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Online Course

Game Theory by Matthew O. Jackson, Kevin Leyton-Brown, Yoav Shoham

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. The course provided 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. Variety of examples including classic games and a few applications were also studied.

The Program Required

  1. Comfort in Mathematical thinking and rigorous arguments
  2. Familiarity with basic probability theory like conditional probability and
  3. some very light calculus would be helpful.

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 :
Passed the final exam with 93 %

 

Instructors

  1. Matthew O. Jackson, Professor of Economics, Stanford University
  2. Kevin Leyton-Brown, Professor of Computer Science, The University of British Columbia
  3. Yoav Shoham, Professor of Computer Science, Stanford University
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