Modeling Climate Policy Instruments in a Stackelberg Game with ...

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4 1 INTRODUCTION also gives insight about sensitivity of important parameters. Finally, a short general analysis of the economic system treats considerations about market imperfections, time consistency and economic growth under exhaustible resources. Sec. 4 focuses on the detailed analysis of policy instruments – the heart of this work. Evaluation is performed along four crucial policy design issues: (1) price vs. quantity policy, (2) input vs. output taxation, (3) competition policy and (4) technology policy. The conclusion in Sec. 5 highlights the most important results and their relevancies for the climate change debate. Additional information is located in the appendix: The reformulation of the time-continuous equations for the numerical treatment with computer programs (A), the derivatives of the used functions (B), the detailed Stackelberg-Leader problem formulation (C) and a brief description of the decomposition analysis (D). A list of all variables and parameters with explanations is located at the end of this thesis (E). Program code of the developed model is available as encrypted ZIP file under: www.pik-potsdam.de/members/kalkuhl/clipide-model Password: policyIAM
5 2 Methods and Economic Theory 2.1 Methods Game Theory In this thesis, the problem of avoiding global warming is treated within game theory. This mathematical theory investigates conflicts and cooperation between rational decision makers (called players), often with applications in economics, management and social sciences. Games are classified as cooperative and noncooperative or as static and dynamic. While in static games there is only one decision at one time to make, dynamic game theory generalizes decision making behavior by considering past and (possible) future behavior. Dockner et al. (2000, pp. 21–22) give the following definition: “A game is said to be dynamic if at least one player can use a strategy which conditions his single-period action at any instant of time on the actions taken previously in the game. Previous actions are those of the rivals but also a player’s own actions.” The dynamics of decision making can be treated by differential equations describing the time-continuous development of state variables (differential game) or time-discrete difference equations (difference game) which are often used for numerical computations. An important question subject to game theoretic analysis concerns the players’ choice of strategies and hence the possible outcome of the game. The Nash equilibrium describes such a possible outcome by denoting a situation (i.e. strategy set) where no individual player has an incentive to deviate from his strategy given the strategy of the other players (see for formal definition Fudenberg and Tirole, 1991, pp. 11-14). Although the Nash equilibrium provides a plausible outcome consistent with typical assumptions of rationality of players, it is not necessarily a good prediction of outcome nor a “good” outcome. The first is the case if players do not play rationally or do not have essential informations for their decision-making. The latter is the case, if there is a strategy set unequal the Nash equilibrium that gives at least one player a higher payoff without reducing of other players’ payoff. Such an improvement is also called Pareto improving. If no Pareto improving change is possible, the outcome is called Pareto efficient or Pareto optimal. A famous example of a Nash equilibrium which is not Pareto optimal is the prisoner’s dilemma with defecting strategies as Nash equilibrium and cooperative strategies as Pareto efficient outcome that benefits both players respectively to the Nash equilibrium (Fudenberg and Tirole, 1991, pp. 9-10). The application of the concept of Nash equilibrium as optimal strategy of each player given the (optimal) strategies of other players to dynamic games requires solving an intertemporal optimization problem of each player (Dockner et al., 2000, ch. 4.1) If there are no asymmetries in information and strategic power, multiplayer games are usually modeled by simultaneous decision making with the Nash equilibrium as outcome. However, Stackelberg games assume a hierarchical asymmetry between players in the form that one player (called Stackelberg leader) makes her decision before the other players (Stackelberg followers) by considering secured information about the reaction of the followers after her move. Alternatively, the leader can commit herself to a public announced strategy which is considered by the followers in the same way as if the leader had made
Page 1: Matthias Kalkuhl Modeling Climate P
Page 5 and 6: CONTENTS III Contents 1 Introductio
Page 7 and 8: LIST OF FIGURES V List of Figures 1
Page 9 and 10: LIST OF ABBREVIATIONS VII List of A
Page 11 and 12: EXECUTIVE SUMMARY IX Executive Summ
Page 13 and 14: 1 “Climate change is a result of
Page 15: 1.3 Scope of this Thesis 3 a wide p
Page 19 and 20: 2.3 Economic Theory and Policy Inst
Page 29 and 30: 2.4 Review of Climate Economic Mode
Page 31 and 32: 2.6 Implications and Challenges 19
Page 33 and 34: 21 3 Model Development and Analysis
Page 35 and 36: 23 Although population growth is an
Page 37 and 38: 3.1 Description of the Basemodel 25
Page 45 and 46: 3.2 Model Extensions 33 3.2 Model E
Page 47 and 48: 3.2 Model Extensions 35 first-stage
Page 49 and 50: 3.2 Model Extensions 37 augments fa
Page 51 and 52: 3.3 Model Calibration 39 Resource S
Page 53 and 54: 3.3 Model Calibration 41 3.3.4 Elas
Page 55 and 56: 3.3 Model Calibration 43 3.5 3 T =
Page 57 and 58: 3.4 Analysis 45 ˜F(K Y , K E , K R
Page 59 and 60: 3.4 Analysis 47 imply lim µ(S −
Page 61 and 62: 3.4 Analysis 49 Ċ = Ẏ − I ˙ (
Page 63 and 64: 3.4 Analysis 51 of Barro and i Mart
Page 65 and 66: 3.4 Analysis 53 Figure 10: Shares o
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55 4 Evaluation of Policy Instrumen
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4.1 Price vs. Quantity Policy 57 Fi
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4.1 Price vs. Quantity Policy 59 To
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4.2 Input vs. Output Taxation 61 Fi
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4.2 Input vs. Output Taxation 65 th
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4.3 Competition Policy 69 should me
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4.3 Competition Policy 71 100 95 Pe
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4.3 Competition Policy 73 equations
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4.3 Competition Policy 75 2.5 2 Mon
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4.4 Technology Policy 77 no tax m e
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4.4 Technology Policy 79 Figure 29:
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4.4 Technology Policy 81 without R&
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4.4 Technology Policy 85 LbD R&D Lb
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4.4 Technology Policy 87 300 250 Ba
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91 5 Concluding Remarks and Reflect
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93 market power, ad-valorem tax pro
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climate policy not only may help to
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97 A Reformulating the Discrete Opt
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99 B Derivatives of Several Functio
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101 C The Stackelberg Leader Optimi
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103 Government C gov =Γ + τ K rK
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105 E List of Variables and Paramet
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E.2 Parameters 107 s elasticity of
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REFERENCES 109 References Abadie, J
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REFERENCES 111 Hanley, N., J. F. Sh
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REFERENCES 113 Pigou, A. C. (1932).
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REFERENCES 115 van der Zwaan, B. C.
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Ehrenwörtliche Erklärung Hiermit
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