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A short introduction to non-cooperative games. Strategic form game. Best response. Pure strategy Nash Equilibrium (PSNE). Mixed strategies and Mixed Strategy Nash Equilibrium (MSNE). Existence of equilibrium. Correlated equilibrium.
Strictly competitive games, Hex: why should white win? Zermelo theorem. Minimax and maximin, security levels, minimax theorem, linear programming and duality.
Applications. Cournot and Bertrand models.
Lattice games. Posets, Lattices, Supermodularity, Increasing differences, Monotone comparative Statics. Tarski fixed point theorem.
Evolutionary stable strategies (ESS). Correlated equilibrium, trembling-hand equilibrium and other extensions.
Bayesian games. Types and Strategies. Bayesian equilibrium.
Extensive form games with complete information. History. Strategies. Nash equilibrium and subgame perfect Nash equilibrium.
Bargaining games.
Repeated games of complete information. Folks? theorems
Extensive form games with simultaneous moves and incomplete information. Sequential rationality. Weak perfect Bayesian equilibrium.
Repeated games of incomplete information.
Applications of asymmetric information games. Adverse selection. Screening and signaling games. Pooling and separating equilibrium. Existence. Moral hazard and optimal contracts (principal-agent).
Communication in games. Hard vs. soft information, disclosure, cheap talk. Bayesian persuasion.
Behavioral game theory: game theory treasures and their contradictions: traveller?s dilemma, asymmetric matching pennies, minimal effort coordination game, Kreps game.
Networks. Simple topologies on networks: regular lattice, Erdos-Renyi graphs, small-world networks. Learning in networks.
Open and closed-loop strategies. Time-consistency. Bequest games, quasi-hyperbolic discounting models and policy games. Markov stationary strategies.
Auctions. Basic types: English, Dutch, first and second price auctions.
Intro to mechanism design. Revelation principle, optimal mechanisms, Vickrey-Clarke-Groves mechanism. Implementation. Efficiency and optimal mechanisms.
Nash bargaining solution. Axiomatization and solution. Cooperative game. Supperadditive games. Characteristic form games (TU). Convex games. Core and Shapley value.
Stable matching: marriage market, Gale-Shapley algorithm.
Nash program and foundations of general equilibrium.
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