conditions, as in the presence 

of network externalities and multi-sided markets, under which extremely ag- 

35 The definition of the relevant market generally depends on an empirical analysis 

of the way demand of substitute products changes with changes in the price of 

the hypothetical dominant firm. Such an analysis can be problematic because the 

market price could be above its competitive level. For instance, a widely used 

method is the SSNIP-test, which defines the relevant market as the smallest 

market where a Small but Significant Non-transitory Increase in Prices (say of 

5-10%) increases the profits of a hypothetical monopolist. This test is ideal when 

prices are close to the competitive level, but otherwise it is biased and leads to a 

too-wide market definition (which in turn may lead to a findingofnodominance 

inawidemarket).Thisproblemisknownasthe‘cellophane fallacy’, from the 

subject of the du Pont case (1956). It should be noticed that such bias should 

not emerge (and the SSNIP-test at the prevailing prices should be valid) when 

the market leader is constrained by endogenous entry (see Etro, 2007,b).


gressive pricing is a normal competitive strategy for a market leader. For 

instance, it is a standard practice for multi-sided markets to charge less one 

side of the market (as readers for a newspaper or end-users for video game 

consoles) and more the other side (advertisers and game developers in these 

examples), 36 without an exclusionary purpose but only to create network effects 

and increase the value of the interactions between the two sides. Often, 

the price on one side is not only below cost, but even below zero (the sale is 

subsidized with free add ons), and nevertheless even such a strategy is not 

necessarily predatory. For these reasons, we believe that the traditional AVC 

remains a better reference than the AAC. 37 

5.4.3 Bundling 

Looking at the approach of the European Commission (2005) on bundling, 

again it appears that its positive principles are not fully carried through. 

Indeed, economists today generally acknowledge that tying can produce positive 

efficiencies and consumer benefits, and that a rule of reason should be 

adopted in evaluating its anti-competitive effects. The pro-competitive effects 

are particularly pronounced in the case of technical tying (when companies 

innovate by linking formerly separate technologies or products, efficiencies often 

emerge through improved performance and quality). Moreover, they can 

also emerge because tying strengthens price competition, and so it can be 

used as an aggressive strategy by leaders facing endogenous entry in the secondary 

market: as we have seen in Section 2.10, under product differentiation 

in this market, such an aggressive strategy by the leader would induce low 

prices without eliminating product diversification in the secondary market. 

The current EU approach, however, perpetuates a biased position against 

bundling per se. 

36 According to the Rochet-Tirole (2003) rule, the higher price should be for the 

market side with higher elasticity of demand and vice versa. But this goes right 

against the fundamental principle of monopoly pricing for which a higher price 

should be for the market side with lower elasticity of demand and vice versa. 

37 In certain sectors, the same proposal uses a long-run average incremental cost 

benchmark (LAIC), instead of AAC. This is usually the case in industries where 

fixed costs are high and variable costs very low. In these cases, the LAIC benchmark 

is used as the benchmark below which predation is presumed. The same 

considerations as before hold also here: there are not economic justifications for a 

change of standard from AVC to LAIC. Moreover, we believe that the LAIC standard 

is inconsistent with business reality because it requires companies to price 

to cover their own average sunk fixed costs that are unrecoverable: this approach 

ignores the economic reality that, when market leaders decide how to price a 

product, they do not consider their own costs that are sunk or unrecoverable, 

even if not a single product is sold.


We have many doubts on the same definition of tying adopted in the EU 

approach, which places too much emphasis on consumer demand for the tied 

product in the context of its “distinct products test” as a proxy for determining 

whether the tying arrangement produces efficiencies. To exemplify our 

doubts, notice that, while there is clearly consumer demand for shoelaces, this 

should not mean that shoes and shoelaces are distinct products for the purposes 

of tying analysis. This issue can only be addressed by asking whether 

there is consumer demand for shoes without shoelaces. In sum, whether or 

not consumer demand exists for the tied product is the wrong question; the 

correct question is whether there is any significant consumer demand for the 

tying product without the tied product. Unless the analysis focuses on this 

question, there is a danger that the mere existence of consumer demand for 

the tied product may prevent the emergence of efficient tying arrangements 

and end up protecting suppliers of tied products at the expense of consumers 

and innovation. 

Moreover, in the case of technical integration of two products that were 

previously distinct, the distinct products test itself may not be helpful for 

understanding market dynamics because, by definition, this test is backwardlooking. 

A better approach in these cases would be simply to ask whether the 

company integrating the previously distinct products can make a plausible 

showing of efficiency gains: since technical tying is normally efficient, market 

leaders would be able to continue producing innovative products benefiting 

consumers without running afoul of the prohibitions on tying. Finally, since 

tying usually enhances price competition, it should never be abusive when 

it is standard commercial practice (which is also indirect evidence that such 

tying generates efficiencies, or that there is no demand for the unbundled 

product). 

We are also concerned that the current approach fails to acknowledge 

that bundling can be used to create value for consumers in markets that experience 

network effects and in multi-sided markets (further analyzed in the 

next chapter). For instance, bundling is a valuable strategy to gain broader 

distribution of the products or services that are subject to network effects. 

And the broader the distribution, the greater the value produced for all consumers. 

This is particularly true when the product or service in question has 

low (or zero) marginal costs, because the supplier can include the product or 

service in bundles with other products at no cost. In a multi-sided market 

multiple types of customers gain from reciprocal interaction, as in the case 

of advertisers and readers for a journal: complex business models resulting 

from multi-sided markets often require bundling practices because the consumption 

on one side of the market is being “sold” on the other side of the 

market, and piece-meal consumption on one side of the market would break 

down the interdependent ecosystem. 38 

38 On the antitrust implications of multi-sided markets see Evans (2003b).


Finally, in the EU approach the standard of proof the antitrust authority 

is required to meet to establish harmful foreclosure effects is too low, particularly 

in light of the fact that the analysis of foreclosure effects can be 

speculative in nature. According to the current EU approach to bundling, 

actual market foreclosure effects are not required: it is enough that such effects 

are “likely” to occur. In other words, the mere risk of foreclosure can 

result in a finding against a dominant company. A standard of proof that 

requires convincing evidence would rather help ensure that companies will 

not be deterred from bringing new products to market as a result of concerns 

about remote and potential foreclosure effects. 

5.4.4 Intellectual Property Rights 

Finally, we want to look at the relationship between antitrust and the protection 

of IPRs. While we noticed that the latter should be the focus of 

legislation and not of the discretionary behavior of antitrust authorities, the 

current EU approach deals with IPRs in the discipline on refusals to supply, 

that is, situations where a dominant company denies a buyer access to an 

input in order to exclude that buyer from participating in an economic activity. 

In general, four conditions have to be fulfilled in order to find a refusal 

to supply be abusive: i) the behavior must be properly characterized as a 

termination of a previous supply arrangement; ii) the refusing undertaking 

must be dominant; iii) the refusal must be likely to have a negative effect 

on competition; and iv) the refusal must not be justified objectively or by 

efficiencies. Only when the dominant supplier has not previously supplied the 

input to a potential buyer, as for IPRs, an additional criterion is added: v) 

the input must be “indispensable” to carry on normal economic activity in 

the downstream market (a so-called “essential facility”). 

Nevertheless, the European Commission (2005) correctly points out that 

“to maintain incentives to invest and innovate, the dominant firm must not 

be unduly restricted in the exploitation of valuable results of the investment. 

For these reasons the dominant firm should normally be free to seek compensation 

for successful projects that is sufficient to maintain investment 

incentives, taking the risk of failed projects into account. To achieve such 

compensation, it may be necessary for the dominant firm to exclude others 

from access to the input for a certain period of time.” The proposal clearly 

states the priority of IPR protection, saying that “imposing on the holder 

of the rights the obligation to grant to third parties a licence for the supply 

of products incorporating the IPR, even in return for a reasonable royalty, 

would lead to the holder being deprived of the substance of the exclusive 

right”. Therefore, another more restrictive criterion is added in the case of 

a refusal to license IPRs: the undertaking which requests the licence should 

intend to produce new goods or services not offered by the owner of the IPRs 

and for which there is a potential consumer demand. This additional criterion 

is in line with established case law, but an exception to this criterion is


introduced by the European Commission (2005). This states that a refusal to 

license IPR-protected technology which is indispensable for follow-on innovation 

may be abusive even if the license is not sought to directly incorporate 

the technology in clearly identifiable new goods and services, since the refusal 

to license an IPR-protected technology “should not impair consumers’ ability 

to benefit from innovation brought about by the dominant undertaking’s 

competitors”. This exception is inconsistent with economic analysis. As we 

have seen in Chapter 4, there are no clear economic arguments supporting 

the view that weakening IPRs could ever strengthen innovation in the long 

run, even when innovation is sequential. As a matter of fact, the opposite is 

true: the protection of IPRs for sequential innovations is more important to 

promote innovation and growth because it creates a multiplicative effect on 

the incentives to innovate and it fosters technological progress and growth. 

Finally, concerning the refusal to supply information needed for interoperability, 

the proposal in European Commission (2005) states that leveraging 

market power from one market to another may be an abuse of a dominant 

position and it may not be appropriate to apply the same high standards for 

intervention even if such information may be considered a trade secret. The 

framework for assessing how such leveraging may occur or when trade secrets 

do not deserve the same high standards for protection has not been developed 

yet. Again, such a broad policy intervention could have chilling effects 

on the incentives to invest and innovate and could ultimately end up protecting 

inefficient competitors that may free ride on the risks and investments of 

the dominant undertaking, therefore in contradiction with the objective of 

protecting competition on the merits. 


In this book we have proposed an alternative approach to antitrust policy. 

Taking into account the endogeneity of entry, we have seen that standard results 

of the post-Chicago literature can be radically modified. The main implications, 

analyzed in this chapter, concern the behavior of market leaders and, 

consequently, the antitrust approach to abuse of dominance. In other parts 

of this book, we have also derived implications for the antitrust approach 

to mergers, collusion and state aids. The overall flavor of our approach to 

antitrust is reminiscent of the Chicago school. Nevertheless, our analysis is 

based on solid game theoretic foundations that the original Chicago view did 

not have. 

The theory of market leaders has shown that whether entry in a market 

is exogenous or endogenous makes a lot of difference for the way leaders 

behave. In markets where entry is independent from the profitability conditions, 

market leaders can adopt accommodating strategies to increase prices 

or aggressive ones to exclude rivals, and their strategies can harm consumers.


When entry is endogenously dependent on the profitability conditions in the 

market, the leaders always adopt aggressive strategies which typically do not 

harm consumers. For instance, a firm competing with a single rival could 

engage in accommodating pricing to increase mark ups, or could engage 

in predatory pricing to induce the exit of the rival, but a firm facing endogenous 

entry of competitors will ordinarily engage in aggressive pricing 

strategies without exclusionary purposes. A monopolist in a primary market 

competing with a single rival on a secondary market may bundle its goods to 

monopolize the secondary market as well, but when the secondary market is 

characterized by endogenous entry the only purpose of bundling can be the 

strengthening of price competition. A firm facing a single rival could adopt 

vertical restraints on its retailers or price discrimination strategies to soften 

price competition, but when the same firm faces endogenous entry of rivals 

these anti-competitive practices will not be in its interest. Of course, notice 

that efficiency reasons can still motivate the adoption of bundling, vertical 

restraints, price discrimination or other strategies. 

The theory of endogenous entry delivers a related and strong result on 

horizontal mergers (see Section 2.13). As well known, even in the absence of 

cost efficiencies, these mergers are often profitable when entry is exogenous 

because they allow the merged entity to increase prices or restrict production 

so as to enhance profitability. These effects are counterproductive when entry 

is endogenous because any accommodating strategy attracts entry. Therefore, 

the only rationale for mergers in markets with endogenous entry must be a 

cost efficiency large enough to (more than) compensate the strategic disadvantages 

associated with the merger. In these cases, mergers are welfare 

improving. 

The theory of endogenous entry also has some implications for the case in 

which collusive cartels are organized between a restricted number of firms (see 

Section 3.5). These cartels, as with any price fixing agreements, always lead 

to higher prices and lower welfare when the number of firms in the market 

is exogenous. However, when entry in the market is endogenous collusive 

cartels are ineffective, unless they act as leaders. In this last case, the cartels 

coordinate aggressive strategies aimed at increasing the market shares of their 

members through low prices, and their implementation is always sustainable 

and does not harm consumers. 

The theory of market leaders and endogenous entry can be applied to 

standard problems of strategic policy to evaluate the role of state aids aimed 

at promoting exports. These are always optimal when the domestic firms export 

in markets where entry is endogenous, and they do not harm domestic 

or foreign consumers. Therefore limitations to state aids and export subsidies 

should be exempted when they concern firms competing in international 

markets where entry is free. 

Finally, the theory of market leaders and endogenous entry has implications 

also in the case of competition for the market. Market leaders invest


more in R&D when threatened by a competitive pressure, while they tend 

to stifle innovation in the absence of such a pressure: hence, persistence of a 

leadership in high-tech sectors can be consistent with effective dynamic competition 

for the market, which leads to a faster rate of technological progress 

in the interest of consumers. 

It is clear that the relevance of our results depends on the relevance of 

the hypothesis that entry is endogenous. As we repeatedly pointed out, it 

does not matter what constrains entry, but simply that some fixed costs of 

production or some opportunity costs of participating to the competition 

endogenously limit entry of firms in the market. One may argue that entry 

can be regarded as endogenous in the medium and long run, but not in the 

short run. If this is the case, and if antitrust policy is aimed at correcting 

distortions in the medium and long run (as opposed to short run distortions), 

then our results are potentially relevant. 

In the next chapter we move on to examine in more detail the markets 

of the New Economy. A recent important article by Segerstrom (2007) on 

technological progress in the New Economy has a simple and suggestive title, 

“Intel Economics”. This title emphasizes the importance of market leaders 

of the high-tech sectors in driving innovation and global growth. In the next 

chapter, we will borrow the style of that title to refer to what is probably 

the major market leader of the New Economy and the subject of some of the 

most representative antitrust cases in recent history.

6. Microsoft Economics 

After examining theoretical and institutional aspects of the behavior of market 

leaders and of the role of antitrust policy, this chapter approaches an 

important example of market leadership and technological leadership which 

is also associated with well known antitrust issues. The choice of Microsoft 

as a symbol of market leadership is somewhat natural: Microsoft is one of 

the most visible and relevant companies in the New Economy, one of the 

most innovative firms in one of the most dynamic industries. The antitrust 

cases in which this company has been involved in both the US and the EU 

attracted primary attention of media, policymakers and observers. Many important 

economists were involved in these antitrust cases in both the US and 

the EU, and many others were inspired by them while developing theoretical 

and empirical analysis on the structure of the software market, on the role 

of Microsoft in this market and on the role of antitrust policy for the New 

Economy. 

In a recent important book, Evans et al. (2006) have emphasized the 

crucial role that software platforms are playing in shaping our economies, 

in enhancing the development of many traditional sectors, and ultimately 

in affecting our way of living. These “invisible engines”, as they call the 

software platforms, power not only the PC industry but also other industries 

like those associated with mobile phones and other handheld devices, 

video games, digital music, and (with strong externalities for the rest of the 

economy) on-line auctions, online searches and web-based advertising. Their 

claim is that software platforms and microprocessors are at the basis of a new 

industrial revolution, exactly as the steam engine had been at the basis of 

the first industrial revolution (1760-1830) and electric power at the basis of 

the second industrial revolution (1850-1930). The third industrial revolution 

began with the introduction of commercial PCs in the early 80s and had a 

second phase starting in the mid 90s with the diffusion of the Internet. 1 Ob- 

1 The Internet is a global network of interconnected computer networks (linked 

by copper wires, fiber-optic cables and wireless connections) that transmit data 

by packet switching using the standard Internet Protocol (IP) and the Transfer 

Control Protocol (TCP). The World Wide Web (WWW) is a collection of interconnected 

documents and other resources (linked by hyperlinks and Uniform 

Resource Locators, or URLs) that is accessible via the Internet, as are many

208 6. Microsoft Economics 

servers have talked about “Intel economics”, “Microsoft economics” or the 

“Internet economics” to refer to this period of innovations in general purpose 

technologies, and to describe the ultimate engine of growth in the New 

Economy. 2 

What follows in this chapter surveys the wide academic debate on these 

issues. Our aim is not to provide a comprehensive analysis of the software 

market or of the role of Microsoft, but to point out relations between our 

theoretical results on the behavior of market leaders and the structure of 

this market, and use this theoretical background to evaluate antitrust issues 

involving Microsoft. 

The chapter is organized as follows. Section 6.1 describes the development 

of the software market within the New Economy, and the role of Microsoft 

in this environment. Section 6.2 describes the genesis of the antitrust cases 

which involved Microsoft and the remaining sections adopt our theoretical 

instruments in evaluating the basic issues emerging in these cases: whether 

Microsoft is a monopoly in Section 6.3, whether its bundling strategies are 

predatory in Section 6.4, and whether its innovations should be disclosed to 

promote interoperability in Section 6.5. We conclude in Section 6.6. 

6.1 The Software Market 

The software market was developed in the last few decades. 3 In the 1960s, the 

computer industry was dominated by IBM, which manufactured mainframe 

computers used by large enterprise customers. These computers were expensive 

to purchase and expensive to maintain. As a result, very few consumers 

had access to computers. Apart from IBM, mainframes were offered by firms 

such as Sperry, Control Data, Philco, Burroughs, General Electric, NCR, ect. 

other services like the emails. Other protocols or applications run on top of this 

structure. In 1958 United States created the Advanced Research Projects Agency, 

which supported first the research of the MIT Lincoln Laboratory in networking 

country-wide radar systems, and then the development of ARPANET, the 

main predecessor of the Internet, activated in 1969 at UCLA. The first TCP/IP 

wide area network was operational by 1983, when the American National Science 

Foundation constructed a university network backbone that would later become 

the NSFNet. In 1991 the European CERN launched the new WWW project 

after having created the Hypertext markup language (html), the predominant 

language for the creation of web pages, the Hypertext transfer protocol (http), 

the application that links and provides access to the files, documents and other 

resources of the WWW, and the first web pages. Popular web browsers emerged 

soon after that. 

2 On the role of the Information and Communication Technology in the recent 

growth experience see Dosi et al. (2007) 

3 Part of this section is based on Etro (2007d).

6.1 The Software Market 209 

In the mid 70s the US market was still dominated by IBM followed by Honeywell, 

Burroughs, Sperry, Control Data, NCR, Digital, G.E. and Hewlett- 

Packard (see Sutton, 1998, Ch. 15). There was little or no interoperability 

among mainframes from different vendors. For the most part, an enterprise 

customer was required to choose an all IBM solution or an all Sperry solution. 

In the 1970s, Digital Equipment achieved considerable success with 

a line of less expensive minicomputers that were well-suited to engineering 

and scientific tasks. Again, however, there was little or no interoperability 

between these minicomputers and mainframes offered by IBM and others. 

The structure of the industry at that time was still largely vertical. By 1980, 

a number of companies had started offering less expensive microcomputers 

which, again, were not interoperable with one another. Early PCs by Altair, 

Tandy, Apple, Texas Instruments, Commodore and Atari ran their own operating 

systems, meaning that applications written for one brand of PC would 

not run on any other brand: the industry was fragmented. Apple, founded by 

Steve Jobs and Steve Wozniak in 1976, developed a very successful software 

platform, especially because of VisiCalc, an electronic spreadsheet which was 

introduced in 1979 and soon became a killer application for Apple II. 

