Game theory is the study of mathematical models to analyse strategic interactions between rational agents. Game-theoretical analysis plays a role in a wide variety of disciplines, ranging from Economics and Political Science to Psychology, Biology, Linguistics, Artificial Intelligence, Computer Science, Logic, and Philosophy. This course will provide an introduction to this fascinating field. The focus will be on the mathematical properties of games. We will cover both cooperative and noncooperative games, and also briefly introduce the basic notions of mechanism design.
Prerequisites: I will expect what sometimes is called mathematical maturity, meaning that you should have some prior experience with working out and writing up mathematical proofs.
Literature: The main reference for this course is the book Essentials of Game Theory by Kevin Leyton-Brown and Yoav Shoham (Morgan & Claypool Publishers, 2008), electronic copies of which are available from the UvA University Library. I will also recommend additional readings, most of them classic papers.
Practicalities: Here is a template for typesetting 2x2 normal-form games in LaTeX (PDF).
| Week | Lectures | Readings | Exercises |
|---|---|---|---|
| 1 | Introduction / Iterated Prisoner's Dilemma Tournament | Essentials (Chapters 1 & 2) | Tutorial #1 |
| Nash Equilibria | Essentials (Chapters 1 & 2) and Nash (1951) | Homework #1 | |
| 2 | Congestion Games | Rosenthal (1973) | Tutorial #2 |
| More Solution Concepts | Essentials (Chapter 3) | Homework #2 | |
| 3 | Zero-Sum Games | Essentials (Chapter 3) and Robinson (1951) | Tutorial #3 |
| Bayesian Games | Essentials (Chapter 7) and Harsanyi (1967) | Homework #3 | |
| 4 | Extensive Games | Essentials (Chapter 4) | Tutorial #4 |
| Imperfect-Information Games | Essentials (Chapter 5) and Kuhn (1953) | Homework #4 | |
| 5 | Auctions | McAfee & McMillan (1987) | Tutorial #5 (self-study) |
| Mechanism Design | Nisan (2007) (Chapter 9) | Homework #5 | |
| 6 | Stability in Coalitional Games | Essentials (Chapter 8) | Tutorial #6 |
| Fairness in Coalitional Games | Shapley (1953) | Homework #6 | |
| 7 | Hedonic Games | Bogomolnaia & Jackson (2002) | Tutorial #7 |
| Matching Markets | Gale & Shapley (1962) |