3 years ago

Game Theory with Applications to Finance and Marketing

Game Theory with Applications to Finance and Marketing

u i (σ i , σ −i )

u i (σ i , σ −i ) for all σ i ∈ Σ i ). A (mixed) strategy σ i is weakly dominatedby σ ′ i for player i if for some σ′ i ∈ Σ i,u i (σ i , σ −i ) ≤ u i (σ ′ i , σ −i), ∀σ −i ∈ Σ −i ,and σ i is strictly dominated if the above inequalities are all strict. Ourfirst equilibrium concept is that rational players will not use strictlydominated strategies. Consider the following normal form game, knownas the prisoner’s dilemma:player 1/player 2 Don’t Confess ConfessDon’t Confess 0,0 -3,1Confess 1,-3 -2,-2In this game, “Don’t Confess” is strictly dominated by “Confess,” andhence the unique undominated outcome is the one where both playersconfess the crime. Note that unlike Walrasian equilibrium, this equilibriumis Pareto inefficient. That equilibria in a game are generallyinefficient is the first lesson to be learned here (and all kinds of economictheory starts from here).6. Based on the implicit assumption that the whole normal form game isthe players’ common knowledge, the above dominance argument can beextended further so that we shall be looking at outcomes that survivefrom the procedure of iterative deletion of strictly dominated strategies.The following is an example.player 1/player 2 L M RU 0,-1 0,0 1,13M 2,3 3,1 2D 4,2 1,1 2, 3 2Note that M is not strictly dominated by L from player 2’s perspective,but since U is strictly dominated by M from player 1’s perspective,and in the absence of U, M is strictly dominated by L from player 2’sperspective, we should not expect player 2 to use M. It follows thatplayer 2 will use L and hence player 1 will use D.4

Observe that we have repeatedly used the assumption that rationalityof all players is the players’ common knowledge. For example, if player2 is not sure about player 1’s being rational, then player 2 may notwant to ignore strategy M.7. Mixed strategies that assign strictly positive probabilities to strictlydominated pure strategies are themselves strictly dominated. A mixedstrategy that assigns strictly positive probabilities only to pure strategieswhich are not even weakly dominated may still be strictly dominated.Consider also the following example:player 1/player 2 L RU 1,3 -2,0M -2,0 1,3D 0,1 0,1The mixed strategy (0.5, 0.5, 0) for player 1 is strictly dominated by D.8. It can be shown that iterated deletion of strictly dominated strategieswill lead to the set of surviving outcomes which is independent of theorder of deletion. The same is not true for iterated deletion of weaklydominated strategies. Consider the following normal form game:Example 3:player 1/player 2 L RU 1,1 0,0M 1,1 2,1D 0,0 2,1If we delete U and then L, then we conclude that the payoff profilewould be (2, 1). If we delete D and then R, then we conclude that thepayoff profile would be (1, 1).9. Definition 5: A normal form game is dominance solvable if all playersare indifferent between all outcomes that survive the iterative procedurewhere all the weakly dominated actions of each player are eliminated5

Master's programme in International Business Marketing-Finance
Shipping Markets and Finance - The McLean Group
A Dynamic Theory of Corporate Finance Based Upon Repeated ...
New markets tax credit financing available for manufacturers
New Markets Tax Credits: The Community Catalyst - Finance Fund
Hargreaves - Game Theory - Critical Introduction (Routledge, 1995)
Search Engine Marketing Applications - Dowitcher Designs
Global Mobile Gaming Market 2019- Strengths And Weaknesses For The Key Vendors
Social Gaming Market in the US 2015-2019: Opportunities And Threats Faced By The Key Vendors
Hargreaves - Game Theory - Critical Introduction (Routledge, 1995)
Master's programme in International Business Marketing-Finance
Market Gaps on Access to Finance - Bank of Valletta
Game Theory Applications: Lecture Notes - Citi - University of ...
The Art of Asset Allocation: Principles and Investment Strategies for Any Market, Second Edition (Professional Finance Investment)
Systemic risk in derivative markets - Institut Finance Dauphine
Unbundled Mortgage Market - International Union for Housing Finance
[+]The best book of the month Rating Based Modeling of Credit Risk: Theory and Application of Migration Matrices (Academic Press Advanced Finance) [PDF]
[+][PDF] TOP TREND Public Finance: A Normative Theory [PDF]
Stock Markets, Corporate Finance, and - Faculty & Research
Sapient Global Markets PowerPoint Template - Finance - CADC 2012
Applications of state space models in finance
Application Server Market Forecasts 2020
What is Marketing-Finance? - School of Business and Economics ...
Strategic Interactions in Markets with Innovative Activity: The ... - Intertic