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 9: Mixed strategies in theory and tennis

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Lecture Details

We continue our discussion of mixed strategies. First we discuss the payoff to a mixed strategy, pointing out that it must be a weighed average of the payoffs to the pure strategies used in the mix. We note a consequence of this if a mixed strategy is a best response, then all the pure strategies in the mix must themselves be best responses and hence indifferent. We use this idea to find mixed-strategy Nash equilibria in a game within a game of tennis.