E1:254 Game Theory
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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)