What is game theory? The theory of rationalchoice; Interacting decision makers.Strategic games; Examples: The prisoner’s dilemma, Bach or Stravinsky,Matching pennies; Nash equilibrium; Examples of Nash equilibrium; Best-response functions; Dominated actions; Equilibrium in a single population:symmetric games and symmetric equilibria.
Introduction; Strategic games in which playersmay randomize; Mixed strategy Nash equilibrium; Dominated actions; Pureequilibria when randomization is allowed, Illustration: Expert Diagnosis;Equilibrium in a single population, Illustration: Reporting a crime; The formation of players’ beliefs; Extensions; Representing preferences byexpected payoffs.
Extensive games with perfect information; Strategies andoutcomes; Nash equilibrium; Subgame perfect equilibrium; Finding subgameperfect equilibria of finite horizon games: Backward induction. Illustrations:The ultimatum game, Stackelberg’s model of duopoly, Buying votes.
Extensions: Allowing forsimultaneous moves, Illustrations: Entry in to a monopolized industry,Electoral competition with strategic voters, Committee decision making, Exitfrom a declining industry; Allowing for exogenous uncertainty, Discussion:subgame perfect equilibrium and backward induction.
Motivational examples; General definitions; Two examples concerninginformation; Illustrations: Cournot’s duopoly game with imperfectinformation, Providing a public good, Auctions; Auctions with an arbitrarydistribution of valuations.Extensive games with imperfect information; Strategies; Nash equilibrium;Beliefs and sequential equilibrium; Signaling games; Illustration: Strategicinformation transmission.
competitive games and maximization; Maximization and Nash equilibrium;Strictly competitive games; Maximization and Nash equilibrium in strictlycompetitive games.Evolutionary Equilibrium: Monomorphic pure strategy equilibrium; Mixedstrategies and polymorphic equilibrium; Asymmetric contests; Variations onthemes: Sibling behavior, Nesting behavior of wasps, The evolution of sexratio.
Repeated games: The main idea; Preferences; Repeatedgames; Finitely and infinitely repeated Prisoner’s dilemma; Strategies in aninfinitely repeated Prisoner’s dilemma; Some Nash equilibria of an infinitelyrepeated Prisoner’s dilemma, Nash equilibrium payoffs of an infinitelyrepeated Prisoner’s dilemma.
Coalitional games. The Core.Illustrations: Ownership and distribution of wealth, Exchanging homogeneousitems, Exchanging heterogeneous items, Voting, Matching. Bargaining as anextensive game; Illustration of trade in a market; Nash\'s axiomatic model ofbargaining