In the early 80s, IBM announced plans to introduce an IBM personal 

computer. The first one was offered with operating systems (OSs) produced 

by others: CP/M-86 from Digital Research (a rewrite of the leading OS at 

the time), UCSD-p System by Softech Microsystems, and PC-DOS developed 

by Microsoft, a company founded by Bill Gates, a young software architect 

who dropped out of Harvard University to create what was going to become 

a symbol of market leadership in the New Economy. Microsoft’s OS won 

the race mainly because it was cheaper than CP/M-86 ($ 40 against $ 240) 

and faster than p-System. Moreover, Microsoft managed to keep the right to 

license its OS to other PC makers, under the name MS-DOS: this drove its 

success in the software market. As Evans et al. (2006) noticed, 

“having multiple operating systems run on a hardware platform is 

a poor strategy. The idea, of course, was to ensure that the hardware, 

not the operating system, became the standard that defined the platformanddetermineditsevolution.Indeed,IBMfollowedanimportant 

economic principle for traditional industries: all firms would like 

everyone else in the supply chain to be competitive. IBM didn’t seem 

to recognize that this was far from a traditional industry... Applications 

are generally written for software platforms, not the underlying 

hardware. The more fragmented the installed base of operating systems, 

the less attractive it is to write an application for any one of 

them.” 

Not surprisingly, IBM’s multiple-OS strategy did not work, the hardware 

sector became always more fragmented, with many PC manufacturers producing 

clones of the IBM PC and most of them running MS-DOS, the exact 

replica of the operating system running on IBM PCs. In the second half of


the 80s IBM reacted by developing a new operating system, OS/2, while 

Microsoft independently developed Windows, whose lead at that point became 

unreachable. According to some observers, IBM based its strategy on 

its brand name and its research capacity, while Microsoft invested more in 

supporting the developers of software applications and in what is often called 

“evangelization”: convincing software producers to develop applications for 

Windows. This was the winning strategy: the share of IBM in the market for 

the so-called IBM-compatible PCs decreased over time (in 2004 IBM arrived 

to the point of selling its PC division to Lenovo), while the market share of 

Microsoft in the software market increased. 

Over time, the computer industry had moved from the old vertical structure 

toward a horizontal structure. This was characterized by a market for 

chips (Intel as a leader, Motorola, ARM, TI, AMD,..), one for hardware and 

peripheral equipment (IBM, Dell, Hewlett-Packard, Packard Bell, Compaq, 

Gateway, Acer, Fujitsu,...), one for operating systems (Windows as a leader, 

OS/2, Unix, Linux, Solaris,..), one for application software (Office, Scientific 

Workplace, Adobe Acrobat, Macromedia Dreamweaver,..) and one for sales 

and distribution, with competition within horizontal levels and higher interoperability 

across levels. A similar horizontal structure has emerged in the 

industries for mobile phones and personal organizers. This is not by chance: 

such decentralized structures can work well when technical interactions between 

complementary products are stable and well defined, while vertical 

structures would become too rigid to control them. Apple, the only large 

player remaining a fully integrated structure producing both hardware and 

software for its PCs and for other devices, had to become quite active in 

attracting applications from other software developers, in order to build network 

externalities. 4 

6.1.1 Network Effects 

A software platform is a software program that makes services available to 

other software programs through external “hooks” called Application Programming 

Interfaces (APIs). Examples are the operating systems running on 

PCs as Windows, Mac OS or Linux, those employed by videogame consoles 

as the Sony one for PlayStation or Windows 2000 for the Xbox, the Symbian 

4 Famous is the 1985 letter by Bill Gates to Apple, which advised its future main 

competitor to license the Mac OS to PC manufacturers to create network effects 

and establish a standard (at the time Microsoft was still earning its revenues 

mainly from software applications, most of which, like Word and Excel, were important 

applications for the Macintosh). As well known, Apple chose the harder 

way, but it is still a strong and extremely innovative company in the PC industry 

today.


operating system for cellular phones, 5 Palm OS for personal digital assistants 

(PDAs), RIM for the BlackBerry, Mac OS for the Apple iPod and iPhone, 

and so forth. 

To understand the peculiarities of the software market in general it is convenient 

to focus briefly on the main functions of PC operating systems. The 

main one is to serve as a platform on which applications can be created by 

software developers. OSs supply different types of functionality, referred to as 

system services, that software developers can call upon in creating their applications. 

These system services are made available through APIs. When an 

application calls a particular API, the operating system supplies the system 

service associated with that API by causing the microprocessor to execute a 

specified set of instructions. Software developers need well-defined platforms 

that remain stable over time. They need to know whether the system services 

on which their applications rely will be present on any given PC. Otherwise 

theywouldhavetowritethesoftwarecodetoprovideequivalentfunctionality 

in their own applications, generating redundancy, inefficiency and a lack of 

interoperability. Moreover, modern OSs provide a user interface, the means 

by which users interact with their computers. User interfaces for computers 

have evolved dramatically over the last decades, from punch card readers, 

to teletype terminals, to character-based user interfaces, to graphical user 

interfaces, first introduced (at a low price) by Apple with Macintosh in 1984. 

Finally, OSs enable users to find and use information contained in various 

storage devices: local ones, such as a floppy diskette, a CD-ROM drive, a 

jump drive or the hard drive built into a PC, or remote ones, such as local 

area networks that connect computers in a particular office, wide area networks 

that connect computers in geographically separated offices, and the 

Internet. 

Over time, the OS of Microsoft became the most popular because Microsoft 

continually added new functionality and licensed it to a wide range 

of computer manufacturers with extremely aggressive price strategies. Microsoft 

recognized early on that an OS that served as a common platform 

for developing applications and could run on a wide range of PCs would 

provide substantial benefits to consumers. Among other advantages, development 

costs would fall and a broader array of products would become available 

because products could be developed for the common platform rather than 

for a large number of different platforms. By providing a single OS that ran 

on multiple brands of PCs, Microsoft enabled software developers to create 

applications, confident that users could run those applications on PCs from 

many different computer manufacturers. In addition, applications developed 

for a single platform are more easily interoperable because they rely on the 

same functionality supplied by the underlying OS. 

5 Symbian is a joint venture founded by Nokia, Ericsson and Motorola (which left 

it in 2003). It is currently owned (in order of shares of stocks) by Nokia, Ericsson, 

Sony Ericsson, Panasonic, Siemens AG and Samsung.


The original winning strategy of Microsoft was the creation of these network 

effects between hardware producers, software developers and consumers: 

computer manufacturers benefit because their PCs can run the many applications 

written for Windows and because users are familiar with the Windows 

user interface; software developers benefit because their applications can rely 

on system services exposed by Windows via published APIs and because they 

can write applications with assurance that they will run on a broad range 

of PCs; consumers benefit because they can choose from among thousands 

of PC models and applications that will all work well with one another and 

because such broad compatibility fosters intense competition among computer 

manufacturers and software developers to deliver improved products 

at attractive prices. But this argument should not be overemphasized: for 

many years, PC-DOS and OS/2 had as many applications as Windows, but 

IBM’s decline did not stop. There is indeed another and more traditional 

element that is fundamental also in the software market: the other crucial aspect 

of the strategy of Microsoft was its aggressive pricing strategy. This was 

strengthened through the development of the same network effects: conquering 

market shares, Microsoft could spread its huge fixed costs of production 

over a larger market and reduce the price, which in turn could enhance the 

network effects. 

6.1.2 Multi-sided Platforms 

Software platforms, as we have seen, deal with multiple sides. Microsoft deals 

with at least three: consumers, software developers and PC manufacturers. 

Apple produces hardware internally, hence it deals with the remaining two 

sides: consumers and software developers. Sometimes relationships are even 

more complex, as in the platform for smart mobile phones where, beyond 

OSs, software developers and handset makers, there are network operators (as 

Vodafone, NTT, T-Mobile, Orange, China Mobile, Telecom Italia Mobile,..) 

playing a coordinating role. 6 

In the presence of multiple sides with network effects between them, the 

choice of which ones should be charged more to use the platform is not simple. 

Rochet and Tirole (2003), Caillaud and Jullien (2003) and Evans (2003a) have 

noticed that software platforms, as other similar multi-sided platforms, give 

rise to market structures that are quite different from the traditional ones. 

For simplicity, here we will refer to two-sided platforms, which connect two 

sides in such a way that for each side the valuation of the interactions with the 

other side depends on the number of agents on the others side. These network 

externalities,andinparticularthenonneutral impact of the pricing structure 

on both sides (and therefore on these externalities) distinguishes a two-sided 

6 Moreover in this ecosystem not only competition within layers is strong, but also 

competition between layers is relevant.


market from a traditional one-sided market with different consumers (and 

possibly price-discrimination between them). 7 

An analogous situation to software platforms emerges in many completely 

different contexts. A classic example, useful to understand the implications 

of any kind of platforms, is given by newspapers. They are sold to readers, 

but they also sell advertising space to advertisers: the reader is not only a 

“customer” of the newspaper, the reader is also a supplier of “eyeballs” that 

the newspaper sells to advertisers. In this case network effects emerge because 

advertisers value their advertising more in a newspaper when the number of 

its readers is higher (the effect in the other direction may exist but is typically 

less important). This has crucial consequences on the pricing structure 

since a low price for the readers increases the number of sold copies and in 

turn enhances the value of advertising. Such a phenomenon is stronger when 

a newspaper is competing with other newspapers, and a low price reduces 

the readers of competing newspapers and the value of advertising on these 

competing newspapers. 

Other two-sided platforms include other media networks as television 

channels, real estate agencies, traditional auction houses, shopping malls, 

night clubs, payment card systems, telephone networks and many industries 

of the New Economy as those related with video game consoles, smart phones, 

digital music, PDAs, i-Mode, search engines (Google), on line communication 

(Yahoo! and Skype), on line social networks (MySpace, asmallworld, or Second 

Life), on line academic articles (JSTORE or SSRN) and on line shopping 

(Amazon and eBay). In many of these markets, multi-homing on at least one 

of the two sides is common: people often buy more than one journal or watch 

more TV channels (as companies advertise on multiple medias), hold multiple 

credit cards (as merchants accept multiple cards) and software developers 

prepare applications for multiple OSs (while individuals typically use only 

one). 

In each one of these examples, network externalities are crucial to the 

success of a software platform, and the pricing structure toward buyers and 

sellers is crucial to the creation of these network effects. In particular, a platform 

typically ends up charging one of the two sides less than the other, taking 

into account demand elasticities and which side values the other side more: 

the aim is to get on board as many agents as possible from one side, so as to 

increase the value of the platform for the other side and earn more revenue 

from it. For instance, when the price is the strategic variable, it is optimal to 

charge the side whose demand is more elastic, because this allows one to maximize 

the total volume of interactions. 8 Prices will be constrained downward 

7 See Section 2.9 for a theoretical analysis of this aspect. An early contribution on 

two-sided markets is due to Baxter (1983). 

8 Consider the simplest case of a monopolistic platform charging a group, say the 

buyers, a price p B per interaction with the other group, say the sellers, and 

charging the sellers a price p S per interaction with the buyers. If total demand


when there are competing platforms (especially in the case of multi-homing), 

and further bias may emerge for strategic reasons, 9 but the general principles 

on the balanced price structure between the two sides remain unchanged. In 

extreme cases, one side may even receive its goods or its services for free or 

even be subsidized so as to maximize earnings from the other side. 

The above theoretical results are fully confirmed by what happens in 

the above mentioned two-sided markets, whose companies typically settle on 

pricing structures that are heavily skewed toward one side of the market or, in 

other words, adopt what is sometimes called a “divide and conquer” strategy. 

Newspapers, television networks and even websites typically earn more from 

advertisers than from consumers, real estate agencies earn more from sellers 

(or from landlords) than from buyers (or renters), auction houses from sellers 

rather than from the buyers, shopping malls from stores rather than from the 

shoppers, night clubs from men rather than from women and payment card 

companies from merchants rather than from cardholders. Similarly, phone 

operators earn more from originating calls rather than from receiving ones, 

video game platforms from royalties on game developers rather than from 

of interactions is D(p B ) for the buyers and D(p S ) for the sellers, the number of 

interactions is D(p B)D(p S). Given a marginal cost per interaction c the profits 

of the platform are: 

π =(p B + p S − c)D(p B )D(p S ) 

whose maximization provides the following Rochet-Tirole (2003) rule p B + p S − 

c = p B / B = p S / S ,where i is the elasticity of demand for i = B,S. Similar 

outcomes emerge in case demand on each side depends on demand on the other 

side, with more complex pricing structures and with competition between platforms 

(see Armstrong, 2006, Rochet and Tirole, 2006, and Goldfain and Kováč, 

2007). 

9 Strategic reasons may bias the pricing structure of platform leaders. In the example 

of the previous footnote, suppose product differentiation on one side occurs 

and, with the usual notation, profits of a representative firm are: 

π =(p B + p S − c)D(p B )D(p S ,β S ) 

Suppose that the leader can commit to a price for the buyers, while, for simplicity, 

the others are given. Firms compete on the prices for the sellers. To verify the 

incentives of the leader, notice that, with the usual notation of Chapter 2 (with 

k =1/p B as preliminary commitment), we have: 

Π L 13(1/p S,β S , 1/p B)=(p Sp B) 2 D(p B)D 1(p S,β S ) < 0 

Assuming that SC holds, this implies that when entry is not free the leader will 

tend to underprice buyers to be accomodating in the competition for the sellers. 

However, when entry in the platform competition is endogenous, the leader will 

tend to overprice buyers to be aggressive in the competition for the sellers.


buyers of consoles (that are often sold below cost), while most of the other 

software platforms, including PC OSs, earn more from end users rather than 

from software developers. 10 

Notice that, in spite of the network effects, most of these two-sided markets 

are also characterized by a certain degree of fragmentation between platform 

providers, often associated with a certain degree of differentiation. Only 

when technological innovation is particularly important and fixed costs of 

investment in R&D are high, while marginal costs of production are particularly 

low, the number of competing platforms is endogenously reduced, as in 

the above mentioned markets of the New Economy. Nevertheless, tipping on 

a single leader rarely happens, especially when product differentiation and 

multi-homing have a role, as for video games. And even in these cases competition 

for the market can be quite effective and induce periods of persistent 

leadership with occasional replacement of the leader: pathbreaking innovations 

(or “killer applications”) are what competitive firms really look for. For 

instance, in the console video game industry, sequential innovations brought 

to leadership a number of companies as Atari (that reached 80% share of the 

market in 1980), Nintendo (90% of the market in 1987), Sega (leader in the 

early 90s), Nintendo again (in the mid 90s) and Sony with the PlayStation in 

different improved versions (during the last decade): recently Microsoft Xbox 

started gaining market shares, and Nintendo is still active, but the leadership 

of Sony (65% market share in 2004) does not appear under threat yet, 

especially after the recent successful launch of PlayStation 3. Similarly, after 

a number of unsuccessful attempts by many companies, Palm’s PDA gained 

success and leadership in the market for OSs for organizers thanks to a simple 

handwriting recognition system (65% market share in 2000) until Microsoft 

competing platform and other handheld devices, including Blackberry and 

(in perspective) Apple’s iPhone, started gaining success. 

Having described the role of network effects and multi-sided relations, it 

is now time to return to the software market, where these elements play a 

crucial role. 

6.1.3 Microsoft 

Microsoft was founded in 1975 by Bill Gates and Paul Allen to develop BA- 

SIC interpreters for the first PC, Altair 8800, and then other programming 

languages. Only later, did it start producing major software programs. In 

1981, Microsoft released its first operating system, MS-DOS, which had a 

10 This happens in different ways however: Microsoft licenses Windows, Palm and 

Symbian license their OSs to manufacturers of PCs, PDAs and cellular phones, 

while RealNetworks licenses access to digital content and Apple sells PCs and 

iPods, but none of these companies charges content owners (Apple and RealNetworks 

actually pay them) or software developers (which are typically subsidized).


character-based user interface that required users to type specific instructions 

to perform tasks. In 1985, Microsoft introduced a new product called 

Windows that included a graphical user interface, enabling users to perform 

tasks by clicking on icons on the screen using a pointing device called a 

mouse (basically the only piece of hardware produced by Microsoft for PCs). 

Windows 3.0, shipped in 1990, was the first commercially successful version 

of Windows. In 1995, Microsoft released Windows 95, which integrated the 

functionality of Windows 3.1 and MS-DOSinasingleoperatingsystem.In 

2000, Microsoft shipped Windows 2000 Professional, a new generation of PC 

operating system built on a more stable and reliable software code base than 

earlier versions of Windows. Windows XP represented a further evolution 

with a range of added functionality for both business and home users. In 

2007 Windows Vista has been released worldwide: it was the fruit of five 

years of work by eight thousand designers, programmers and testers and of 

an estimated investment of $ 10 billion to rewrite from scratch a new code. 

This impressive effort was probably related to the competitive pressure coming 

from the open source community, which is strongly supported by many 

large corporations willing to strengthen valid alternatives to Windows. 

Even if complete and homogenous data are unavailable, consistent evidence 

suggests that the market share of Windows on sales of OSs for PCs 

rapidly increased towards 80% in the first half of the 90s to gradually arrive 

at 92% in 1996, 94% in 1997, 95% in 1999, 96% 2001, and remained above 

90% since then (while the average consumer price of Windows, calculated as 

average revenue per licence to PC manufacturers based on Microsoft sales, 

remained around $ 44-45). Nevertheless, one should keep in mind that Linux, 

after having made inroads into corporations’ server computers, is now expanding 

into a much broader market, that of employees’ PCs, that a minor 

group of PC users (but strongly increasing in number, especially between expert 

users) downloads open source OSs from the Internet, 11 and that on the 

11 Estimates for the percentage of server computers running Linux worldwide are 

in the range of 20-25%, while desktop computers running Linux are around 3%. 

According to the Wall Street Journal (March13, 2007, Linux Starts to Find Home 

on Desktops), “market researcher IDC said licenses of both free and purchased 

versions of Linux software going into PCs world-wide rose 20.8% in 2006 over the 

previous year and forecast that licenses will increase 30% this year over last. That 

compares with 10.5% growth in 2004, according to IDC. Whether Linux gains a 

stronger footing in PCs depends partly on whether PC makers start supporting 

it more strongly. To date, neither Dell Inc.norHewlett-PackardCo.haveoffered 

PCs preloaded with Linux. But Dell has been soliciting input from its customers 

to help guide its plans for Linux — which some industry observers say could lead 

the company to start making Linux PCs [...] H-P says it has recently signed deals 

— on an ad hoc, custom basis — to provide Linux PCs to large customers.”


top of this market there are Apple computers running Mac OS. 12 It is clear 

that Microsoft has reached a robust leadership in the PC operating systems 

market for Intel-compatible computers. In line with our previous discussion, 

Evans et al. (2006) state four key strategies that have driven Microsoft to 

become the leader of the PC industry: 

“(1) offering lower prices to users than its competitors; (2) intensely 

promoting API-based software services to developers; (3) promoting 

the development the development of peripherals, sometimes 

through direct subsidies, in order to increase the value of the Windows 

platform to developers and users; and (4) continually developing 

software services that provide value to developers directly and to end 

users indirectly.” 

