Game Theory

Yale,, Fall 2007 , Prof. Ben Polak

Updated On 02 Feb, 19

Overview

Introduction - Putting yourselves into other peoples shoes - Iterative deletion and the median-voter theorem - Best responses in soccer and business partnerships - Nash equilibrium: bad fashion and bank runs - Nash equilibrium: dating and Cournot - Nash equilibrium: shopping, standing and voting on a line - Nash equilibrium: location, segregation and randomization - Mixed strategies in theory and tennis - Mixed strategies in baseball, dating and paying your taxes - Evolutionary stability: cooperation, mutation, and equilibrium - Evolutionary stability: social convention, aggression, and cycles - Sequential games: moral hazard, incentives, and hungry lions - Backward induction: commitment, spies, and first-mover advantages - Backward induction: chess, strategies, and credible threats - Backward induction: reputation and duels - Backward induction: ultimatums and bargaining - Imperfect information: information sets and sub-game perfection -Subgame perfect equilibrium: matchmaking and strategic investments - Subgame perfect equilibrium: wars of attrition - Repeated games: cooperation vs. the end game - Repeated games: cheating, punishment, and outsourcing - Asymmetric information: silence, signaling and suffering education - Asymmetric information: auctions and the winner

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Lecture 21: Repeated games cooperation vs. the end game

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Lecture Details

We discuss repeated games, aiming to unpack the intuition that the promise of rewards and the threat of punishment in the future of a relationship can provide incentives for good behavior today. In class, we play prisoners dilemma twice and three times, but this fails to sustain cooperation. The problem is that, in the last stage, since there is then is future, there is no incentive to cooperate, and hence the incentives unravel from the back. We related this to the real-world problems of a lame duck leader and of maintaining incentives for those close to retirement. But it is possible to sustain good behavior in early stages of some repeated games (even if they are only played a few times) provided the stage games have two or more equilibria to be used as rewards and punishments. This may require us to play bad equilibria tomorrow. We relate this to the trade off between ex ante and ex post efficiency in the law. Finally, we play a game in which the players do not know when the game will end, and we start to consider strategies for this potentially infinitely repeated game.