What is game theory? The theory of rational choice; Interacting decision makers. Strategic games; Example: The prisoner’s dilemma; 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 players may randomize; Mixed strategy Nash equilibrium; Dominated actions; Pure equilibria when randomization is allowed, illustration; Equilibrium in a single population, illustration; The formation of players’ beliefs; Extensions; Representing preferences by expected payoffs.
Extensive games with perfect information; Strategies and outcomes; Nash equilibrium; Subgame perfect equilibrium; Finding subgame perfect equilibria of finite horizon games.
Extensions: Allowing for simultaneous moves, illustration: entry in to a monopolized industry; Discussion: subgame perfect equilibrium and backward induction.Coalition games; The core; Illustration: ownership and the distribution of wealth; Other solution concepts.
Motivational examples; General definitions; Two examples concerning information; Illustration: auctions; Auctions with an arbitrary distribution of valuations. Extensive games with imperfect information; Strategies; Nash equilibrium; Beliefs and sequential equilibrium; Signaling games; Illustration: strategic information transmission.
Strictly competitive games and maximization; Maximization and Nash equilibrium; Strictly competitive games; Maximization and Nash equilibrium in strictly competitive games. Rationalizability; Iterated elimination of strictly dominated actions; Iterated elimination of weakly dominated actions; Dominance solvability.
Monomorphic pure strategy eulibrium; Mixed strategies and polymorphic equilibrium; Asymmetric contests; Variations on themes: Sibling behavior, Nesting behavior of wasps, the evolution of sex ratio. Repeated games: The main idea; Preferences; Repeated games; Finitely and infinitely repeated Prisoner’s dilemma; Strategies in an infinitely repeated Prisoner’s dilemma; Some Nash equilibria of an infinitely repeated Prisoner’s dilemma.
Nash equilibria of general infinitely repeated games; Subgame perfect equilibria of general infinitely repeated games; Finitely repeated gazmes; Imperfect observability. Bargaining as an extensive game; Trade in market as an illustration; Nash’s axiomatic model; Relation between strategic and axiomatic models.