Beyond OSs, Microsoft is the leader in other markets for software applications. 

Some essential applications have been freely bundled with the operating 

system: for instance a basic word processing software (WordPad), a 

browser to access Internet (Internet Explorer) and media player functionality 

(Windows Media Player) have been gradually added for free to subsequent 

versions of Windows when they became standard components of a modern 

OS. Other more sophisticated applications are supplied separately. Most notablythisisthecaseoftheOffice 

Suite consisting of the word processor 

Word (first edition released in 1983), the spreadsheet Excel (1985), the presentation 

software PowerPoint (1987) and more. The main two applications, 

Word and Excel, have been successfully competing against alternative products 

like WordPerfect, WordStar, AmiPro and others on one side and Lotus 

1-2-3, Quattro and others on the other side. Liebowitz and Margolis (1999) 

have shown convincing evidence for which a better quality-price ratio together 

with network effects were at the basis of this evolution (it is important to note 

that Microsoft achieved leadership in the Macintosh market, hence without 

exploiting the presence of its own OS, considerably earlier than in the PC 

market). 

In the market for word processing applications, Microsoft’s market share 

was hardly above 10% at the end of the 80s, but gradually increased to 28% 

in 1990, 40% in 1991, 45% in 1992, 50% in 1993, 65% in 1994, 79% in 1995, 

90% in 1996, 94% in 1997 and arrived to 95% in 1998, remaining around this 

level afterward. Meanwhile the average consumer price of Word (calculated as 

average revenue per license) decreased from $ 235 in 1988 to $ 39 in 2001. In 

the market for spreadsheet applications, Microsoft followed a similar progress, 

with a market share of 18% in 1990, 34% in 1991, 43% in 1992, 46% in 1993, 

68% in 1994, 77% in 1995, 84% in 1996, 92% in 1997 and 94% in 1998, with 

12 As pointed out by Foncel and Ivaldi (2005), there is a certain variability between 

countries. The DOS/Windows platform is on 88 % of PC sales in Japan and 

98% in Germany. Data for the second half of the 90s are from International Data 

Corporation.


minor progress in the following years, while the average consumer price of 

Excel was decreasing from $ 249 in 1988 to $ 42 in 2001. 

Finally, Microsoft is also active in other strategic markets as a follower, 

in particular with the personal finance software Money (the leader being 

Intuit Quicken), the operating systems for smart phones Windows Mobile 

(the leader being Symbian, with a 60% market share in 2004), the video 

game console Xbox (the leader being Sony PlayStation, with a 65% market 

share in 2004), the search engine based portal Windows Live (the leader being 

Google, with more than 80% of searches on the Internet) and more. In 2006, 

Microsoft, led by the CEO Steve Ballmer, had revenues of $ 44.2 billion, 60% 

of which derives from Windows and Office, and net income of $ 12.4 billion, 

80-90% of which derives from Windows and Office. 

6.2 The Antitrust Cases 

Microsoft’s leading position induced large opposition in the industry and the 

emergence of multiple antitrust cases with importance at the global level. 13 

Microsoft has been under investigations in the US by the Federal Trade Commission 

and the Department of Justice since 1990, primarily for its contracts 

with computer manufacturers and for bundling secondary products with its 

OSs. 14 However, the most important US case began only in the late ’90s under 

the Democratic Clinton Administration, followed after a few years by the 

EU case. 

6.2.1 The US Case 

In the main Microsoft vs. US case, started in 1998, the software company was 

accused of protecting its monopoly in the OS market from the joint threat 

of the Internet browser Netscape Navigator and the Java programming language, 

15 which could have developed a potential substitute for OSs allowing 

13 This section is partly derived from Etro (2006d). 

14 Alreadyinthemid90swecouldseeimportanteconomistsinactionintheseearly 

cases. In 1995 the Nobel prize Kenneth Arrow intervened saying that “Microsoft 

appearstohaveachieveditsdominantpositioninitsmarketasaconsequence 

of good fortune and possibly superior products and business acumen” and that 

Microsoft’s licensing practices toward original equipment manufacturers “made 

only a minor contribution to the growth of Microsoft’s installed base. Even this 

minor contribution overstates the impact of Microsoft’s licensing practices on its 

installed base barrier to the entry and growth of competing operating systems” 

(Declaration of Kenneth Arrow, U.S..v.MicrosoftCorp., Civil Action No. 94- 

1564 (SS), January 17, p. 11-12). 

15 The dramatic expansion of the World Wide Web started in 1993 after the development, 

by a team from the University of Illinois, of the first graphical web

6.2 The Antitrust Cases 219 

software applications to run on hardware independently from the desktop 

OS. Basically, the hypothetical threat for Microsoft was the development of 

an alternative to the software platform based on the OS, a sort of middleware 

platform or a web-based platform leading to the “commoditization” of 

the OS (as ten years before the software platform led to the commoditization 

of hardware), and hence to the loss of leadership of Microsoft. Microsoft 

reacted by improving its Internet Explorer (IE) browser, engaging in contractual 

agreements with computer manufacturers and Internet service providers 

to promote preferential treatment for IE (notably AOL, whose “You’ve got 

mail” sound track was attracting more than 20 millions Americans at the 

time), and finally tying Windows with IE. For perspectives by economists 

who were active in the case see Fisher and Rubinfeld (2001) and Bresnahan 

(2001) on the side of US Government, and the essays in Evans (2002), 

especially Elzinga et al. (2002), on the opposite side. 16 

As Klein (2001) pointed out in an academic survey on the Journal of 

Economic Perspectives (Symposium on the Microsoft case), “Microsoft spent 

hundreds of millions of dollars developing an improved version of its browser 

software and then marketed it aggressively, most importantly by integrating 

it into Windows, pricing it at zero and paying online service providers and 

personal computer manufacturers for distribution. All of this was aimed at 

increasing use of Microsoft’s Internet Explorer browser technology, both by 

end users and software developers, to blunt Netscape’s threat to the dominance 

by Windows of the market for personal computer operating systems.” 

Microsoft’s investments in browser technology, which largely improved IE until 

it became a superior product compared to Netscape Navigator (see the 

empirical analysis in Liebowitz and Margolis, 1999), and Microsoft’s pricing 

of IE at zero (as always since then) appear to us as examples of aggressive 

strategic investment and aggressive pricing by a market leader facing competition, 

and not as anti-competitive strategies. 17 According to Klein (2001), 

browser, Mosaic. Netscape, founded in 1994, hired most of its developers to create 

Navigator. Java was developed at the same time by Sun as a middleware 

product to allow programmers to write applications that would run on line on 

any computer regardless of the underlying OS. 

16 For economic surveys on the case see Gilbert and Katz (2001), Klein (2001) and 

Economides (2001). For retrospective views see Motta (2004, Ch. 7) and Evans 

et al. (2005). 

17 In our view, the US case was characterized by a too limited focus on rigorous 

economic arguments in support of the different thesis. It is ironic that Microsoft’s 

internal documents and emails including aggressive expressions toward competitors 

were used to support the idea that Microsoft undertook its browser development 

for entry deterrence purposes. It is hard to see how the aggressive language 

of business people can prove more than competitive intent (on the use of internal 

documents to prove antitrust violations, see Manne and Williamson, 2005).


“a crucial condition for anticompetitive behavior in such cases is 

that the competitive process is not open. In particular, we should be 

concerned only if a dominant firm abuses its market power in a way 

that places rivals at a significant competitive disadvantage without 

any reasonable business justification. Only under these circumstances 

can more efficient rivals be driven out of the market and consumers 

not receive the full benefits of competition for dominance. The only 

Microsoft conduct ... that may fit this criteria for anticompetitive 

behavior are the actions Microsoft took in obtaining browser distribution 

through personal computer manufacturers” 

This is correct: a number of contractual restraints imposed by Microsoft 

on its distributors were potentially harmful and have been correctly forbidden. 

After a failed attempt by Judge Richad Posner to mediate in settlement 

negotiations, Judge Thomas Penfield Jackson decided to impose heavy behavioral 

and structural remedies on Microsoft, including the break up in an 

operating system and an application company (the so-called “Baby Bills”, as 

Baby Bells were the companies derived from the 1984 break up of AT&T). 

At the time, this draconian remedy was criticized by many economists with 

different perspectives on the case, for excessively penalizing the company 

without a clear relation between the punishment and the alleged crime, and 

for inducing perverse consequences for consumers. For instance, on the pages 

of The New York Times, Paul Krugman pointed out the risk of creating two 

monopolists engaging in double marginalization: 

“The now ‘naked’ operating-system company would abandon its 

traditional pricing restraints and use its still formidable monopoly 

power to charge much more. And at the same time applications software 

that now comes free would also start to carry heftly price tags” 

(Krugman, 2000a). 18 

18 Judge Jackson was later disqualifiedforviolatinganumberofethicalprecepts 

and being manifestly biased against Microsoft. The government proposal of splitting 

Microsoft into two companies, which was adopted by the Judge without 

substantive changes, had been supported by declarations of important economists, 

including Paul Romer and Carl Shapiro. For instance, Shapiro declared 

that, while “network monopolies can be very strong, they are most vulnerable to 

attack by firms with a strong position in the provision of a widely-used complementary 

product”, hence “the proposed reorganization of Microsoft into separate 

applications and operating systems businesses will lower entry barriers, encourage 

competition and promote innovation” (Declaration of Carl Shapiro, U.S. v. 

Microsoft Corp., Civil Action N0. 98-1232 (TPJ), p. 7 and p 29). Nevertheless, 

other economists were critical of the consequences of the break up on innovation. 

Krugman (2000b) again criticized a systematic reference to the promotion 

of innovation as a vague justification for the remedy: “we don’t know very much

6.2 The Antitrust Cases 221 

After the appeal phase and the return of the Republican Administration 

with George W. Bush, the DOJ changed attitude looking for a settlement. 

The November 2002 ruling of the District of Court decided on behavioral 

remedies aimed at preventing Microsoft from adopting exclusionary strategies 

against firms challenging its market power in the market for OSs. Moreover, 

the Court adopted forward looking remedies that required limited disclosure 

of APIs, communication protocols, and related technical information in order 

to facilitate interoperability, and created a system of monitoring of Microsoft’s 

compliance which has been working quite well in the last years. Since other 

derivative private actions have also been dismissed or settled, it seems that 

this long-standing conflicthasarrivedtoitsendintheUS. 

6.2.2 The EU Case 

The Microsoft vs. EU case was subsequently developed on somewhat similar 

issues. In particular, Microsoft has been accused of abuse of dominance in 

the market for OSs through technological leveraging and in particular in two 

ways: first, by bundling Windows with Media Player, a software for downloading 

audio/video content, and, second, by refusing to supply competitors with 

the interface information needed to achieve interoperability between work 

group server OSs 19 and Windows. Contrary to the US case, the bundling 

part of the EU case is a traditional case of bundling, since the competitors in 

the secondary market, notably RealNetworks, do not represent a threat for 

Windows, the primary product of Microsoft. 

In the famous antitrust decision of March 24, 2004, Competition Commissioner 

Mario Monti imposed on Microsoft the largest fine in the history 

of antitrust (€ 497 million), required Microsoft to issue a version of its Windows 

operating system without Media Player, and mandated the licensing of 

intellectual property to enable interoperability between Windows PCs and 

about what promotes innovation, and even some of what we think we know may 

not be true. For example, advocates of the breakup of Microsoft like to point 

to the breakup of AT&T, which everyone thinks was purely positive in its effects 

on innovation. It’s a bad parallel in many ways, but still it is interesting 

to notice that next-generation telecommunications is not yet a hot issue in the 

United States, because thanks to the fragmentation of our cellular system we 

are lagging well behind Europe and Japan in mobile phone technology. And that 

fragmentation is in part a legacy of the AT&T breakup. My point is not that it 

is wrong to consider the impact of policy on innovation; it is that because the 

determinants of innovation are not well understood, clever advocates can invoke 

technological progress as an all-purpose justification for whatever policy they 

favor”. 

19 A work group server OS is a software providing services to share files and printers 

and other administration services to a group of users connected in a network, 

typically in office environments.


work group servers on one side, and competitor products on the other side. 

After this decision, Microsoft paid the fine, developed and released a version 

of Windows without Media Player, and entered into extensive discussions 

with the Commission about the implementation of the remedies concerning 

interoperability. In the original decision this required to prepare a complete 

and accurate interface documentation describing portions of Microsoft server 

operating system software and to license innovations created by Microsoft 

under “reasonable and non discriminatory” (so-called RAND) terms to competitors. 

These imply that the royalties should be set at levels that enable 

use by other developers in a commercially practicable way with reference to 

standard valuation techniques, to an assessment of whether the protocols are 

innovative, and with reference to market rates for comparable technologies. 

Over time, the new Competition Commissioner Neelie Kroes has continued 

to extend the scope of the information required, from information that 

would enable interoperability with Windows PCs and servers for the purpose 

of creating new products for which there is unmet consumer demand, to 

information that would allow a competitor to produce clones or “drop-in replacements” 

of the Windows server OS. Even more controversially, the Commission’s 

Competition Directorate-General has sought to loosen the terms 

under which Microsoft would be able to licence its information, so as to allow 

products implementing its technical specifications to be released under 

so-called Open Source licences (DG Competition was prepared to make an 

exception for technologies that involved an inventive step and were considered 

novel by comparison with the prior art, thus meeting the criteria for 

patentability). Such release, by revealing to the world Microsoft’s own implementations 

of its technical specifications, would irreparably undermine 

the trade secret protection to which these technologies, some of which are 

not patented, are subject. In a further shift, the Commission made clear in 

Spring of 2007 that it expected Microsoft to forego royalty payments on any 

technologies that were not covered by patents. With the compliance process 

made more difficult on both sides by the technical complexity of the material 

and key policy differences (e.g. over the intellectual property issues), 

DG Competition challenged Microsoft to comply with the interoperability 

remedy by 15 December 2005, on pain of massive penalty payments for noncompliance. 

In early 2006, Microsoft provided further information needed for 

interoperability purposes, and even made available to its competitors selective 

access to the source code of Windows. Nevertheless, in July 2006 the 

Commission levied fines of € 1.5 million a day from the December hearing 

onwards (for a total of other € 280.5 million), and threatened to double the 

fine if the company did not comply. At the time of writing, the case is still 

unresolved: Microsoft’s Appeal of the Commission’s 2004 landmark decision

6.3 Is Microsoft a Monopolist? 223 

was heard by the European Court of First Instance in April 2006, 20 and a 

decision is expected by September 2007, after this book will be completed. 

In either case, both Microsoft and the Commission may also appeal to the 

European Court of Justice, which is the EU’s highest court. 21 

A common element in both the US and EU cases has been the substantial 

involvement of competitors of Microsoft on the side of the antitrust authorities. 

In a neat article about the US vs. Microsoft case on Business Week, 

Robert Barro noticed that: 

“a sad sidelight in the Microsoft case is the cooperation of its 

competitors, Netscape, Sun and Oracle Corp., with the government. 

One might have expected these robust innovators to rise above the 

category of whiner corporations [...] The real problem is that whining 

can sometimes be profitable, because the political process makes it 

so. The remedy requires a shift in public policies to provide less 

reward for whining. The bottom line is that the best policy for the 

government in the computer industry is to stay out of it” (Barro, 

1998) 

Nevertheless,IBM,Sun,Oracle,Novellandthewideopensourcemovement 

have also been active against Microsoft in the EU case. 

6.3 Is Microsoft a Monopolist? 

While a comprehensive analysis on the PC operating system market and 

of the role of Microsoft is beyond our scope, we can try to provide a basic 

interpretation of a few features of this market through the simple ideas developed 

in the theoretical part of this book. The technological conditions in 

the software market are relatively simple. Production of an operating system, 

as any other software, takes a very high up-front investment and a roughly 

constant and low (close to zero) marginal cost. 22 Demand conditions are 

20 Also in this case important economists played a crucial role: for instance with 

Joseph Stiglitz on the European Commission side and David Evans on the Microsoft 

side. 

21 Another antitrust case focused on bundling issues has taken place in South Korea: 

in 2005 Microsoft had to pay a fine of $ 32 million and produce more than 

one version of Windows for the country (one with Windows Media Player and 

Windows Messenger and one without them). 

22 However, notice that the initial fixed costs of production are not independent 

from the future scale of production: higher production requires a better product, 

which requires higher R&D investments. Moreover, diminishing returns to scale 

are typical in the production of new software, which may explain why the price 

of software has not been declining as much as the price of hardware in the last 

decades.


more complex. What drives demand is not the traditional concept of product 

differentiation, which is of course present, but the development of network 

externalities: network effects are crucial in the development of a market for 

an OS and the pricing structure is fundamental to get on board both end 

users and application developers. Beyond this, a firm producing OSs faces 

competitors: the entry conditions in the market for OSs are quite debated, 

but there are good reasons to believe that even though entry into the software 

market may entail large costs, it is substantially endogenous. First of 

all, there are already many companies distributing OSs (for instance Solaris 

by Sun Microsystems, many versions of Unix and Linux, those by Red Hat 

and Novell), there are many firms producing OSs for related industries (smart 

phones, PDAs and videogames) which could be scaled-up to run on desktop 

computers (especially on low cost PCs), and there are even more potential 

entrants (think of the giants in adjacent sectors of the New Economy, hardware 

and telecommunications in particular). Second, it is hard to think of 

a market which is more “global” than the software market: demand comes 

from all over the world, transport costs are virtually zero, and the knowledge 

required to build software is accessible worldwide. 

Nevertheless, it has been claimed that in the market for OSs, the high 

number of applications developed by many different firms for Windows represents 

a substantial barrier to entry. It is probably true that high quality 

products make life harder to the competing products, but this should not lead 

to the conclusion that quality is a barrier to entry, especially in sectors where 

innovation should drive competition. Moreover, it is true that competitors 

need to offer a number of standard and technologically mature applications 

upon entry to match the high quality of the Windows package and create 

network effects (and some do offer many already), but the cost of offering 

these applications is unlikely to be prohibitive compared to the global size of 

this market. 23 There are at least two reasons for this. First, notice that the 

alleged “applications barrier to entry” is often erroneously associated with 

thousands of applications written for Windows, while it is actually limited 

to a handful of applications such as word processing, spreadsheet, graphics, 

internet access and media player software, which really satisfy the needs of 

most active computer users (McKenzie, 2001). Second, the competitors of 

Microsoft should not (and the existing ones do not) even finance the development 

of all the needed applications: they should just fund and encourage 

23 There are many examples of markets with network effects where subsequent 

entrants managed to create network effects and challenge incumbents. Within 

traditional sectors, examples abound in the fashion industry and many industries 

where creating new successful brands requires building network effects. In the 

New Economy a clear example emerges in the case of payment cards (where 

network effects are crucial, to say the least), which absorbed sequential entry by 

Diners Club (1950), American Express (1958), Visa (1966), MasterCard (1966) 

and Discover (1985), to name the most famous actors of this market.


other firms to write applications for their OSs, or have old applications originally 

written for other OSs “ported to” theirs, which is what already happens 

since multi-homing is common practice on the side of software developers. 24 

In essence, the software market is characterized by network effects, high 

fixed costs of R&D, constant marginal costs of production close to zero and 

substantially open access by competitors able to create new software. According 

to the theory of market leaders, these are the ideal conditions under 

which we should expect a leader to produce for the whole market with very 

aggressive (low) prices. Hence, it should not be surprising that, at least in 

the market for operating systems, a single firm, Microsoft, has such a large 

market share. We can see the same fact from a different perspective: since 

entry into the software market is endogenous, the leader has to keep prices 

low enough to expand its market share to almost the whole market. 

