Game theory

  • Introduction. What is a game? Basic elements of noncooperative games: players, strategies, payoffs. Examples. Randomized choices.
  • The extensive form representation of a game. Game tree, games of perfect information, the concept of an information set. Randomized choices.
  • The normal form representation of a game. Mixedstrategies. Behaviorstrategy. Connection between extensive form representation of a game and normal form representation of a game. Perfect recall.
  • Simultaneous-movegames. Dominant and dominated strategies. Strictly and weakly dominated strategies. Iterated deletion of strictly dominated strategies. Funny examples.
  • Pure and mixed strategy Nash equilibrium. Glass’ method for normal form representation of a game (2*M). ExistenceofNashequilibrium.
  • Zero-sumgames. Minimaxandmaximin. Saddlepoints. Securingpayoffs. Security strategies. Minimaxtheorem.
  • Dynamic Games. Noncredible treat. Sequential rationality. Backward induction in finit games of perfect information. Zermelo’s theorem. Subgame perfection. Cournot duopoly. * * Stackleberg leadership model. Funny examples.
  • Infinitely repeated games. The One-Shot Deviation Principle. Prisoner’s Dilemma.
  • Game of incomplete information. Cournot model with incomplete information. Bayesian Nash Equilibrium
  • Ultimatum Bargaining Game (Guth et al. 1982).
  • Auction Theory. Introduction.
  • Matching theory