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 18: Imperfect information information sets and sub-game perfection

4.1 ( 11 )

Lecture Details

We consider games that have both simultaneous and sequential components, combining ideas from before and after the midterm. We represent what a player does not know within a game using an information set a collection of nodes among which the player cannot distinguish. This lets us define games of imperfect information; and also lets us formally define subgames. We then extend our definition of a strategy to imperfect information games, and use this to construct the normal form (the payoff matrix) of such games. A key idea here is that it is information, not time per se, that matters. We show that not all Nash equilibria of such games are equally plausible some are inconsistent with backward induction; some involve non-Nash behavior in some (unreached) subgames. To deal with this, we introduce a more refined equilibrium notion, called sub-game perfection.



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

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Great course. Thank you very much.