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Unformatted text preview: Game Theory: PureStrategy Nash Equilibrium Todd Sarver Northwestern University Econ 3102 – Fall 2011 Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 1 / 28 Outline 1 NonDominance Solvable Games 2 PureStrategy Nash Equilibrium 3 Best Responses 4 Relating the Solution Concepts 5 Games without PureStrategy NE 6 A Healthy Dose of Rationality Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 2 / 28 Not All Games are Dominance Solvable While iterated elimination of strictly dominated strategies can give us a prediction for many games, there are also many games in which either: 1 There are no strictly dominated strategies; or 2 The process of iterated elimination of strictly dominated strategies ends leaving more than one possible strategy for each player. Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 3 / 28 Not All Games are Dominance Solvable While iterated elimination of strictly dominated strategies can give us a prediction for many games, there are also many games in which either: 1 There are no strictly dominated strategies; or 2 The process of iterated elimination of strictly dominated strategies ends leaving more than one possible strategy for each player. Example (Battle of the Sexes) Chris Boxing Opera Pat Boxing 2 , 1 , Opera , 1 , 2 In this game, neither player has a strictly dominated strategy. Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 3 / 28 Outline 1 NonDominance Solvable Games 2 PureStrategy Nash Equilibrium 3 Best Responses 4 Relating the Solution Concepts 5 Games without PureStrategy NE 6 A Healthy Dose of Rationality Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 4 / 28 Nash Equilibrium What solution concept should we use to make predictions for games like Battle of the Sexes that are not dominance solvable? Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 5 / 28 Nash Equilibrium What solution concept should we use to make predictions for games like Battle of the Sexes that are not dominance solvable? Definition A profile of strategies for the players constitutes a (PureStrategy) Nash equilibrium if no player would like to change her strategy given the strategies of the other players. Todd Sarver (Northwestern University) Game Theory Econ 3102 – Fall 2011 5 / 28 Nash Equilibrium What solution concept should we use to make predictions for games like Battle of the Sexes that are not dominance solvable? Definition A profile of strategies for the players constitutes a (PureStrategy) Nash equilibrium if no player would like to change her strategy given the strategies of the other players....
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This note was uploaded on 01/03/2012 for the course ECON 3102 taught by Professor Sarver during the Spring '08 term at Northwestern.
 Spring '08
 SARVER
 Microeconomics, Game Theory

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