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.
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.
Who is this class for: This course is aimed at students, researchers, and practitioners who wish to understand more about strategic interactions. You must be comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; but you should be familiar with basic probability theory (for example, you should know what a conditional probability is), and some very light calculus would be helpful.
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
Graded: Problem Set 1
Week 2: Mixed-Strategy Nash Equilibrium
pure and mixed strategy Nash equilibria
Graded: Problem Set 2
Week 3: Alternate Solution Concepts
Iterative removal of strictly dominated strategies, minimax strategies and the minimax theorem for zero-sum game, correlated equilibria
Graded: Problem Set 3
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.
Graded: Problem Set 4
Week 5: Repeated Games
Repeated prisoners dilemma, finite and infinite repeated games, limited-average versus future-discounted reward, folk theorems, stochastic games and learning.
Graded: Problem Set 5
Week 6: Bayesian Games
General definitions, ex ante/interim Bayesian Nash equilibrium.
Graded: Problem Set 6
Week 7: Coalitional Games
Transferable utility cooperative games, Shapley value, Core, applications.
Graded: Problem Set 7
Week 8: Final Exam
The description goes here
Graded: Final Exam
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