Overview
ABOUT THE COURSE: This is an advanced course in game theory, with a particular emphasis on the role of information. We begin with static games and cover the basic notations there. About 65% of the course concerns dynamic games where we introduce information structures, role of information structure on equilibria, Bayesian games and information asymmetry. We then cover the basic concepts of mechanism design. We do a quick overview of signaling and screening, and introduce information design. As a final topic we do a study of pre-play communication – achievable payoffs and correlated equilibria. We finally end with a few applications of game theory in finance.INTENDED AUDIENCE: Graduate students in engineering and economics.INDUSTRY SUPPORT: Stock and commodity exchanges, platforms like Ola, Uber, Amazon.
Syllabus
Week 1: Outline of the course, Definition of a game, Nash equilibrium, Examples of Nash equilibrium, Weakly dominated strategies.
Week 2:Strictly dominated strategies, Aumann model of incomplete information, Knowledge operator, Common knowledge, Structure theorem of common knowledge.
Week 3:Dynamic games, Information structures, Commitment, Mixed and Behavioral strategies, Kuhn’s theorem, Bayesian games, Bayesian Nash equilibrium. Mechanism design(ContdProof of the structure theorem of common knowledge, Aumann model of incomplete information with belief, Aumann’s agreement theorem, Zero-sum game definition, Security strategies, Saddle point strategies.
Week 4:Further properties of saddle point strategies, Mixed strategies, Existence of mixed saddle point strategies, Von-Nuenmann minmax theorem.
Week 5:Computation of mixed saddle point strategies for various matrix games, Existence of nash equilibrium for non zero-sum game via Kakutani fixed point theorem
Week 6:Existence of Nash equilibrium for infinite strategy space via Brower’s fixed point theorem, Quantal response: definition and examples, Dynamic game definition, solution concept, Standard normal form of a dynamic game, Threat equilibrium.
Week 7:Extensive Form Game, Single Acts Games, Informationally Inferior Games
Week 8:Information Structure in Single Act Games, Nested and Ladder Nested Extensive, Equilibrium Algorithm Lecture, Stagewise Multi-Act Game, Feedback Nash Equilibrium, Stagewise Multi-Act Game, Feedback Nash Equilibrium
Week 9:Mixed & Behavioral Strategies, Conditions for Equivalence of Mixed & Behavioral Strategies, Kuhn’s Theorem, Equivalence of Mixed and Behavioral Strategies
Week 10:Games of Incomplete Information, Bayesian Nash Equilibrium, Self-enforcement of Nash Equilibrium, Stackelberg game
Week 11:Principal-Agent Models, Moral Hazard and Adverse Selection, Games with Contracts
Week 12:Correlated Equilibrium, Bayesian Game with Mediated Communication, Revelation Principle, Bayesian Nash Equilibrium