6.3.1 Why Is the Price of Windows so Low? 

Many economists agree on the fact that Microsoft sells Windows at an extremely 

low price. For instance, Fudenberg and Tirole (2000) notice that 

both sides in the US Microsoft case admit that “Microsoft’s pricing of Windows 

does not correspond to short run profit maximization by a monopolist. 

Schmalensee’s direct testimony argues that Microsoft’s low prices are due at 

least in part to its concern that higher prices would encourage other firms 

to develop competing operating systems” even if, they add, “neither side has 

proposed a formal model where such ‘limit pricing’ would make sense.” 

To verify in the simplest way that the price of Windows does not correspond 

to the monopolistic price for the OS market, assume for simplicity 

that the marginal cost of producing Windows is zero, and that the price of 

hardware is constant and independent from the price of Windows. Demand 

for Windows is clearly a derived demand, in the sense that it depends on 

the demand for PCs and on the total price of PCs in particular. Standard 

economic theory implies that the monopolistic price for an operating system 

should be the price of the hardware divided by − 1, where is the elasticity 

of demand for PCs (including both hardware and software): it means that a 

1% increase in the price of PCs reduces demand by %. 25 Now, this rela- 

24 In 2000, it has been estimated that 68 % of software companies developed applications 

for Windows, 19 % for Apple (which requires adapting to both unique 

software and hardware), 48 % for various versions of Unix and Linux and 36 % 

for other proprietary OSs (see Lerner, 2001). Notice that the respective percentages 

in 1992 were 71%, 12%, 33%and 31%, therefore competing OSs experienced 

an increase in software developers compared to Microsoft during the 90s. 

25 Formally, let us assume that the price of the hardware is fixed and independent 

from that of the software. Given a demand D(h + w) decreasing in the price of 

the hardware h plus the price of Windows w, the gross profit ofamonopolist 

in the OS market would be wD(h + w) and would be maximized by a price of


tionship tells us that, if the basic price of the hardware is € 1000, which is 

about the current average price for a PC, the monopolistic price for Windows 

would be other € 1000 if =2,itwouldbe€ 500 if =3,itwouldbe€ 

333 if =4and so on. Foncel and Ivaldi (2005) estimate this elasticity on 

the basis of a panel data of all PC brands sold in the G7 countries over the 

period 1995-1999 and derive a value between =1.5 and =3with a best 

guess slightly above two. The moral is that it would take really unreasonable 

values of demand elasticity to even get close to the real price of Windows, 

which is around € 50. 26 Moreover, the above estimate of the monopolistic 

price is very conservative. In the real world, we can imagine that the price 

of hardware is not completely independent from the price of Windows: if 

the latter would double tomorrow, hardware producers would be forced to 

somewhat reduce their prices (eventually switching to lower cost techniques 

and/or lower quality products). 27 Even if this effect may be limited by the 

high level of competition in the hardware sector, it works in the direction of 

further increasing the hypothetical monopolistic price, that is, even beyond 

the actual price of Windows. Finally, let us remember what we pointed out 

in our previous discussion on the software platforms: a two-sided platform 

like Windows earns its revenue entirely from end-users, and not from software 

developers, which are typically subsidized by Microsoft to develop new 

and better applications to strengthen network externalities. Hence, the low 

Windows w ∗ such that D(h + w ∗ )+w ∗ D 0 (h + w ∗ )=0or: 

w ∗ = 

h 

− 1 

with elasticity of demand. 

26 This point was first made by Richard Schmalensee, a testimony in the Microsoft 

vs. US case on behalf of the Microsoft Corporation (see Schmalensee, 2000). 

It was criticized by the US Government’s economic witnesses at the trial (see 

Fisher and Rubinfeld, 2001), who argued that Microsoft did not maximize short 

run profits, but did actually maximize long run profits taking into account the 

positive impact of a lower price on network effects. This last point may have 

been correct for the initial pricing strategies of Microsoft, but it does not explain 

why the price of Windows has remained so low after two decades. 

27 Formally, think that the price of hardware h(w) is decreasing in that of Windows 

(we could endogenize the actual effect but this is beyond the scope of this 

discussion). Then, we can rework the monopolistic price of Windows as: 

w ∗ = 

h(w ∗ ) 

[1 + h 0 (w ∗ )] − 1 

which is higher that in absence of this translation effect (remember that h 0 (w ∗ ) < 

0): a monopolist would price Windows even more because part of the potential 

reduction in demand due to a higher price would be avoided thanks to an induced 

reduction in the price of the hardware.


price of Windows appears further away from what should be the hypothetical 

monopolistic price. 

Hall and Hall (2000) developed similar calculations to the one above assuming 

Nash competition in quantities in the hardware market and suggested 

that Microsoft has to adopt a low price for Windows as a rational strategy in 

front of endogenous entry in the PC market. Their conclusion is consistent 

with the results of the theory of market leaders and endogenous entry: “not 

only is the price of Windows brought down to a small fraction of its monopoly 

price, but the social waste of duplicative investment in operating systems is 

avoided as well.” 

It has been claimed that low Windows pricing may be explained with 

higher pricing of the complementary applications, as the Microsoft Office 

suite. However, the combined price of Windows and the average application 

package sold with it is still below the monopolistic price. Moreover, these applications 

are not sold at lower prices for other OSs. As Nicholas Economides 

pointed out: 

“Windows has the ability to collect surplus from the whole assortment 

of applications that run on top of it. Keeping Windows’ 

price artificially low would subsidize not only MS-Office, but also 

the whole array of tens of thousands of Windows applications that 

are not produced by Microsoft. Therefore, even if Microsoft had a 

monopoly power in the Office market, keeping the price of Windows 

low is definitely not the optimal way to collect surplus” (Economides, 

2001). 

What does all this tell us? Simply that Microsoft is not an unconstrained 

price-setter, while its prices are limited well below the monopolistic price 

to compete aggressively with the other firms active in the operating system 

market and with the potential entrants in it. Economides (2001) concludes in 

a similar fashion: “Microsoft priced low because of the threat of competition. 

This means that Microsoft believed that it could not price higher if it were to 

maintain its market position.” The empirical work of Foncel and Ivaldi (2005) 

supports the same conjecture: “Microsoft seems to behave as if it fears that 

charging monopoly prices today would cause it to lose substantial profits to 

competitors in the future.” 

Indeed, we can say more than just that Microsoft is not a monopoly. 

What the post-Chicago approach suggested about leaders in markets with 

price competition was that they should be accommodating and exploit their 

market power, setting higher prices than competitors, or otherwise engage 

in predatory pricing and, after having conquered the whole market, increase 

prices. But in the last 10-15 years of global leadership, Microsoft has done 

neither of these things. Microsoft has been constantly aggressive, which, according 

to the theory of market leaders developed in this book, is exactly 

what a leader under the threat of competitive pressure would do.


The theory of market leaders has shown that a market leader in these 

conditions would price above marginal cost in such a way to compensate for 

the fixed costs of investment and obtain a profit margin (over the average 

costs of production) thanks to the economies of scale derived from the large 

(worldwide in the case of Microsoft) scale of production. Its (quality adjusted) 

price should be below that of its immediate competitors, or just low enough 

to avoid that they can exploit profitable opportunities in the market. 28 The 

low price of Windows induced by competitive pressure and network effects 

explains its large market share. As Posner (2001, p. 278) has pointed out 

acutely, in such a market “a firm may have a monopoly market share only 

because it is not charging a monopoly price.” 

The significant preference that customers attribute to Windows even in 

the presence of good alternative products, some of which are supplied at no 

charge (!), suggests that Microsoft is still providing the package with the 

best quality-price ratio in the software market, at least if we believe in the 

rationality of consumers. 29 

6.3.2 Does Microsoft Stifle Innovation? 

It is also important to look at competition in the software market in a dynamic 

sense, that is competition for the market, as opposed to the competition 

in the market examined until now. As we have emphasized many times, 

high-tech sectors can be seen as races to develop new products before others 

and conquer large market shares with the new products. On the basis of the 

so-called Arrow effect, we know that incumbent monopolists that do not face 

endogenous pressure in the competition for the market have small incentives 

to invest in R&D because, by innovating, they only obtain the difference between 

the value of the next technology and that of their current technology, 

28 IBM initially priced its OS/2 at $ 325 against $ 149 for Windows 3.0. It would 

be more interesting to compare the price of Windows and Mac OS, but the latter 

is integrated in Apple computers. However, as Evans et al. (2006) notice, “there 

is a clue: the 1990 upgrade to Windows 3.0 was $ 50, about half the price ($ 

99) of a 1991 upgrade to Apple’s System 7.0. Another useful clue comes from a 

comparison between computers with similar hardware: in this same period the 

average price of an Apple PC was over $ 200 more than the average price of 

a similarly equipped and powerful Compaq PC sold with Microsoft operating 

systems.” 

29 Nevertheless, it is sometimes claimed, also between economists, that there are 

better OSs that provide better services, and that a lack of information and myopic 

behavior induce collective hysteresis in the choice of Windows. It is hard to 

imagine how irrational choices could last so long, and it is even more surprising 

that economists, always ready to assume rational behavior under the most extreme 

circumstances, can believe that consumers suddenly become irrational or 

myopic when choosing software.


while outsiders obtain the full value of replacing the incumbents. However, 

the theory of market leaders developed in Chapter 4 has shown that, when 

leaders face competitive pressure, they are induced to invest more in R&D 

than any other competitor, with the incentive of defending their leadership 

from a rapid replacement. 

Let us look at the incentives to invest in the software market. Of course, 

the overall expected value of Windows Vista for Microsoft can be quite high, 

but the net value of replacing Windows XP with Vista has been only a 

small percentage of that value, especially if we take into account that the 

real price is not likely to increase and that the introduction of Vista is only 

gradual (and associated to the change of hardware for most customers). At 

the same time, the value of developing a successful OS for a competitor 

of Microsoft is incomparably higher. The Arrow effect would suggest that 

Microsoft has lower incentives to invest in R&D than the other active firms if 

further entry in the competition for the OS market is not possible. However, 

the theory of market leaders replies that this is not the case when entry is 

endogenous. Accordingly, this supports the idea that only strong pressure 

in the competition for the market could have led Microsoft to undertake 

an unprecedented investment to rewrite from scratch, develop and release a 

brand new OS as Windows Vista. This pressure, we conjecture, comes mainly 

from the new actors in the software market, the open source community and 

the commercial companies that are active around this community. At the 

same time, it is reasonable to conjecture that the wide and fast growing open 

source community and the commercial companies behind it are investing so 

much in R&D exactly because they envision the possibility of replacing the 

leadership of Microsoft. In light of this, the software market appears as a 

dynamic sector characterized by strong competition for the market and by a 

leader that is both a source and a cause of innovation, quite the opposite of 

how it is sometimes depicted. 

Similar ideas appear behind the words of the leading scholar of the 

Chicago school on the software industry: 

“We have seen all manner of firms rise and fall in this industry– 

falling sometimes from what had seemed a secure monopoly position. 

The gale of creative destruction that Schumpeter described, in 

which a sequence of temporary monopolies operates to maximize innovation 

that confers social benefits far in excess of the social costs 

of the short-lived monopoly prices that the process also gives rise 

to, may be the reality of the new economy. This is especially likely 

because quality competition tends to dominate price competition in 

the software market industry. The quality-adjusted price of software 

has fallen steadily simply because quality improvements have vastly 

outrun price increases” (Posner, 2001, pp 249-50). 

In spring 2007 Microsoft unveiled a revolutionary new product called Microsoft 

Surface, a combination of ground breaking software and hardware


technology that will change the way we interact with digital content. 30 Sooner 

or later the technological leadership of Microsoft in the software market will 

end, but other companies will have to be more innovative to replace its products. 

6.4 Bundling 

Virtually any product is a bundle, since it combines multiple basic products 

which could be or are sold separately: drugs bundle different molecules, 

shoes bundle shoes without laces and shoelaces, a car bundles many separate 

components, a computer bundles hardware, an operating system and 

basic software applications of general interest. In some cases, bundling is 

just a contractual restriction used to force customers to purchase an ancillary 

product in an aftermarket for goods or services, while in other cases 

bundling improves a finished product by integrating new components or features 

into it: of course, only the first situation should be subject to antitrust 

investigation. In all of its main antitrust cases, Microsoft has been accused of 

abusive leveraging through bundling strategies, first between Windows and 

the browser Internet Explorer, and then between Windows and the Windows 

Media Player software. 

As we noticed in the previous chapter, there are contrasting views on 

bundling. The Chicago school has advanced efficiency rationales in its favor 

with positive, or at worst ambiguous, consequences on welfare, including 

production or distribution cost savings, reduction in transaction costs for 

customers, protection of intellectual property, product improvements, quality 

assurance and legitimate price responses. In the case of bundling of software 

applications in an OS, in particular, there are efficiencies in internal software 

design due to componentization and code sharing (which facilitate product 

development, design and testing), there are network externalities made available 

encouraging and facilitating the development of applications that rely on 

a bundled functionality and there are reductions in customer support costs 

which ultimately lead to cost savings for final end-users, whose experience is 

also largely simplified by bundling. 31 

Moreover, according to the Chicago view only efficiency purposes can 

motivate bundling because a firm cannot monopolize another market by 

bundling two products: according to the so-called “single monopoly profit 

30 Microsoft Surface is a display in a table-like form that is easy for individuals or 

small groups to interact with in a way that feels familiar. It can recognize dozens 

of movements such as multiple touches, gestures and actual unique objects that 

have identification tags similar to bar codes, it eliminates the need for a mouse 

and a keyboard and allows multiple users to directly interact through the screen. 

31 See Davis et al. (2002).


theorem”, as long as the secondary market is competitive, not even a monopolist 

in a separate market can increase its profits in the former by tying the 

two products. Actually, in the presence of complementarities, it can only gain 

from having competition and high sales in the secondary market to enhance 

demand in its monopolistic market. A similar idea has been advanced at a 

theoretical level by Davis and Murphy (2000) to explain the tying strategies 

of Microsoft: they also emphasize a well known basic principle, for which 

a monopolist will choose lower prices for two complement goods than the 

prices chosen by two separate monopolists, which suggests that the bundling 

strategies of Microsoft reduce permanently the prices of both Windows and 

the bundled products. Motta (2004) adds that a positive impact on prices 

emerges also for independent products when there are network effects, because 

in the secondary market “it might be very difficult to leapfrog the 

current leader, and a firm that can rely on important R&D, marketing and 

financial assets might manage to achieve what a small firm might not have.” 

With particular reference to the US case, Economides (2001) notes that 

Microsoft could not have been interested in the browser market when this 

was perfectly competitive, but only when this market became dominated by 

Netscape for two main reasons. “First, Netscape had a dominant position in 

the browser market, thereby taking away from Microsoft’s operating system 

profits to the extent that Windows was used together with the Navigator. 

Second, as the markets for Internet applications and electronic commerce 

exploded, the potential loss to Microsoft from not having a top browser increased 

significantly... Clearly, Microsoft had a pro-competitive incentive to 

freely distribute IE since that would stimulate demand for the Windows platform.” 

The very same point could be made for the more recent bundling of Media 

Player with Windows offers a very low price. 32 Actually, this motivation for 

bundling Windows and Media Player (aimed at increasing the attractiveness 

of the former and promoting applications for the latter) appears the main 

direct driver in the European case. Today there are no serious threats on 

Windows that could come from an alternative media player software (while 

browsers could represent a potential threat for Windows in the mid 90s). 

However, there is a different class of motivations for bundling that we need 

to examine: these are the indirect or strategic motivations. 

32 Notice that, since at the time of launch we were in front of cases of pure (and 

not mixed) bundling, we do not know the implicit prices of IE and MediaPlayer 

in the bundled versions of Windows. However, they must have been quite low or 

close to zero because there were not apparent increases in the price of the new 

versions of Windows. Moreover, the recent unbundled version (without Media 

Player) is sold at the same price as the bundled version.


6.4.1 Strategic Bundling 

The post-Chicago approach has shown that, when the bundling firm has some 

market power in the primary market, commitment to bundling can only be 

used for exclusionary purposes since it enhances competition in the secondary 

market and increases the profits of the leader only if it excludes rivals from 

this secondary market (Whinston, 1990). Nevertheless, even the same proponent 

of this theory has expressed doubts on its applicability to the case of 

Microsoft: evaluating the tying of Windows and IE, Whinston (2001) notes 

that “Microsoft seems to have introduced relatively little incompatibility with 

other browsers. Since marginal cost is essentially zero, bundling could exclude 

Netscape only if consumers, or computer manufacturers for them, faced other 

constraints on adding Navigator to their system”, which did not appear to be 

the case. The same holds in the case of Windows Media Player. It is true that 

Microsoft bundling in both markets reduced the average prices of browsers 33 

and media players, but this did not lead to the deterrence of entry (new 

successful browsers such as Firefox have appeared). 

As we have formally shown (in Section 2.10), the theory of market leaders 

emphasizes that when entry in the secondary market is endogenous, an 

incumbent can gain from bundling exactly because this creates a sort of commitment 

to apply a low price to the bundle as a whole, which may end up 

increasing the overall profits for the leader (compared to those obtained only 

in the primary market without bundling). Nevertheless, the price of the two 

goods together would be reduced and entry of alternative secondary products 

would be still viable. This kind of rationale for bundling is more likely 

to emerge when there are some complementarities between the products, 

or there are unexploited network effects (which can be enhanced through 

bundling); ultimately, even sales and profits in the primary market may increase. 

What matters for our purposes is that bundling is not an extreme 

strategy adopted by an incumbent firm to deter entry, but a standard aggressive 

strategy that, by reducing the final prices, may indeed reduce entry 

of followers, without excluding entry overall. As a matter of fact, under some 

level of product differentiation, the impact on the competitors is quite limited 

and only marginal firms of the secondary market would be driven out of 

it. Hence, in a world of price competition, it appears hard to conclude that 

bundling could be used as a predatory strategy when it does not even lead 

to the exit of all the competitors, but just to a permanent reduction of the 

price level. 

33 Netscape charged many private and corporate users for its browser until started 

facingsubstantialcompetition.Pricesrangedbetween$39in1995to$79in 

1996 for a premium version. This was quite a high price if we think that the 

average price of the entire OS Windows was in this same range during those 

years.


To sum up our general point, when approaching a bundling case we suggest 

verifying the entry conditions of the secondary market. If there is a 

dominant firm in this market as well, the main problem is not the bundling 

strategy, but the lack of competition in the secondary market, and it should 

be addressed within that same market: punishing the bundling strategy would 

just guarantee the monopolistic (or duopolistic) rents of the dominant firm 

in the secondary market. However, things are different when the secondary 

market is not monopolized but open to endogenous entry (even if it is not perfectly 

competitive, in the sense that firms do not price at marginal cost). In 

such a case, and especially in the presence of product differentiation, bundling 

is a pro-competitive strategy and punishing it would hurt consumers. 

