Popularized by movies such as "A Beautiful Mind," game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Beyond what we call `games' in common language, such as chess, poker, soccer, etc., it includes the modeling of conflict among nations, political campaigns, competition among firms, and trading behavior in markets such as the NYSE.
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How could you begin to model keyword auctions, and peer to peer file-sharing networks, without accounting for the incentives of the people using them? The course will provide the basics: representing games and strategies, the extensive form (which computer scientists call game trees), Bayesian games (modeling things like auctions), repeated and stochastic games, and more. We'll include a variety of examples including classic games and a few applications.
Syllabus
WEEK 1
Introduction and Overview
Introduction, overview, uses of game theory, some applications and examples, and formal definitions of: the normal form, payoffs, strategies, pure strategy Nash equilibrium, dominant strategies.
WEEK 2
Mixed-Strategy Nash Equilibrium
pure and mixed strategy Nash equilibria.
WEEK 3
Alternate Solution Concepts
Iterative removal of strictly dominated strategies, minimax strategies and the minimax theorem for zero-sum game, correlated equilibria.
WEEK 4
Extensive-Form Games
Perfect information games: trees, players assigned to nodes, payoffs, backward Induction, subgame perfect equilibrium, introduction to imperfect-information games, mixed versus behavioral strategies.
WEEK 5
Repeated Games
Repeated prisoners dilemma, finite and infinite repeated games, limited-average versus future-discounted reward, folk theorems, stochastic games and learning.
WEEK 6
Bayesian Games
General definitions, ex ante/interim Bayesian Nash equilibrium.
WEEK 7
Coalitional Games
Transferable utility cooperative games, Shapley value, Core, applications.
WEEK 8
Final Exam
