E1:254 Game Theory

Lecture Notes:

Part I: Noncooperative Game Theory

                      Introduction to Game Theory
                      Extensive Form Games
                      Strategic Form Games
                      Dominant Strategy Equilibria
                      Pure Strategy Nash Equilibrium
                      Mixed Strategy Nash Equilibrium
                      Von Neumann - Morgenstern Utility Theory
                      Rationalizable Strategies
                      Sperner's Lemma, Fixed Point Theorems, and Existence of Nash Equilibrium
                      Computation of Nash Equilibrium
                      Complexity of Computing Nash Equilibrium
                      Matrix Games (Two Player Zerosum Games)
                      Bayesian Games
                      Subgame Perfect Equilibrium

Part II: Mechanism Design

                      Introduction to Mechanism Design
                      Social Choice Functions and Mechanisms
                      Incentive Compatibility and Revelation Theorem
                      Properties of Social Choice Functions
                      Gibbard Satterthwaite Theorem and Arrow Impossibility Theorem
                      Quasilinear Mechanisms
                      Vickrey-Clarke-Groves Mechanisms
                      Bayesian Incentive Compatible Mechanisms
                      Revenue Equivalence Theorem
                      Optimal Auctions and Myerson Auction
                      Case Study: Sponsored Search Auctions
                      Other Topics in Mechanism Design
                      Mechanism Design -- Tutorial (Part 1)
                      Mechanism Design -- Tutorial (Part 2)

Part III: Cooperative Game Theory

                      Correlated Strategies and Correlated Equilibrium
                      The Two Person Bargaining Problem
                      Coalitional Games
                      The Core
                      The Shapley Value
                      Other Concepts (Stable Sets, Bargaining Sets, Kernel, Nucleolus, Gately Point)