In the case of Microsoft, in both bundling situations, that of Windows 

with Internet Explorer and that of Windows with Media Player, the tied 

market was characterized by endogenous entry. Paradoxically, this became 

even more evident since Microsoft entered in these markets: just think of new 

successful browsers as Mozilla Firefox, Netscape, Safari, Opera, Konqueror 

and media player software as RealPlayer, Apple’s QuickTime, Adobe’s Flash, 

MusicMatch and many others. 34 Consequently the bundling strategy of Microsoft 

could be simply seen as an aggressive and competitive strategy of a 

market leader active in a secondary market where entry is indeed endogenous. 

Moreover, in these markets the standard strategy is to provide free software 

to enhance network effects and earn from externalities associated with the 

use of the software (a typical strategy in multisided markets, as we have 

seen). For instance, in the case of digital media platforms, Microsoft looks 

for network effects on licenses of its OS, Real earns from content subscriptions, 

Apple from sales of digital audio and video devices (the iPod and, in 

perspective, the iPhone) 35 and Adobe from Flash server sales. Even if these 

companies adopt very different business models, competition is quite intense 

especially because multi-homing is common practice: end users typically use 

multiple media players (that are characterized by a certain degree of hori- 

34 Entry in the market for software applications is definitely easier today, since most 

software is installed through on line downloading in a few seconds. Since most 

PCs are endowed with a browser (which, ironically, is largely due to Microsoft 

bundling IE with Windows), the market for software applications has become 

one of the most transparent and competitive. 

35 This implies different levels of platform integration and interoperability with 

different platforms. As Evans et al. (2006) noticed: “At one extreme is Apple. Its 

iPod/iTunes platform is integrated into the hardware and content-provider sides 

of the media platform, and its doesn’t interoperate with any other platform. At 

the other extreme is Microsoft, whose media platform is integrated into neither 

hardware nor content and which interoperates with all other media platforms 

that allow it to do so. In the middle are vendors like RealNetworks, which limit 

interoperability - but not completely - and integrate - but only partially - into 

the content provider side.”


zontal differentiation), and also PC manufacturers typically install multiple 

competing mediaplayers at their will (while this is not the case for digital 

music devices and mobile phones). Finally, multi-homing is a clear symptom 

that media players are horizontally differentiated (some are better for music 

content, others for videos, others for storing files, and so on): from our previous 

discussion on bundling for secondary markets with endogenous entry 

and product differentiation, it follows that these are precisely the conditions 

under which bundling assumes a competitive nature rather than a predatory 

one. 

6.4.2 Technological Bundling 

Beyond the debate on the nature of the strategic reasons for which firms may 

engage in bundling strategies, there are technological reasons why bundling 

mayemerge.ThesehavetypicallybeenatthebaseofMicrosoftdefenseinits 

antitrust cases. In dynamic markets like the software market, the same concept 

of a good is changing over time, since both demand and supply change. 

If demand by PC users for media player functionality was limited just a few 

years ago, now it appears that these functionalities are an essential component 

of an OS. Because of this, an increasing number of software applications 

and on line services are associated with media player functionalities, so that 

demand is strengthened by network effects. If supply of media player functionalities 

was inefficient through bundling a few years ago, and it was mostly 

left to specific add ons, improvements in hardware processing power, in the 

cost of hard disk storage and random access memory, and in the streaming 

technology made it simple and efficient to bundle media player functionality 

within current OSs. As a consequence of this, bundling has a natural technological 

rationale and should emerge endogenously when the size of demand 

is large enough and the cost of supply is low enough. In other words, while 

a few years ago an OS and a media player could be regarded as separate 

goods whose union could be associated with a bundling strategy, nowadays 

an OS must incorporate media player functionalities (as it must incorporate 

a browser) so that we cannot even talk of a traditional form of bundling. 36 

36 This is common for software. For instance, word processors and spell checkers 

were in separate markets many years ago, not today. Voice recognition is separate 

today, but we can expect that it will be integrated in word processors at some 

point. Navigators for cars are still optional tools in the automobile industry, 

but are likely to become essential components in the near future and bundle 

new applications and new content. At the same time, videogame consoles and 

PCs are likely to enter in the television ecosystem and bundle new features and 

capabilities in the attempt to gain the socalled “control of the living room”. In 

a sense, bundling creates new industries and is a source of competition for the 

market in itself.

6.5 Intellectual Property Rights 235 

In this perspective, attempts of antitrust authorities to stop or delay the 

evolution of OS through additional features, as browsers and media players, 

appear quite dangerous: while it is difficult to verify in which moment it would 

be optimal to bundle secondary products in an evolving primary product, it 

is not clear why antitrust authorities should have a better guess than market 

driven firms. 

Notice that since the 2004 Commission’s decision, Microsoft had to prepare 

and commercialize a version of Windows without Media Player in Europe. 

37 Demand for the version of Windows without Media Player has been 

virtually zero in Europe, a likely sign that Microsoft bundling strategy was 

at least not hurting consumers. 

6.5 Intellectual Property Rights 

In the previous chapters we discussed the role of market leaders in innovative 

markets and the importance of the protection of IPRs in stimulating investment 

in R&D and technological progress. Both aspects are quite relevant in 

the understanding of the dynamics of the software market and the Microsoft 

case. 

The software market is a major example of an industry where competition 

is mainly for the market, and in such a case, as we have seen, large 

market shares by single firms are a typical outcome. The counterpart of this, 

of course, is that these industries can exhibit catastrophic entry where innovators 

can replace current leaders quite quickly. As we noticed in Chapter 4, 

in such an environment, it is exactly when competition is open that leaders 

have incentives to invest deeply to retain their leadership. On the contrary, 

when competition for the market is limited, technological leaders are able to 

have a quiet life, invest less in R&D and accept the risk that someone will 

come up with a better product. When competition for the market is open, 

this same risk is too high and incumbents prefer to accept the challenge and 

try to innovate first: this leads to a more persistent leadership. 

When entry is endogenous, innovation by leaders creates a virtuous circle 

that also has important implications for the way we can evaluate such a 

market (see Section 4.3). The endogenous persistence of the technological 

leadership has a value that creates incentives for all firms to invest even 

more, which in turn strengthens the same incentives of the leader to invest 

and retain its leadership, and so on. In other words, persistence of leadership 

is a source of strong competition for the market (through investments in R&D 

to replace the current leader), and, given that leaders have higher incentives 

to invest as long as the race to innovate is open, we can also conclude that 

37 The version of Windows XP without Media Player was called Windows XP N, 

a choice of the European Commission between nine potential names submitted 

by Microsoft.


strong competition for the market is a source of persistence of leadership. 

This circular argument may appear paradoxical, but is the fruit of a radical 

distinction between static and dynamic competition: once again, there is no 

consistent correlation between market shares and market power in dynamic 

markets. 

The endogenous multiplicative effect of the value of leadership that we 

have just summarized implies that in dynamic markets the rents of a leader 

may be spectacularly larger than those of its competitors, and the market 

value of a leadership may be extremely large even if the market is perfectly 

competitive in a dynamic sense (see Segerstrom, 2007, for a related point). In 

our view, this is something not too far from what we can see in the software 

market and in the leadership of Microsoft, but also in many other high-tech 

sectors. 

6.5.1 Patents, Trade Secrets and Interoperability 

Thesourceofthevalueofinnovation,thestartingpointofthechainofvalue 

that we just described, must be a fundamental rent associated with innovations 

and protected through IPRs. Hence, all forms of IPRs are the ultimate 

source of leadership, innovation and technological progress. As we already 

noticed, the role of patent legislation is exactly to trade off the benefits of 

patents in terms of incentives to innovate with the costs related to temporary 

monopolistic pricing. In our opinion, there is no reason why antitrust 

authorities should interfere with this legislation when patent protection appears 

inconsistent with other goals. And even if these goals are legitimate 

and relevant, introducing a discretionary evaluation of IPRs would create 

uncertainty and jeopardize the investment, which, after all, goes against the 

ultimate objective of the same antitrust authorities. 

Nevertheless, in the Microsoft case the EU Commission has taken this 

dangerous direction, asking Microsoft to disclose a wide amount of technologies. 

38 More recently (Statement of Objections of March 1, 2007), the 

Commission has asked to make them available royalty free unless they have 

38 At the beginning of the Appeal on the Microsoft case on April 24, 2006, the 

author of this book expressed a similar concern in an interview for La Libre 

Belgique: “Microsoft a été forcé de révéler certaines informations pour assurer 

l’interopérabilité entre Windows et d’autres systèmes d’exploitation. Mais les demandes 

de la Commission Européenne ne sont toujours pas claires; elle ne cesse 

de réclamer plus de la part de la firme américaine. Microsoft a révélé récemment 

le code source de son système Windows: c’est la documentation ultime du 

software. Que peut-on encore demander de plus? L’impact de cette décision serat-il 

négatif? Le débat économique futur va porter sur les gains qui résultent du 

fait que l’on a forcé une entreprise à révéler des secrets technologiques protégés 

par copyright... Mais y a-t-il des gains? Devait-on le faire? Sur le long terme, 

c’est contre-productif. Qui va investir dans l’innovation et dans la recherche si


an innovative nature (meaning that they involve an inventive and novel step 

compared to the prior art). 39 Finally, it has started questioning the same 

innovative nature (and with it the license pricing) of most technologies that 

Microsoft was forced to disclose, technologies which are also covered by many 

patents approved by US and EU patent offices. This creates an even stronger 

contradiction between patent law and antitrust policy in the EU, and also 

a substantial divergence between the US approach to IPRs and the EU approach, 

with the former much more careful in protecting IPRs and promoting 

R&D. 

It is important to add that new ideas, including those underlying Microsoft 

software, are not protected only with patents. Not all inventive and 

innovative activities fall under the scope of patentability and it is not always 

in the interest of a firm to patent every single innovation. In most high-tech 

sectors, firms adopt a combination of patents and trade secrets to protect 

products that are the result of multiple innovations. Defending (intellectual 

or material) property rights is one of the fundamental conditions for proper 

functioning of the market economy: defending trade secrets should not play 

a minor role in this context. 

Some of the most famous trade secrets are the formulas of Coca-Cola, 

Chanel No. 5 and Campari. Consider the first example and imagine that 

Coca-Cola was required to disclose its secret formula: anyone could reproduce 

the very same drink, “clone” it under a different name if you like, but it is hard 

to believe that this would create large gains for consumers. Close substitutes 

to Coke already exist and there are small margins to substantially reduce 

prices. However, the incentives for any other firminthesameindustryto 

invest and create new products could be drastically reduced if trade secrets 

were not protected. 40 

High-tech sectors are more complicated. In these sectors, patents and 

trade secrets often cover fundamental inventions and protecting those inventions 

amounts to promoting innovations that today are the main engine of 

growth. In some fields, however, there maybe, at least apparently, a trade-off 

between trade secret protection and “interoperability” between products - 

les droits de propriété intellectuelle sont bafoués? On crée un dangereux précédent 

d’autant que l’industrie de haute technologie est souvent caractérisée par 

des investissements massifs en recherche et développement” (Contre-productif, 

dangereux pour l’innovation et la recherche, by Martin Buxant). 

39 Notice that these are features needed for patentability, but not for trade secrets, 

which may just protect technologies that are not novel or innovative, but nevertheless 

developed with effort and costs. Therefore, the most recent approach 

of the Commission forces disclosure of similar technologies, and excludes at the 

same time that they could be licensed for a positive royalty: this is a way of 

denying de facto the right of protection of trade secrets. See Kanevid (2007) for 

a related analysis of compulsory licensing. 

40 On the story of Coke’s trade secret and its implications see Etro (2005,c).


broadly speaking, this is the ability of heterogeneous information technology 

systems, components and services to exchange and use information and data, 

especially in networks. Interoperability is important in the PC industry and, 

as we have seen in Section 6.1, the level of interoperability has strongly increased 

in the last decades. Problems arise, however, when interoperability 

is confused with “interchangeability” or with a right to clone the innovations 

of the competitors. 

For instance, take in consideration the leading on line search engine in the 

world, Google. We may look at Google’s patented innovations, starting with 

the 2001 patent on the invention of the PageRank by Larry Page (founder 

of Google with Sergey Brin), 41 but we would need to know its trade secrets 

to fully discover the mechanism of its precious algorithms. Forcing disclosure 

of such trade secrets would help many software companies and websites to 

interoperate with Google even better than they already do, as it would allow 

other search engines to improve their performances compared to that of the 

leading search engine. But after that, surely, few companies would invest 

huge resources and take substantial risks to create a better search engine 

or other brilliant ideas like Google when they can just free ride on others’ 

ideas and/or they can’t be sure of their return. The same argument would 

apply for the trade secrets of Microsoft or Apple on the source codes of 

their OSs and to many other trade secrets of innovative leading companies. 

Any forced disclosure of similar trade secrets represents an expropriation 

of legitimate investments and establishes inappropriate legal standards with 

perverse effects on the incentives to innovate. 

6.5.2 Licenses and Standards 

Fortunately, giving up the precious role of IPRs in promoting innovations is 

not the only way to solve interoperability challenges. The market can do it 

much better: valuable ideas can be selectively commercialized on a voluntary 

basis through licenses, for instance under RAND (reasonable and non discriminatory) 

terms, a type of licensing typically used during standardization 

processes to promote the rapid adoption of standards and new technologies 

41 The abstract of US patent 6285999 (filed in 1998) for a method for node ranking 

in a linked database, reads as follows: “A method assigns importance ranks to 

nodes in a linked database, such as any database of documents containing citations, 

the world wide web or any other hypermedia database. The rank assigned 

to a document is calculated from the ranks of documents citing it. In addition, 

the rank of a document is calculated from a constant representing the probability 

that a browser through the database will randomly jump to the document. 

The method is particularly useful in enhancing the performance of search engine 

results for hypermedia databases, such as the world wide web, whose documents 

have a large variation in quality.” Of course, by now, this is just the beginning 

of Google’s ranking mechanism.


and to encourage entry. The RAND terms include a definition of reasonable 

royalties, and can include further restrictions as field-of-use clauses (that allow 

licensees to utilize a patented technology in a use that is directly related 

to the implementation of the standard), reciprocity clauses, or limits to sublicensing. 

42 

Coase (1960) has clarified that whenever there is social value to generate, 

the market will properly allocate all the property rights. This is also true 

for the intellectual property rights: market mechanism can allocate them efficiently, 

insure the accessibility of the information that fuels interoperability 

and acknowledge legitimate ownership rights of the innovators, so as to enhance 

R&D investments. 43 Suppose firm A invests, innovates and obtains a 

patent, and firm B has a new idea to improve firm A’s innovation, but this 

idea cannot be used without infringing the patent. Of course, forced interoperability 

would lead firm B to implement its idea. However, in such a case 

firm A will not invest to start with, and no idea will be actually implemented. 

Consider now private agreements between the two firms. First, firm A could 

license its patent to firm B for a price between the expected profits that A 

and B can respectively obtain from marketing alone their respective ideas. 

The price depends on the respective bargaining power, the best idea is implemented, 

and firm A has all the interest to invest ex ante.Second,firm B could 

sell its idea to firmAatapriceatmostequaltothedifference in expected 

profits that firm A can obtain respectively with firm B’s idea and without 

it, with the price again depending on the bargaining power. Also in this case 

the incentives for firm A to invest ex ante would be preserved. This suggests 

that it may often be a unique firm to buy others’ innovations (especially if 

this firm has developed a comparative advantage in marketing products), and 

it may often happen that only outsiders take the initiative to invest in new 

fields with the aim of reselling their innovations. 44 This is indeed the way 

technological progress evolves in many industries under protection of IPRs. 

Finally, in the presence of network effects, dynamic market forces can do 

even more: as long as IPRs are well protected and firms can invest with the 

safe confidence that successful innovations will be rewarded, market forces 

can select the best standard when multiple standards are available and interoperability 

is only partial. Liebowitz and Margolis (1999) have shown that 

42 Notice that extreme open source licenses can create frictions with RAND terms 

associated with other licenses, so as to jeopardize useful innovative activity - 

this is the case of the GNU General Public License, which is incompatible with 

technologies licensed with any positive royalty, field-of-use limitations or other 

standard restrictions. 

43 See Scotchmer (2004, Ch. 6) on an interesting discussion on licensing, R&D joint 

ventures and antitrust policy. 

44 This also suggests that in the presence of sequential innovations, primary innovations 

deserve stronger patent protection than later ones, since their social value 

is higher.


this is the case in many episodes. For instance, in the adoption of the common 

QWERTY keyboard for PCs (so-called from the first five letters on the 

top left): for years it has been claimed that the allocation of letters of this 

keyboard was an inefficient standard, while these researchers found that evidence 

suggests that the Qwerty keyboard, somehow selected by the market, 

is not worse than any other alternative. 45 

In conclusion, also in this field, markets can properly balance the short 

run and long run interests of consumers better than policymakers: promote 

innovation, enable an efficient degree of interoperability and select the best 

standards. It would be better to leave the ruling of intellectual property 

protection and of its limits to the legislative level rather than creating an 

important precedent for which antitrust authorities could force firms to reveal 

their IPRs. 

Much of the residual contrast between Microsoft and the European Commission 

depends on the approach to interoperability and on its ambiguity. 

The Commission’s 2004 antitrust decision mandated the licensing of intellectual 

property to enable full interoperability between Windows PCs and work 

group servers and competitor products. This mandate has turned out to be 

the most problematic in the case. The picture that is emerging is of a Commission 

that has continued to extend the scope of the information required, 

and more recently has also tried to control Microsoft pricing (a tool of regulatory 

authorities, not of antitrust ones), while not spelling out exactly what 

would constitute compliance with the remedy. Microsoft has been forced to 

licence more than a hundred technologies, and it has even made available to 

its competitors selective access to the source code of Windows. Nevertheless 

in Europe (differently from the US), not one of its competitors has taken out 

a license, a likely sign that the existing level of interoperability is not as low 

as it was depicted. 46 


In this chapter we have focused our attention on the New Economy, which 

was developed in the last decades around the PC industry and the Internet. 

The New Economy has spread rapidly all over the world thanks to what 

45 Another example is VHS winning out over Betamax for home video recording. 

46 One could read the facts in a more negative way. The long effort of the EU 

Commission to force Microsoft to reveal its technologies at better terms may 

prevent European firms from licensing any technology at the current terms until 

the case will be solved. We believe that an antitrust authority that decides the 

name of the products of a private company (as for Windows XP N), forces public 

disclosureofitsIPRs,andtriestodecideitspricesaswell,iswellbeyondthe 

limits between antitrust policy and regulatory policy. See Mastrantonio (2005) 

for an interesting analysis from the law & economics point of view.


we are used to call globalization. Markets in the New Economy work in a 

radically different way from markets in the Old Economy. First of all, while 

traditional sectors are often characterized by competition in the market with 

substantial product differentiation and U-shaped cost functions, many markets 

of the New Economy are often driven by competition for the market 

taking place through high fixed costs of investment in R&D, and production 

is typically characterized by small and constant marginal costs. Beyond this, 

many markets of the New Economy exhibit network effects and are often 

multi-sided, in the sense that firms act as platforms for different types of 

customers with complex network effects between them. 

