Game Theory

Yale,, Fall 2007 , Prof. Ben Polak

Updated On 02 Feb, 19


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


Lecture 10: Mixed strategies in baseball, dating and paying your taxes

4.1 ( 11 )

Lecture Details

We develop three different interpretations of mixed strategies in various contexts sport, anti-terrorism strategy, dating, paying taxes and auditing taxpayers. One interpretation is that people literally randomize over their choices. Another is that your mixed strategy represents my belief about what you might do. A third is that the mixed strategy represents the proportions of people playing each pure strategy. Then we discuss some implications of the mixed equilibrium in games; in particular, we look how the equilibrium changes in the tax-complianceauditor game as we increase the penalty for cheating on your taxes. Mixed strategy equilibria are calculated in simple normal form games. Applications of mixed strategies are discussed in sports such as tennis, baseball and football. Mixed strategies are checked for equilibrium by comparing them with all possible pure strategy deviations. It is shown that this is sufficient for equilibrium. Mixed strategy equilibrium is calculated for the Battle of the Sexes game. A game of tax is developed and its outcomes are compared with tax payment rates in a few countries. Finally, simple comparative statics are discussed in this context.



2 Ratings
comment person image


Excellent course helped me understand topic that i couldn't while attendinfg my college.

comment person image


Great course. Thank you very much.