Game Theory 2024

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).

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)