These strong differences require a new approach to the analysis of markets 

and of the behavior of their leaders. In the absence of such a new approach, 

it is not surprising that in the last years the attention of antitrust authorities 

around the world has been often biased against market leaders in the 

sectors of the New Economy. These dynamic sectors are certainly not less 

competitive than others, but are often characterized by large market shares 

for their leaders and aggressive strategies which are the symptom of heavy 

competition. Leaders might enjoy high market shares yet be subject to massive 

competitive pressure to constantly create better products at lower prices 

due to threats from innovative competitors and potential entrants. Following 

our theoretical analysis, in this chapter we tried to argue that the behavior 

of leaders as Microsoft and other firms of the New Economy can be better 

interpreted through the concept of Stackelberg competition with endogenous 

entry.

7. Epilogue 

The objective of this book is to develop a theory of market leadership and endogenous 

entry. In the previous chapters we analyzed the choice of strategic 

investments before competition takes place and analyzed first mover advantages 

under competition in the market where quantities or prices are the 

strategic variables, and under competition for the market where investments 

in innovations are the strategic variables. We compared the results in the 

presence of exogenous and endogenous entry, and we used this theoretical 

framework to derive normative implications for antitrust policy. 

In this final chapter we will mainly focus our attention on the descriptive 

implications of the theory of market leadership and endogenous entry. In Section 

7.1 we point out the main empirical predictions of our theory that need 

future empirical investigations, in Section 7.2 we emphasize a few principles 

of business administration emerging from our analysis, and in Section 7.3 we 

suggest directions for future theoretical research. In Section 7.4 we conclude. 

7.1 Empirical Predictions of the Theory of Market 

Leaders 

The primary empirical implications of the theory of market leaders concern 

the discrimination between alternative strategies adopted by market leaders 

facing an exogenous or an endogenous number of competitors. 1 Therefore 

any empirical investigation of our results should be based on a non-trivial 

analysis of the entry conditions. 2 Some markets are clearly characterized by 

1 A good introduction to empirical studies of industrial organization can be found 

in Martin (2002). 

2 Most of the empirical work on the reaction of incumbents to entry takes entry 

as given. The problem of endogeneity of entry is briefly discussed in Thomas 

(1999), who examines the reactions of incumbents in the US ready-to-eat cereal 

industry. He finds that incumbents are accommodating between themselves, but 

they adopt aggressive pricing to face new entrants. This result may be due to the 

typical behavior of market leaders facing endogenous entry: while price competition 

would lead leaders to be accommodating when facing an exogenous number 

of firms, an aggressive pricing strategy is forced by endogenous entry.

244 7. Epilogue 

exogenous constraints on the number of firms: for instance, when there are 

legal barriers to entry, when only a restricted number of firms have licenses, 

patents or other essential inputs needed to produce a certain good or service, 

or when a certain activity is confined to a predetermined number of subjects 

with special permission, we are in front of a market where the number of 

competitors is exogenous. Some other markets are clearly characterized by 

entry open to domestic and international firms that changes over time, reacts 

rapidly to variations in demand and supply conditions, and reduces to zero 

the supra-normal profits of the marginal entrants: when this is the case, we 

are in front of a market where the number of competitors can be regarded as 

endogenous. In other markets the situation is not so clear, therefore we need 

to add a few remarks to clarify how one could approach the concept of entry 

in an empirical investigation aimed at testing the theory of market leaders. 

First, there are markets in which processes of liberalization or deregulation 

have radically changed the entry conditions, from a situation with a 

fixed number of competitors to one with endogenous entry: these shocks may 

represent interesting natural experiments for a test of our theory. 3 Other 

exogenous shocks leading to entry of new firms may create interesting natural 

experiments. 4 A related situation emerges in markets with IPRs: when a 

3 Spiller and Favaro (1984) have studied the behavior of market leaders in the 

process of deregulation of the commercial banking sector (with data on the 

Uruguay experience in the late 70s). The “results are consistent with a von 

Stackelberg type of industry where the degree of oligopolistic interaction among 

the leading firms is reduced as a consequence of the relaxation of the legal entry 

barriers.” In recent times, it would be interesting to verify the impact of online 

banking, which has dramatically increased entry (also of international banks) 

and competition in the banking sector of many countries: in such a case, the 

theory of market leaders would imply the emergence of leaders offering better 

conditions on savings accounts (think of the Orange Savings Account by ING 

Direct). 

4 Goolsbee and Syverson (2006) have examined how incumbents respond to the 

threat of entry of competitors. They use a case study from the American passenger 

airline industry, namely the evolution of Southwest Airlines’ route network 

between 1993 and 2004, to identify routes where the probability of future entry 

rises suddenly for major US carriers as American, Continental, Delta, Northwest, 

TWA, United and US Airways. Notice that this is a market characterized by a 

limited degree of product differentiation (mostly driven by frequent flyer miles 

programs), by U-shaped cost functions, and by competition in prices between airlines 

active on each route. When Southwest begins operating in airports on both 

sides of a route but not the route itself, the probability that it will start flying 

that route in the near future increases. Examining the pricing of the incumbents 

on threatened routes in the period surrounding these events, and controlling for 

a number of airport-specific operating costs, it emerges that incumbents cut fares 

significantly when they have faced an exogenous number of competitors in the

7.1 Empirical Predictions of the Theory of Market Leaders 245 

patent or a copyright expire, endogenous entry suddenly takes place, and the 

effect on the behavior of the incumbents could be used to test our results. 5 Another 

interesting situation that could be used for empirical purposes emerges 

in markets that, after a period of protection from international competition, 

are opened to entry of foreign firms: this represents another experiment in 

past, but expect endogenous entry in the future. More exactly, 3 to 4 quarters 

before Southwest starts its operations on a new route, the fares of the market 

leader on that route have fallen about 7 %, and by 1 to 2 quarters prior, they 

have fallen 10 %, while when Southwest actually starts operating, prices are almost 

12 % lower, and after entry the total drop in fares is about 26%. However, 

price cuts (in the run up to Southwest starting operations) are absent in lowconcentration 

routes, that is in the routes where, most likely, entry was already 

free. 

Furthermore, the empirical analysis of Goolsbee and Syverson (2006) reveals 

a switch toward the aggressive behavior of market leaders facing endogenous 

entry and without exclusionary purposes. They test whether there are differences 

between the reactions of incumbents when pre-emptive deterrence is possible 

(Southwest’s entry is likely after starting operations on both sides of a route, but 

could be avoided through price cuts) and when it is not (Southwest’s entry in the 

route is announced simultaneously with its start of operations in the airport). 

The pricing strategies of the incumbent are quite similar in the two samples, 

and the conclusion is that “even on routes where deterrence is impossible, the 

incumbents engage in the same pre-emptive price cutting behavior. Thus the 

behavior cannot be motivated as seeking to deter entry.” Following the traditional 

theory of price leadership which generates an accommodating behavior of the 

leaders, Goolsbee and Syverson (2006) are forced to conclude that “the firms are 

instead accommodating entry”, which can be quite misleading since these leaders 

are radically reducing their prices rather than increasing them. The paradox 

disappearsoncewerealizethatweareinfront of price leaders facing endogenous 

entry, and that our theory tells us that these leaders should be aggressive and 

also reduce their prices when they are not trying to deter entry. 

5 A similar experiment, which could be re-interpreted in the terms of our theory, 

is in Ellison and Ellison (2007). They examine the behavior of market leaders 

in the pharmaceutical industry in the periods around the expiration of patent 

protection for their patented drugs. Advertising by incumbents declines before 

entry occurs. Drug prices always decline when entry occurs, and also before the 

expiration of the patent, but only if the probability of entry is high. Again, these 

preliminary results are consistent with an aggressive strategy by the leaders, 

which is induced by endogenous entry. Bergman and Rudholm (2003) examine 

the Swedish pharmaceutical market where the commitment to a low price is 

enforced by a particular regulation (for which, if a price is reduced, it is impossible 

to increase it again). They show that the prices of the incumbent leaders fall at 

thetimeofthepatentexpiration(evenbeforeactualentryoccurs)by5-8%for 

products with small sales volumes.


which endogenous entry suddenly takes place. 6 In all of these examples, one 

can compare the behavior of market leaders relative to the behavior of the 

followers before and after endogenous entry takes place. Ideally, any empirical 

methodology should control for the differences between the leader and all of 

the other firms (our basic testable predictions refer to the behavior of leaders 

facing competition from equally efficient firms). 7 

Second, there are intermediate situations in which entry can be regarded 

as exogenous in the short run, but endogenous only in the medium-long run 

simply because entry takes time. This time can be different in different sectors: 

rather than being a limit to the testability of the theory of market 

leaders, this variability in the degree of reactivity of entry to profit opportunities 

could be exploited as a useful control variable, especially if one has 

good instruments available to identify the entry conditions. 8 

Third, one has to take into consideration entry in the competition in the 

market but also entry in the competition for the market: the former is visible 

and active in the same market, while the latter is often not visible because 

firms may be effectively competing for a market and investing in R&D, but 

they will not enter in the market until they actually develop a successful 

product. 

Fourth, one has to distinguish between effective entry and potential entry: 

while the former is visible and the latter is not, the existence of potential entry 

is the essential element of a market in which entry is endogenous compared 

to a market in which the number of competitors is exogenous. 

Another important preliminary issue concerns the form of competition 

in the market. It is well known that the difference between competition in 

prices and in quantities is more a theoretical abstraction than a clear-cut 

element of differentiation between sectors. However, there are some markets 

in which price choices are an essential component of competition, and others 

where production decisions determine, to a large extent, the equilibrium 

6 In a similar vein, Scherer and Keun (1992) looked at the increase in high-tech 

imports in US and found that incumbents in sectors without barriers to entry 

react more aggressively to endogenous entry, increasing R&D/sales more than 

other firms. 

7 Thomas (1999) has studied the behavior of incumbents in the ready-to-eat cereal 

industry, which is characterized by competition in prices, product differentiation 

and large advertising. The main result is that “incumbent firms accommodate 

one another on price but respond aggressively using advertising. Entrants on the 

other hand are more likely to be met with an aggressive price response.” The 

difference in the behavior of market leaders may indicate a switch in strategy 

from a situation with an exogenous number of competitors (the incumbents) and 

a situation where entry (of new firms) is endogenous. 

8 In this perspective, a good empirical strategy to measure the entry conditions, 

would involve measuring the likelihood of entry in a market and estimating its 

determinants.


price: markets for highly differentiated goods typically belong to the first 

group, while markets for homogenous goods belong more often to the second 

group. These broad differences should be kept in mind when comparing results 

from different markets. This is particularly important because, as we 

have seen repeatedly, entry conditions can fundamentally change the behavior 

of market leaders under competition in prices. Furthermore, when firms compete 

in multiple strategies, it is important to understand which preliminary 

investments or commitments can substantially affect competition: the different 

behavior of market leaders in undertaking strategic investments compared 

to other firms is a crucial element of the theory of market leaders. 9 

Finally, our predictions refer to the behavior of market leaders versus 

the behavior of their followers, and the definition of leaders and followers 

requires some additional specifications. In this case, market shares can be 

useful because it is normal to associate first mover advantages to the leading 

firm in terms of market share. One may consider more than one firm as a 

leader according to the sector under consideration: our analysis has shown 

that multiple leaders would tend to replicate the behavior of a single leader. 

Of course, there can be differences between firms that are beyond the strategic 

advantages: for instance costs differences, differences in product quality 

or locational differences. Since our results refer to symmetric firms from a 

technological point of view, these exogenous differences should be used as 

control variables in the analysis. 

Given these short but important methodological premises, in what follows 

we will list some of the empirical predictions of the theory of market leaders 

that distinguish between markets with an exogenous number of firms and 

markets with endogenous entry. 

In Chapters 1 and 3 we have seen that, with competition in the market, 

endogenous entry turns market leaders into more aggressive players comparedtoasituationinwhichallfirms 

(leaders and followers) do not face 

entry threats. In particular, our analysis allows one to discriminate a radical 

change of strategy under competition in prices: when the number of firms 

is exogenous, market leaders should choose higher prices than the followers, 

9 Röller and Sickles (2000) have performed the first empirical study of a twostage 

competition with preliminary investment in cost reducing capacity. They 

considered the European airline industry in the period 1976-1990, before the 

recent liberalization efforts. On the basis of a panel of the largest carriers (Air 

France, Alitalia, British Airways, Iberia, KLM, Lufthansa, SABENA and SAS) 

and a large dataset on cost, network and demand data, they have shown that 

airline companies behaved as puppy dogs: underinvesting in capacity to keep 

high prices. It would be interesting to compare that situation with the current 

situation in which EU liberalization is promoting the entry and competition: 

according to our the theory of market leaders, we would expect leading carriers 

to turn into top dogs and overinvest in capacity to reduce their relative marginal 

costs.


when entry is endogenous they should choose lower prices. This strong implication 

does not necessarily hold when firms compete in quantities, but in 

all cases we would expect that the price of the leaders decreases compared to 

the price of the followers when endogenous entry occurs. Therefore, our first 

testable implication is a weak one and can be expressed as follows: 

P.1a : The gap between the price of the leaders and the average price of 

the followers decreases with entry. 

When this prediction is satisfied in the data, one can look at the stronger 

result, which is supposed to hold for markets with competition in prices, and 

test the following implication: 

P.1b: Market leaders facing exogenous entry choose higher prices than the 

followers; market leaders facing endogenous entry choose lower prices than 

the followers. 

Of course, the stronger hypothesis P.1b implies the weaker hypothesis 

P.1a, while the opposite is not true. Eventually, one could test further predictions 

of the basic model of Stackelberg competition with endogenous entry. 

For instance, in the presence of homogenous goods, increasing marginal costs, 

and competition in quantities we would expect that the equilibrium price corresponds 

to the marginal cost of the leader but it is higher than its average 

cost, while the same price is above the marginal cost of the marginal entrant 

but just enough to match its average cost. This is consistent with positive 

profits for the leader and endogenous entry. When one introduces product 

differentiation, also the equilibrium price for the leader is above its marginal 

cost according to a mark up which increases in the degree of product differentiation, 

but the equilibrium price of the followers is still equal to their average 

cost. These predictions could be tested against other hypotheses using the 

tools of the new empirical industrial organization, 10 and are summarized as 

follows: 

P.2: In a sector with homogenous goods and increasing marginal costs, the 

equilibrium price of a market leader facing endogenous entry is equal to its 

marginal cost and above its average cost, and the equilibrium price for the 

marginal entrant is above its marginal cost and equal to its average cost; an 

increase in product differentiation increases the equilibrium price above the 

marginal cost of the leader. 

Let us move to the case of strategic investments by market leaders. In 

Chapter 2 we have seen that, with competition in the market, entry conditions 

affect the way leaders undertake preliminary investments. In particular, using 

the classic taxonomy of business strategies, we have seen that leaders facing 

endogenous entry always act as top dogs or with a lean and hungry look, 

10 See Bresnahan (1987) and Berry et al. (2004) on the US automobile market, and 

Kadiyali (1996) with particular reference to entry deterrence and accommodation 

in the US consumer market for photographic film in the period 1970-1990, when 

Kodak was the leader and Fuji the follower.


and never as puppy dogs or fat cats: ultimately, they are always aggressive 

compared to the entrants in the competition in the market, which is in line 

with the previous results. Between the many commitments we analyzed, some 

can be particularly interesting for empirical investigations. For instance, we 

analyzed cost reducing and demand enhancing investments. From the first 

category we obtained neat predictions (leaders invest more in cost reducing 

activities when facing endogenous entry), and later we will revisit them again 

when dealing with more general forms of investments in R&D. From the 

second category we obtained results that depend crucially on the kind of 

demand enhancing investments under consideration. 

Consider product quality. Here, our focus will be on the implications of 

the theory of market leaders in the presence of a double choice on both the 

quality and the price of the products. Summarizing the strategies with the 

quality-price ratio, a strong prediction deriving from our characterization 

(based on Prop. 3.9) would be the following: 

P.3: Market leaders facing an exogenous number of firms choose a lower 

quality-price ratio than the followers; market leaders facing endogenous entry 

choose a higher quality-price ratio than the followers. 

Given the complex strategic interactions emerging in a situation where 

firms choose multiple variables, it could be reasonable to limit the analysis to 

a weaker implication like the following: the quality-price ratio of the leaders 

increases with entry compared to the quality-price ratio of the followers. 

Another form of demand enhancing investment is the expenditure on nonprice 

advertising aimed at increasing demand. If we focus on markets with 

product differentiation and competition in prices, our theory (Prop. 2.5) implied 

the following strong testable prediction: 

P.4: Market leaders spend more than the followers in nonprice advertising 

(as a percentage of turnover) when the number of firmsisexogenous,and 

less when entry is endogenous. 

Finally, after pointing out empirical implications for the policies concerning 

price, product and promotion, we emphasize an implication for the 

last strategic investment that characterizes the marketing mix of a firm (the 

fourth P), place which stands for distribution. From our analysis on the choice 

of wholesale prices to retailers in the presence of downstream distribution 

channels (Prop. 2.9), we have the following prediction: 

P.5: Market leaders set higher wholesale prices for their retailers than 

their competitors when the number of firmsisexogenous,whiletheysetlower 

prices when entry is endogenous. 

Concerning financial issues, we need to take care of a more subtle differentiation 

on the source of uncertainty in the market, which can be used as an


additional control variable. 11 Then, on the basis of our analysis (Prop. 2.6), 

we have the following prediction based on the hypothesis of competition in 

prices: 

P.6: The financial structure of market leaders is biased toward debt financing 

compared to the financial structure of the followers when the number 

of firms is exogenous, while it is biased toward equity financing when entry 

is endogenous, as long as uncertainty is mainly on the demand side (while 

uncertainty on costs pushes the predictions in the opposite direction). 

Notice that under competition in quantities our model always implies 

abiastowarddebtfinancing for the leader, therefore, once again, we can 

distinguish a weaker hypothesis from the strong one stated above: the debtequity 

ratio of the market leaders should increase with entry. 

As we noticed earlier, investments in cost reductions aimed at reducing 

the price of a good give rise to neat predictions under competition in prices: 

in particular, market leaders should spend less than the other firms in R&D 

investments in cost reductions when the number of firms is exogenous, and 

they should spend more when entry is endogenous. One should always keep 

in mind that this hypothesis holds under competition in prices, while under 

competition in quantities the leader would generally spend more than the 

followers in cost reductions under both entry conditions. However, we can 

generalize our result under general forms of competition for the market. In 

Chapter 4 we have seen that the theory of market leaders provides radical 

predictions concerning the incentives to invest in R&D by the firms already 

present in a market with the leading products. We can express the main 

implications in different ways. We start from the weakest possible prediction, 

which is already in contrast with the traditional result of the theory of 

innovation: 12 

P.7: Incumbent market leaders facing endogenous entry in the competition 

for the market invest in R&D. 

11 An interesting related analysis on the effect of debt on prices is in Chevalier 

(1995), but that treatment does not take into account the source of uncertainty 

and the endogeneity of entry. 

