Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Recitations: 1 session / week, 1 hour / session
This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from engineered/networked systems (including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, multi-agent systems, pricing and investment decisions in the Internet), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments.
The course is geared towards engineering, operations research, or computer science students who need to use game theory in their research. The course is also aimed at covering recent advances and open research areas in game theory.
A course in probability (6.041 or equivalent) and mathematical maturity. A course in analysis (18.100 or equivalent), and a course in optimization (6.251, 6.255 or equivalent) would be helpful, but is not required.
There will be about 6 homework sets. Together with the TA's feedback, they will count for 20% of the final grade. Homework solutions will be handed out on the day that the homework is due. Late homework will be heavily discounted.
You may interact with fellow students when preparing your homework solutions. However, at the end, you must write up solutions on your own. Duplicating a solution that someone else has written or providing solutions to be copied is not acceptable. If you do collaborate on homework, you must cite, in your written solution, your collaborators.
There will be a term project, which accounts for 50% of the final grade. The project involves choosing a topic of your interest in game theory-mechanism design area, picking 2-3 major papers in the area, and understanding, critically evaluating, and possibly extending the research. You will need to write a project report and prepare a presentation in the final two weeks of classes.
We provide a reading list, which contains potential topics and major recent papers that are relevant. The reading list will be expanded as we go along. This is aimed at giving you a starting point. You are more than welcome to suggest other research topics and relevant papers.
- Introduction to game theory (1 lecture): Games and solutions. Game theory and mechanism design. Examples from networks.
- Strategic form games (4-5 lectures): Matrix and continuous games. Iterated strict dominance. Rationalizability. Nash Equilibrium; existence and uniqueness. Mixed and correlated equilibrium. Supermodular games. Potential/congestion games.
- Learning, evolution, and computation (3 lectures): Myopic learning; fictitious play. Bayesian learning. Evolutionarily stable strategies. Computation of Nash equilibrium in matrix games.
- Extensive games with perfect information (2 lectures): Backward induction and subgame perfect equilibrium. Applications in bargaining games. Nash bargaining solution.
- Repeated games (3 Lectures): Infinitely/finitely repeated games. Trigger strategies. Folk theorems. Imperfect monitoring and perfect public equilibrium.
- Games with incomplete information (2-3 lectures): Mixed and behavioral strategies. Bayesian Nash equilibrium. Applications in auctions. Different auction formats. Revenue and efficiency properties of different auctions.
- Mechanism design (3-4 lectures): Optimal auctions; revenue-equivalence theorem. Social choice viewpoint. Impossibility results. Revelation principle. Incentive compatibility. VCG mechanisms. Mechanisms in networking, decentralized mechanisms.
- Network effects and games over networks (2-3 lectures): Positive and negative externalities. Utility-based resource allocation. Selfish routing. Wardrop and Nash equilibrium. Partially optimal routing. Network pricing. Competition and implications on network performance. Strategic network formation. Price of anarchy.