Week 1: Introduction, the game of chess, proof of chess theorem, normal form games
Week 2:Dominance, Nash equilibrium, Maxmin strategies, elimination of dominated strategies, preservation of pure Nash equilibrium (PSNE), matrix games, relation between maxmin and PSNE in matrix games
Week 3:Mixed strategies, mixed strategy Nash equilibrium (MSNE), finding MSNE, MSNE characterization theorem, algorithm to find MSNE
Week 4:Correlated equilibrium (CE), computing CE, extensive form games, subgame perfection, limitations of subgame perfect Nash equilibrium
Week 5:Imperfect information extensive form games (IIEFG), strategies in IIEFGs, equivalence of strategies in IIEFGs, perfect recall
Week 6:Equilibrium in IIEFG, game theory in practice: P2P file sharing, Bayesian games, strategy and utility in Bayesian games, equilibrium in Bayesian games
Week 7:Introduction to mechanism design, revelation principle, introduction and proof of Arrow’s impossibility result, introduction to social choice setup
Week 8:Introduction and proof of Gibbard-Satterthwaite theorem, domain restriction, median voter theorem
Week 9:Task sharing domain, uniform rule, mechanism design with transfers, examples of quasi-linear preferences, Pareto optimality and Groves payments
Week 10:Introduction to VCG mechanism, VCG in Combinatorial allocations, applications to Internet advertising, slot allocation and payments in position auctions, pros and cons of VCG mechanism
Week 11:Affine maximizers, single object allocation, Myerson’s lemma, optimal mechanism design
Week 12:Single and multi-agent optimal mechanism design, examples of optimal mechanisms
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