12 See Malerba and Orsenigo (1999), Blundell et al. (1999), Czarnitzki and Kraft 

(2007a) and Hughes (2007) on evidence on the high investment in R&D by 

market leaders. The empirical study by Blundell et al. (1999) witnesses a positive 

relationship between market power and innovation activity, which is consistent 

with strategic investment in R&D by the leaders. This result holds in a panel 

data with many sectors, but especially in the pharmaceutical sector, which is a 

sector with a high R&D-sales ratio, strong patent protection and where firms 

typically recognize that they are in races to develop innovations (in this sector 

a few drug companies on their own undertake truly innovative research, and a 

number of mergers in the mid-90s were even motivated to enhance leadership in 

the patent races).


Of course the theory of market leaders suggests more than this. First of 

all, we saw that leaders invest more than the followers when entry is endogenous. 

This was true in all of our models of competition for the market, 

independently from the kind of strategic interaction between firms (remember 

that investments could be strategic substitutes or complements in alternative 

models). Therefore, we state this as an intermediate hypothesis: 

P.8: The investment rate in R&D of market leaders is higher than the average 

investment rate in R&D of the followers when entry in the competition 

for the market is endogenous. 

We also have a radically strong hypothesis that derives from our favorite 

model in which the investments of the firms are strategic complements: 13 

P.9: Market leaders invest less in R&D (as a percentage of turnover) than 

the followers when the competition for the market is between an exogenous 

number of firms, they invest more when entry is endogenous. 

Finally, our theory of sequential innovation by leaders suggests a way 

to discriminate between different degrees of persistence of leadership in innovative 

sectors. When entry of firms in the competition for the market is 

endogenous we should expect that technological leaders invest a lot and their 

persistence is more likely. Of course, when there is no competition for the 

market we should expect that the monopolistic leadership is also persistent. 

However, when the degree of competition for the market is intermediate (entry 

is not free but more than one firm invests), we should expect that the 

incumbent does not invest much in R&D and that its leadership is more likely 

to be replaced. This suggests our last prediction: 

P. 10: The degree of persistence of leadership should follow and inverted 

U relation with the degree of entry in the competition for the market. 

These testable implications could be brought to the data in future research. 

Of course, the analysis of this book was limited to the issues that 

we considered interesting to understand the behavior of market leaders and 

to derive implications for antitrust policy. Many other issues could be studied 

through the market leaders approach and, accordingly, other empirical 

implications could be derived and eventually tested. 

13 Tournaments for team sports are an ideal context to test the theory of innovation 

by leaders since entry is definitely endogenous in these contests. Casual evidence 

from Formula 1 racing, the America’s Cup, or the European soccer Champions 

League suggests that leading teams do invest more than the followers and their 

leadership is partially persistent. Sport economics may investigate further the 

issue.


7.2 Implications for Business Administration 

In this book we looked at the behavior of market leaders from a descriptive 

point of view. The attempt was to understand how leaders behave in different 

competitive scenarios. There is another way to read the results of this book. 

This is the point of view of business administration: our results may suggest a 

rule of behavior for the management of the leading firms. A vast literature on 

marketing (see Kotler, 1999) and business strategy (see Porter, 1985) exists 

which questions what should be the optimal marketing mix and the optimal 

strategic investments. Here we have emphasized that the right answer may 

depend on the entry conditions in a crucial way. 

Consider a generic market where products are highly differentiated and 

firms compete in prices. When entry in the market is limited to a predetermined 

number of firms and there are profitable opportunities for all of 

these firms, the management should always follow an accommodating philosophy. 

This requires high prices, high investments in advertising, delegation 

of the distribution to downstream sellers with high wholesale prices, limited 

investments in R&D and expansion through horizontal mergers. In such a 

situation, an aggressive management is counterproductive because it induces 

retaliation by the rivals and reduces profits in the long run. 

The optimal management rule changes radically when the market is characterized 

by high reactivity of entry to the profitable conditions. In such a 

case, entry is pervasive and can reduce profits at low levels, but a firm can acquire 

a leadership and preserve high profits by adopting a correct marketing 

philosophy. This must be an aggressive philosophy, which requires the exact 

opposite of what we have seen before: low prices, low investments in advertising, 

delegation of the distribution with wholesale prices below cost and high 

fees, high investments in R&D and expansion through internal growth. 

The general principle is that the management should follow an aggressive 

or an accommodating philosophy according to the entry conditions, be able 

to monitor these conditions and adopt the right marketing mix and strategies 

accordingly. 

7.3 Implications for Economic Theory 

In this section we would like to emphasize a few areas where further theoretical 

research on the theory of market leaders could be fruitful. The model of 

Stackelberg competition with endogenous entry can be generalized in many 

other dimensions and applied to other specific forms of market structures. 

The same holds for the model of strategic investment with endogenous entry. 

Our discussions of the investments in cost reducing activities, in persuasive 

advertising and our analysis of the optimal financial structure related to the 

competition in the market were purely introductory and need further investigations. 

The literature on multi-sided markets is just taking off, therefore we

7.3 Implications for Economic Theory 253 

look forward to further applications. Concerning bundling, vertical restraints 

for interbrand competition, price discrimination and horizontal mergers we 

limited our results to basic attempts to approach these issues within a new 

perspective: further studies should generalize the outcomes and, most of all, 

verify their applicability for antitrust purposes. Growing literature on innovation 

by leaders already exists, but further theoretical work is needed in 

this field as well, especially for the understanding of the relationship between 

competitionforthemarketandinthemarket.Finally,wehaveseenthatthe 

theory of endogenous entry has some general consequences for the approach 

to antitrust policy, and may limit the validity of some of the implications of 

the post-Chicago approach. Hopefully, our results will be useful in improving 

our understanding of the behavior of market leaders under different entry 

conditions, and in deriving a unified economic approach to antitrust issues. 

Interesting results could be developed in the field of government policy 

aimed at helping domestic firms in international markets: we briefly analyzed 

the choice of the optimal state aids and subsidies for exporting firms 

and some issues concerning privatizations, but many other issues could be 

investigated. One could extend the analysis to more general forms of export 

promoting policies, as general forms of strategic trade policy, competitive 

devaluations in partial equilibrium and R&D subsidies in an international 

competition for the market. 14 Theroleofnon-profit firms could be investigated 

in an analogous way to our analysis of public firms. Furthermore, it 

would be interesting to analyze further the Schumpeterian model sketched 

in our analysis on sequential innovations with leaders driving technological 

progress and growth. 

The analysis of full-fledged models of competition for the market with 

endogenous entry, and eventually with asymmetries between leaders and 

followers, leads naturally to other applications in macroeconomics. Recent 

newkeynesian research has been limited to the analysis of competition in 

prices between an exogenous number of firms (or in situations where the 

number of firms was indeterminate or irrelevant), and has introduced sticky 

prices in this environment. We hope that this book contributes to suggest 

the relevance of endogenous entry under both competition in prices and in 

quantities, and the relevance of asymmetries between leaders and followers 

which can have important consequences over the business cycles. Moreover, 

we believe that the study of sticky entry in these markets can have interesting 

consequences for the same understanding of the business cycle (maybe more 

than the usual study of sticky prices). For instance, we have seen that entry 

heavily affectspricesandmarkupsinmarketswithrelevantfixed costs of 

production, and endogenous entry affects the pricing behavior of the existing 

14 While we neglected general equilibrium considerations, a deeper analysis of endogenous 

entry with market leaders in a 2 × 2 × 2 model could be fruitful.


firms (which can be seen as leaders in such a case). These factors could be 

fruitfully introduced in the general equilibrium macroeconomic analysis. 15 

Potentially, one could also apply the principles of the behavior of market 

leaders in other contexts of economic theory. The simple contest where 

a leader and its followers exert effort to obtain a compensation can be introduced 

in a principal-agent framework. A principal could choose the compensation 

for the agent that achieves the desired result, and could also choose the 

appropriate hierarchical structure between agents. Assigning a leadership to 

one of the agents may reduce total effort and the probability of achieving the 

desired result, but it may also avoid the waste in fixed costs of participation 

associated with multiple agents. 

The model of competition for a prize can also be re-interpreted in terms of 

a rent-seeking contest, and it foresees that incumbent lobbyists should invest 

more than entrants when there are no barriers to rent seeking. 

Political leadership can be analyzed in a related way as a function of the 

entry conditions in the electoral competition. One could think of incumbent 

politicians running for new elections in a parallel way to our incumbent monopolists 

that are leaders in the competition for the market. The strategies 

of competing politicians would affect the incentives of the political leaders to 

engage in the electoral campaign, spend resources and effort in fund raising, 

promote the endorsement of opinion makers, and finally (if possible) commit 

to challenging policies and promises that benefit the citizens. In the case 

of an electoral competition between two predetermined parties or coalitions 

where there is no space for the entry of other parties we could expect a systematic 

leapfrogging of the political opposition on the incumbent party. In 

the presence of electoral systems allowing for endogenous entry of candidates 

(when there are chances to replace the political contestants) we could expect 

the incumbent politicians to engage in more aggressive political campaigns 

to preserve political power. 16 

Finally, we cannot exclude that the role of entry conditions in inducing 

aggressive or accommodating behavior extends to more general interactions 

between persons, like those emerging in small communities, clubs, or circle of 

friends where leaders and followers interact to achieve personal satisfaction. 

The wide development of behavioral and psychological economics in the last 

years, may find related results in the study of social interactions. These could 

be the subject of further empirical investigations in experimental economics. 

15 See Bilbiie et al. (2007) for an important macroeconomic analysis of endogenous 

entry in the competition in the market, and Etro (2007,a) on endogenous entry 

also in the competition for the market. 

16 Of course, this parallel is limited by the ideological component which is present 

in political competitions, and it is confined to democratic political systems.



Entry manages to discipline competition more than any government policy. 

In particular, endogenous entry forces market leaders to act in an aggressive 

or pro-competitive way that creates benefits for the consumers, avoids welfare 

reducing mergers and can even reduce the effectiveness of collusive cartels. 

These results are quite close to those of the Chicago school, but have found a 

game theoretic formalization in this book and in the emerging literature on 

endogenous entry. 

On this basis we believe that industrial policy should be aimed at preserving 

free entry conditions and promoting competition in and for all the 

markets. More specifically, antitrust policy should intervene only in markets 

where entry is exogenously blocked or in which a firm attempts to build artificial 

barriers to entry. Other than that, we believe that the invisible hand 

of endogenous entry drives markets better than any other exogenous intervention. 

With these considerations we have arrived to the end of our book on 

market leaders and endogenous entry. As Jerry Seinfeld once said, “the big 

advantage of a book is it’s very easy to rewind: close it and you’re right back 

at the beginning.”

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2007, Technological Revolutions and the Evolution of Industrial Structures. 

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Erkal, Nisvan and Daniel Piccinin, 2007b, Cooperative R&D under Uncertainty 

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2007 Intertic Conference 

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Etro, Federico, 1998b, Tax Evasion by Firms, DP 321, University of Bologna 

Etro, Federico, 1999, A Note on an Inexistent Theorem by Rothschild and 

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Endogenous Persistence of Monopoly, mimeo, Harvard University, published 

on Rivista Internazionale di Scienze Sociali, 2007, 115, 1, 81-108 

Etro, Federico, 2002, Stackelberg Competition with Free Entry, mimeo, Harvard 

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Etro, Federico, 2004, Innovation by Leaders, TheEconomicJournal, 114, 4, 

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5-7 

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Etro, Federico, 2006d, Antitrust Policy, the Theory of Market Leaders and 

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Edited by P. Waelbroeck, Ecole Nationale Supérieure des Télécommunications, 

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of Milan, Bicocca, Dept. of Economics 

Etro, Federico, 2006f, Strategic Export Promotion, WP 101, University of 

Milan, Bicocca, Dept. of Economics 

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Etro, Federico, 2007b, The Economics of Competition Policy and Dominant 

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Etro, Federico, 2007d, Competition Policy for the New Economy, in Abuse of 

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Etro, Federico, 2008, Stackelberg Competition with Endogenous Entry, The 

