Overview
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.
Requirements/Prerequisites
You must be comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; 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.
Course Structure
The course consists of the following materials:
Suggested Readings
The following background readings provide more detailed coverage of the course material:
Grading
Your grade in the course will be based solely on the problem sets (70 percent of your grade) and the final exam (30 percent of your grade).
You are free to follow the course without completing the problem sets or final, but then will not receive a certificate of completion.
Questions
If you have any questions, please do not contact the professors directly, as with over one hundred thousand of students it is infeasible for us to respond. The course includes on-line Q&A forums where students can post and respond to questions. This will go live in parallel with the first lectures. Students rank questions and answers, so that the most important questions and the best answers bubble to the top. TAs and the professors will periodically monitor these forums, so that important questions not answered by other students will be addressed.
Course Topics
Week 1: Introduction
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 Available