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Index 

Abreu, Dilip, 8 

Absorptive capacity, 29 

Abuse of dominance, 6, 171, 174, 195, 

197, 200 

Accommodating philosophy, 252 

Acemoglu, Daron, 156 

Ad valorem tax, 53, 57 

Adobe, 210, 233 

Adverse selection, 84 

Advertising, 63, 70, 78, 249 

Aerts, Kris, 159 

Aggressive philosophy, 252 

Aghion, Philippe, 29, 31, 34, 141, 148, 

150, 155, 157, 160, 162, 164 

Ahlborn, Christian, 176 

Airbus, 66, 120 

Aircraft industry, 66, 120 

Airline industry, 244, 247 

Akerlof, George, 84 

Allen, Paul, 215 

Amazon, 213 

America Online, 219 

America’s Cup, 251 

American Express, 224 

Amir, Rabah, 16, 52, 76 

Anant, T.C.A., 155 

Anderson, Simon, 21, 46, 55, 107, 113, 

116, 123, 124 

Apple, 131, 209—211, 215, 225, 228, 233 

Application Programming Interfaces, 

210 

Areeda, Phillip, 198 

Areeda-Turner rule, 198 

Armani, 21 

Armstrong, Mark, 78 

Arrow’s paradox, 27, 31, 133, 137, 140, 

146, 187, 228 

Arrow, Kenneth, 28, 31, 133, 218 

Article 81 of EU Treaty, 172 

Article 82 of EU Treaty, 172, 195 

Asymmetric information, 69, 84, 85, 

177 

Asymmetries between leaders and 

followers, 109 

AT&T, 93, 220, 221 

Atari, 215 

Aumann, Robert, 8 

Automobile industry, 15 

Average Avoidable Cost, 200 

Average Total Cost, 16, 199 

Average Variable Cost, 198, 199, 201 

Bain,Joe,3,93,178 

Ballmer, Steve, 218 

Banking sector, 183, 244 

Barriers to entry, 33, 108, 178, 186, 

224, 244 

Barro, Robert, 29, 155, 157, 223 

Baumol, William, 3, 14, 21, 93, 105, 

176, 179 

Baxter, William, 213 

Bayer, 25 

Bayesian equilibrium, 2, 69, 84 

Beath, John, 133 

Becker, Gary, 70 

Benetton, 21 

Bergman, Mats, 245 

Berry, Stephen, 248 

Bertrand equilibrium, 86

276 Index 

Bertrand, Joseph, 20, 46, 54, 56, 106, 

162 

Bessen, Jim, 151, 191 

Bilbiie, Florin, 254 

BlackBerry, 211, 215 

Bloom, Nick, 150 

Blundell, Richard, 31, 34, 134, 150, 156, 

160 

Boeing, 66 

Boldrin, Michele, 156, 193, 194 

Bonanno, Giacomo, 43, 82—84, 177, 185 

Bonus-malus insurance, 85 

Boone, Jan, 122 

Bork, Robert, 79, 88, 119, 174, 179, 182 

Boston Consulting Group, 186 

Bowley model, 46 

Boycko, Maxim, 123 

Brander, James, 43, 72, 74, 120, 177 

Brealey, Richard, 72 

Bresnahan, Timothy, 219, 248 

Brin, Sergey, 238 

Bulow, Jeremy, 42, 68, 114, 177 

Bundling, 43, 79, 185, 201, 205, 221, 

230, 232, 234 

Bush, George W., 221 

Buxant, Martin, 237 

Cable, John, 155 

Caillaud, Bernard, 212 

Cambini, Carlo, 63 

Campari, 237 

Capital-labour ratio, 115 

Carlton, Dennis, 93 

Cartels, 118, 150, 205 

Cawley, John, 85 

Cellophane fallacy, 200 

CES demand, 55, 57, 107, 127 

Chamberlin, Edward, 46 

Champions League, 251 

Chandler, Alfred, 132, 187 

Chanel, 237 

Chevalier, Judith, 75, 250 

Chiappori, Pierre Andre, 85 

Chicago school, 44, 79, 88, 119, 173, 

174, 186, 204, 229, 230, 255 

Clayton Act, 175 

Clinton, Bill, 218 

Coase, Ronald, 239 

Coca-Cola, 237 

Cohen, Wesley, 141 

Collusion, 7, 26, 118, 148, 150 

Competition for the market, 1, 25, 27, 

31, 45, 108, 124, 131, 135, 142, 151, 

159, 186, 189, 195, 196, 198, 203, 

205, 229, 235, 246, 250 

Competition in prices, 2, 20, 41, 44, 50, 

54, 67, 71, 73, 79, 82, 84, 100, 106, 

115, 121, 183, 212, 227, 246, 249, 252 

Competition in quantities, 1, 4, 16, 18, 

36, 41, 44, 50, 66, 70, 73, 76, 91, 100, 

111, 115, 121, 180, 197, 227, 246, 248 

Competitive strategy, 59, 252 

Corporate finance, 43, 72 

Cost reductions, 66 

Cournot duopoly, 5, 111 

Cournot, Augustin, 1, 52, 102 

Court of First Instance, 172, 223 

Cowell, Frank, 53 

Cozzi, Guido, 154, 194 

Credit cards, 78, 224 

Cremer, Jacques, 77 

Czarnizki, Dirk, 133, 149, 250 

D’Aspremont Claude, 46 

Darwinian selection effect, 161 

Dasgupta, Partha, 133, 136 

Davidson, Carl, 87 

Davis, Stephen, 231 

De Bondt, Raymond, 67, 151 

de Palma, Andrè, 21, 46, 55, 107, 116, 

123, 124 

Debt financing, 72, 150, 250 

Deep pocket theory of predation, 76 

Dell,210,216 

Demsetz, Harold, 188 

Deneckere, Raymond, 87 

Denicolò, Vincenzo, 151, 154, 161, 162, 

194 

Department of Justice, U.S.A., 171, 

218, 221

Index 277 

Diners Club, 224 

Dinopoulos, Elias, 155 

Director, Aaron, 174 

Discover, 224 

Distinct products test for bundling, 202 

Dixit, Avinash, 2, 41, 55—57, 60, 91, 93, 

127, 177 

Dominance, 171, 174, 186, 196, 200 

Dominant firm theory, 93 

Dorfman, Robert, 71 

Dorfman-Steiner condition, 71 

Dosi,Giovanni,208 

Du Pont, 132, 200 

Ducati, 121 

Dynamic inefficiency, 159 

Eaton, Jonathan, 120, 122 

eBay, 213 

Economides, Nicholas, 113, 227, 231 

Economies of scope, 68 

Efficiency defense, 196 

Ellison, Glenn, 245 

Ellison, Sarah, 245 

Elzinga, Kenneth, 219 

Encaoua, David, 116 

Endogenous costs of entry, 38 

Endogenous entry, 2, 3, 9, 12, 16, 17, 

19, 22, 23, 26, 27, 30, 32, 36, 38, 42, 

49, 53, 54, 57, 59, 63, 67, 71, 74, 77, 

81, 83, 86, 88, 91, 97, 102, 107—109, 

119, 121, 134, 138, 144, 146, 150, 

178, 199, 224, 228, 232, 236, 243, 252 

Endogenous leadership, 113 

Engers, Maxim, 113 

Entry deterrence, 3, 7, 13, 18, 20, 24, 

27, 32, 36, 66, 69, 77, 79, 91, 98, 104, 

108, 111, 177, 181, 197 

Equity-Debt ratio, 72, 250 

Erkal, Nisvan, 87, 104, 116, 117, 150, 

151, 194 

Erkal-Piccinin model, 88 

Escape competition effect, 29, 30, 34, 

140, 143, 145, 148, 149, 159 

Essential facility, 203 

Etro, Federico, 12, 31, 33, 42, 53, 63, 

74, 85, 92, 97, 111, 121, 122, 134, 

138, 146, 150, 153, 154, 158, 159, 

163, 178, 179, 191, 195, 200, 218 

European Commission, 172, 195—197, 

200, 201, 203, 204, 218, 221, 223, 

235, 236, 240 

European Court of Justice, 172, 223 

European Parliament, 191 

Evans, David, 176, 202, 207, 209, 212, 

217, 219, 223, 228 

Excel, 210, 217 

Exclusive dealing, 83 

Exclusive territories, 83 

Export promoting policy, 120 

Farrell, Joseph, 6 

Fashion industry, 21 

Fat cat strategy, 63, 72, 248 

Favaro, Edgardo, 244 

Federal Trade Commission, U.S.A., 

171, 218 

Ferrari, 15 

FIAT, 15 

Financial predation, 76 

Financial structure, 72, 250 

Firefox, 192, 233 

First degree price discrimination, 84 

Fisher, Franklin, 219, 226 

Foncel, Jerome, 226, 227 

Ford, 15 

Formula 1, 251 

Franchise fees, 82 

Free Software Movement, 192 

Friedman,James,8 

Front-loading effect, 161 

Fudenberg, Drew, 2, 8, 42, 60, 61, 63, 

72, 96, 133, 177, 225 

Fudenberg-Tirole taxonomy, 61 

Gabszewicz, Jean, 46 

Galbraith, John, 132, 187 

Galilei, Galileo, 189 

Gap, 21 

Gates, Bill, 209, 210, 215

278 Index 

Geanakoplos, John, 42, 68, 114, 177 

General Motors, 15 

GeneralPublicLicense,192,239 

Ghironi, Fabio, 254 

Gilbert, Richard, 111, 133, 140, 148 

GlaxoSmithKline, 25 

Goldfain, Katerina, 59 

Google, 213, 218, 238 

Goolsbee, Austan, 244 

Green, Jerry, 56 

Grieben, Wolf-Heimo, 159 

Griffith, Rachel, 29, 31, 34, 134, 148, 

150, 156, 160, 162, 164 

Griliches, Zvi, 141, 156 

Grossman, Gene, 120, 122 

Gual, Jordi, 172, 173 

Gucci, 21 

H&M, 21 

Hagiu, Andrei, 209, 217, 228 

Hall,Brownin,156 

Hall,Chris,227 

Hall, Robert, 227 

Hamilton, Jonathan, 113 

Harley & Davidson, 121 

Harrington, Joseph, 93 

Harris, Christopher, 133 

Harsanyi, John, 2 

Hart, Oliver, 76 

Hausman, Jerry, 156 

Hellwig, Martin, 172, 173 

Helpman, Elhanan, 120 

Hewlett-Packard, 132, 192, 209, 210, 

216 

Hirshleifer, Jack, 69 

Hoffmann-La Roche, 25 

Holmstrom, Bengt, 76 

Homogenous goods, 4, 16, 52, 101 

Honda, 121 

Horizontal differentiation, 45 

Hotelling model, 45, 62 

Hotelling, Harold, 45 

Howitt, Peter, 141, 150, 155, 157, 160 

Hughes, Danny, 188 

Hyperbolic demand, 53, 102, 105 

IBM, 132, 192, 193, 208, 212, 223, 228 

Implications of the theory of market 

leaders for business administration, 

252 

Impullitti, Giammario, 159 

Industrial revolution, 208 

Information and Communication 

Technology, 207 

Informative advertising, 70, 79 

Insurance market, 84, 85 

Intel, 66, 131, 132, 192, 206, 208 

Interbrand competition, 82, 185, 249 

International Chamber of Commerce, 

195 

Internet, 207, 218, 219 

Interoperability, 43, 81, 204, 222, 235, 

236, 240 

Ionascu, Delia, 122 

iPhone,131,193,211,215 

iPod, 131, 211, 233 

IPRs, 121, 151, 164, 187, 189, 192, 194, 

203, 204, 223, 235, 236, 238—240, 244 

Ivaldi, Mark, 226, 227 

Java, 218 

Jobs, Steve, 209 

Jullien,Bruno,212 

Kadiyali, Vrinda, 248 

Katsoulacos, Yannis, 133, 172, 186 

Katz,Michael,76 

Keen, Michael, 53 

Keun, Huh, 133, 246 

Klein, Benjamin, 219 

Klemperer, Paul, 42, 68, 114, 177 

Klepper, Steven, 141 

Kodak, 132, 248 

Kortum, Samuel, 141, 156 

Koski, Heli, 192 

Kotler,Philip,59,70,252 

Koulovatianos, Christos, 159 

Kovac, Eugen, 68, 122 

Kraft, Kornelius, 133, 149, 250 

Kreps, David, 177 

Kroes, Neelie, 222

Index 279 

Krugman, Paul, 120, 220, 221 

Laffont, Jean-Jacques, 62, 69 

Lambin, Jean-Jacques, 70 

Lambson,Eugen,52 

Lazzati, Natalia, 76 

Leadership in prices, 23, 106, 107, 115, 

122, 183 

Leadership in quantities, 10, 12, 17, 19, 

100, 102, 111, 115, 121, 180 

Lean and hungry look, 63, 64, 248 

Leapfrogging, 157, 254 

Learning by doing, 43, 66 

Lee, Tom, 133, 142 

Lerner, Josh, 192, 225 

Leverage buyouts, 75 

Leverage theory of tied good sales, 79, 

81 

Levine,David,156,193,194 

Levinsohn, James, 248 

Lewis, Tracy, 43, 72, 74, 177 

Liberalizations, 123 

Licenses, 238 

Liebowitz, Stan, 217, 219, 239 

Limit pricing, 3, 7, 13, 18, 20, 24, 36, 

66, 69, 77, 91, 104, 177, 181, 197, 225 

Linn, Joshua, 156 

Linux, 192, 210, 216, 224, 225 

Logit demand, 21, 54, 57, 107, 116, 127 

Long-purse theory of predation, 76 

Long-run Average Incremental Cost, 

201 

Loury, Glenn, 59, 133, 136 

Maggi, Giovanni, 120 

Malerba, Franco, 132, 250 

Mankiw,Gregory,103 

Mann, Ronald, 191 

Margolis, Stephen, 217, 219, 239 

Marketing, 59, 252 

Marketing mix 4 P’s model, 59, 249, 

252 

Marshall equilibrium, 2, 9, 16, 19, 22, 

26, 30, 41, 49, 53, 54, 57, 59, 64, 138, 

144, 149, 153, 166, 181 

Marshall, Alfred, 2 

Martin,Stephen,243 

Mas-Colell, Andreu, 56 

Maskin, Eric, 8, 85, 151, 191 

MasterCard, 224 

McFadden, Daniel, 21 

McGee, John, 175, 199 

McKenzie, Richard, 224 

Melitz, Marc, 254 

Merchant guilds, 134 

Merck, 25, 132 

Mergers, 6, 43, 87, 171, 205 

Merges, Robert, 191 

Microsoft, 31, 34, 132, 207, 208, 210, 

212, 215, 218, 223, 225, 228, 230, 

235, 240 

Microsoft Surface, 193, 229, 230 

Microsoft vs. EU case, 221 

Microsoft vs. US case, 218 

Milgrom, Paul, 59, 69, 177 

Miller, Merton, 72 

Minniti, Antonio, 159 

Modigliani, Franco, 3, 72, 93 

Modigliani-Miller Theorem, 43, 72, 76 

Monopolistic competition, 58 

Monopoly, 5, 7, 53, 79, 118, 176, 185, 

188, 189, 193, 223, 228, 251 

Monti, Mario, 221 

Moore’s Law, 131 

Mosaic, 219 

Most-favored-customer clause, 63 

Motorola, 132, 210, 211 

Motta, Massimo, 87, 171, 231 

Mozilla, 192, 233 

MP3 players, 131 

Mueller, Dennis, 155 

Mukherjee, Arijit, 87 

Multi-homing, 79, 213, 225, 234 

Multi-sided markets, 43, 76, 185, 198, 

201, 202, 212, 217, 226 

Multimarket competition, 68 

Multiple leaders, 110 

Multiple strategies, 114 

Murphy,Kevin,70,231

280 Index 

Myers, Stewart, 72 

Myerson, Roger, 2 

Myles, Gareth, 53 

Nash equilibrium, 1, 8, 16, 19, 22, 25, 

29, 41, 48, 52, 54, 57, 59, 61, 138, 143 

Nash, John, 1 

National Champions, 120 

Netscape, 218, 219, 223, 231—233 

Network effects, 43, 76, 184, 188, 198, 

201, 202, 210, 212, 217, 225, 226, 

232, 234, 239 

Newbery, David, 140, 148 

Nichols, Albert, 219 

Nintendo, 215 

Nokia, 132, 211 

Non-drastic innovations, 148 

Nordhaus, WIlliam, 189 

Novell, 192, 223, 224 

Novshek, William, 2, 52 

NTT, 212 

Ogilvie, Sheilagh, 134 

Open source software, 192, 193, 222, 

229 

Operating System, 192, 209, 210, 213, 

215, 218, 221, 223, 225, 228—230, 238 

Optimal export subsidy with price 

competition, 122 

Optimal export subsidy with quantity 

competition, 121 

Optimal protection of IPRs, 189, 190, 

194, 196, 203, 235 

Oracle, 192, 223 

Orsenigo, Luigi, 132, 250 

Padilla, Jorge, 176 

Page,Larry,238 

Pakes, Ariel, 156, 248 

Palm OS, 211 

Panzar, John, 3, 14, 21, 93, 105, 176 

Patent races, 133, 135, 142, 152, 155 

Patentability of Computer Implemented 

Inventions, 191 

Patents, 34, 151, 189, 191, 192, 194, 

203, 204, 223, 235, 236, 238, 240, 244 

PC industry, 207, 208, 210, 225 

Peretto, Pietro, 157 

Perloff, Jeffrey, 93 

Perrot, Anne, 172, 173 

Persistence of leadership, 27, 29—32, 34, 

66, 131, 135, 138, 142—144, 146, 148, 

151—153, 155, 157—159, 162, 186, 189, 

194, 195, 203, 205, 228, 235, 236, 

250, 251 

Pfizer, 25, 132 

Pharmaceutical sector, 25, 190, 245 

Philipson, Tomas, 85 

Photographic film industry, 248 

Piccinin, Daniel, 87, 104, 116, 117, 150 

PlayStation, 210, 215, 218 

Poisson process, 136 

Political leadership, 254 

Polo, Michele, 172, 173 

Pooling equilibrium, 69, 84, 85 

Porter, Michael, 59, 252 

Posner, Richard, 79, 88, 119, 174, 175, 

184, 220, 228, 229 

post-Chicago approach, 69, 173, 176, 

177, 186, 204, 227, 232, 253 

PowerPoint, 217 

Prantl, Susanne, 160 

pre-Chicago approach, 174, 176 

Predatory pricing, 7, 69, 175, 177, 183, 

197, 205 

Prescott, Edward, 113 

Price discrimination, 43, 84, 185, 205 

Principal-agent models, 59, 254 

Privatizations, 123 

Product differentiation, 18, 88, 104, 

106, 181, 183, 246 

Public enterprises, 123 

Public production of private goods, 123 

Public-private partnerships, 190 

Puppy dog strategy, 62, 248 

Quadratic utility function, 51, 116 

Quality-price ratio, 115, 249 

Quantity discounts, 82, 84 

QWERTY, 240

Index 281 

Röller, Lars-Hendrick, 247 

R&D Cartels, 26, 151 

R&D investment, 25, 27, 31, 66, 131, 

135, 142, 151, 159, 186, 189, 194, 

203, 228, 235, 249, 250 

R&D leadership, 26, 31, 66, 108, 131, 

139, 144, 146, 150, 153, 157, 186, 

235, 250 

R&D subsidies, 26, 121, 159 

RAND terms, 222, 238 

Ready-to-eat cereal industry, 71, 246 

Reagan, Ronald, 176 

RealNetworks, 215, 221 

Rebates, 82 

Red Hat, 192, 224 

Refusal to supply, 203 

Reinganum, Jennifer, 133, 143, 145, 153 

Reksulak, Michael, 190 

Rent seeking, 45, 59, 254 

Repeated games, 8 

Resale price maintenance, 83 

Research Joint Ventures, 151 

Retailers, 82, 185, 249 

Rey, Patrick, 43, 62, 77, 82, 84, 172, 

173, 177, 185 

Reynolds, Roberts, 87 

Rhee, Ki-Eun, 171 

Riley, John, 69, 85 

Roberts, John, 59, 69, 177 

Rochet, Jean-Charles, 78, 212 

Rochet-Tirole rule, 78, 201, 214 

Rockefeller, 175 

Romer, Paul, 155, 220 

Rothschild, Michael, 84, 85 

Rothschild-Stiglitz model, 84 

Rubinfeld, Daniel, 219, 226 

Rudholm, Niklas, 245 

Rule of reason, 175, 198, 201 

Sala-i-Martin, Xavier, 155, 157 

Salaniè, Bernard, 85 

Salant, Stephen, 87, 149 

Schelling, Thomas, 2 

Scherer, Frederic, 133, 246 

Schmalensee, Richard, 72, 207, 209, 

217, 226, 228 

Schmidt, Klaus, 172, 173 

Schmidt, Tobias, 159 

Schumpeter, Joseph, 31, 132, 135, 157, 

187 

Schumpeterian growth, 155, 158, 160, 

166 

Scotchmer, Suzanne, 151, 156, 159, 188, 

239 

Second degree price discrimination, 84 

Sega, 215 

Segerstrom, Paul, 155, 156, 159, 206, 

236 

Seinfeld, Jerry, 255 

Selten, Reinhard, 2 

Separating equilibrium, 69, 84, 85 

Sequential innovations, 151, 152, 154, 

187, 229, 235 

Shakespeare, William, 63 

Shapiro, Carl, 6, 76, 220 

Shapley, Lloyd, 8 

Sherman Act, 171 

Shleifer, Andrei, 123 

Showalter, Dean, 72, 74 

Shubik demand, 117 

Shubik, Martin, 116 

Shughart II, William, 190 

Sickles, Robin, 247 

Siemens, 211 

Signaling, 69 

Slutsky, Steven, 113 

Smart phones, 131, 211, 212 

Software market, 191, 192, 207, 208, 

210, 212, 215, 218, 223, 225, 228, 

230, 235, 240 

Software platforms, 212 

Sony, 210, 211, 215, 218 

Southwest Airlines, 244 

Specific tax,53 

Spence, Michael, 55, 69, 91 

Spencer, Barbara, 120 

Spiller, Pablo, 244 

SSNIP test, 200

282 Index 

Stackelberg equilibrium, 2, 10, 17, 19, 

23, 27, 31, 94, 100, 106, 108, 138, 144 

Stackelberg equilibrium with endogenous 

entry, 3, 12, 17, 19, 21, 23, 

27, 32, 36, 38, 91, 94, 97, 102, 105, 

107—110, 113, 114, 121, 139, 146, 149, 

153, 162, 167, 180, 183, 187, 241, 

248, 252 

Stackelberg, Heinrich von, 2, 52, 91, 

100 

Stallman, Richard, 192 

Standard Oil Trust, 175 

Standards, 238 

State aids, 120, 205 

Steiner, Peter, 71 

Stenbacka, Rune, 172, 173 

Sticky entry, 253 

Stigler, George, 179 

Stiglitz, Joseph, 2, 41, 43, 55—57, 74, 

82, 84, 85, 127, 133, 136, 177, 185, 

223 

Strategic commitments, 23, 41, 42, 59, 

61, 63, 118, 120, 123, 150, 184, 232, 

249 

Strategic complementarity, 42, 47, 

49—52, 56, 60—63, 65, 68, 74, 81, 92, 

96, 99, 106, 143 

Strategic substitutability, 42, 47, 49—51, 

59—63, 65, 66, 68, 74, 92, 96, 99, 102, 

108 

SubGame Perfect Equilibrium, 2, 10, 

12, 63, 94, 97, 113 

Sun Microsystems, 192, 219, 223 

Sunk costs, 38, 179 

Supergames, 8 

Supermarkets vs retail business, 176 

Sutton, John, 38, 66, 179, 209 

Switzer, Sheldon, 87 

Sylos Labini, Paolo, 3, 93 

Symbian, 211, 218 

Syverson, Chad, 244 

Tax evasion, 53 

Tax incidence, 53, 57 

Tesoriere, Antonio, 111, 112, 114 

Testing the theory of market leaders, 

243 

Theory of contestable markets, 3, 14, 

21, 93, 105, 176 

Third degree price discrimination, 85 

Thisse, Jean Francois, 21, 46, 55, 107, 

116, 123, 124 

Thomas, Louis, 243, 246 

Tirole, Jean, 2, 42, 60—63, 69, 70, 72, 

76—78, 81, 83, 84, 96, 133, 177, 192, 

212, 225 

Tollison, Robert, 190 

Top dog strategy, 62, 64, 79, 248 

Torvalds,Linus,192 

Toyota, 15 

Trade Policy, 120 

Trade secrets, 236, 237 

Tullock, Gordon, 59 

Turner, Donald, 198 

Tying, 79, 177, 185, 201, 219, 221, 230 

U-shaped cost functions, 15, 16, 103, 

181, 198 

Ulph, David, 133, 186 

US Patent and Trademark Office, 191 

Valletti, Tommaso, 63 

Van Reenen, John, 31, 134 

Vandekerckhove, Jan, 67, 151 

Venture capital financing, 150 

Vernon, John, 93 

Vertical differentiation, 71, 115 

Vertical integration, 82 

Vertical restraints, 43, 82, 185, 205, 249 

VHS, 240 

Vickers, John, 43, 82—84, 133, 163, 177, 

185 

Vickrey, William, 46 

Videogame industry, 210, 215 

Vinogradov, Viatcheslav, 68 

Visa, 224 

Viscusi, Kip, 93 

Vishny, Robert, 123 

Visscher,Michael,113 

Vives, Xavier, 95, 111, 113

Index 283 

Vodafone, 212 

von Weizsacker, C.C., 2, 17 

Webb-Pomerene Act, 120 

Weiss, Andrew, 74 

Welfare analysis, 14, 104, 108, 126, 127, 

141, 148 

Whinston, Michael, 43, 56, 79, 81, 83, 

103, 177, 185, 232 

Wiethaus, Lars, 29 

Wikipedia, 193 

Wilde, Louis, 133, 142 

Williamson, Oliver E., 6 

Willig, Robert, 3, 14, 21, 93, 105, 176 

Wilson, Robert, 177 

Windows, 210, 216, 218, 219, 221, 225, 

229, 231 

Windows MediaPlayer, 217, 221, 231 

Word, 210, 217 

World Trade Organization, 120 

WorldWideWeb,207,218 

Wozniak, Steve, 209 

Xbox, 210, 215, 218 

Yahoo, 213 

Yves Saint Laurent, 21 

Zanchettin, Piercarlo, 161, 162 

Zara, 21 

Zeira, Joseph, 157 

Zigic, Kresimir, 67, 68, 122

Competition, Innovation, and Antitrust. A Theory of Market ... - Intertic

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