Game Theory 2020


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 be 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 (see also the official course description).

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). 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).

LectureSlidesReadingsHomework
1 Tuesday, 4 February 2020 Introduction Essentials, Chapters 1 & 2 IPD Tournament (due: 7 February 2020)
2 Wednesday, 5 February 2020 Nash Equilibria Essentials, Chapters 1 & 2
Nash (1951)
Homework #1 (due: 11 February 2020)
3 Tuesday, 11 February 2020 Congestion Games Rosenthal (1973)
4 Wednesday, 12 February 2020 More Solution Concepts Essentials, Chapter 3 Homework #2 (due: 18 February 2020)
5 Tuesday, 18 February 2020 Zero-Sum Games Essentials, Chapter 3
Robinson (1951)
6 Wednesday, 19 February 2020 Bayesian Games Essentials, Chapter 7
Harsanyi (1967)
Homework #3 (due: 25 February 2020)
7 Tuesday, 24 February 2020 Extensive Games Essentials, Chapter 4
8 Wednesday, 26 February 2020 Imperfect-Information Games Essentials, Chapter 5
Kuhn (1953)
Homework #4 (due: 3 March 2020)
9 Tuesday, 3 March 2020 Auctions McAfee & McMillan (1987)
10 Wednesday, 4 March 2020 More Mechanism Design Nisan (2007) [Chapter 9] Homework #5 (due: 10 March 2020)
11 Tuesday, 10 March 2020 Stability in Coalitional Games Essentials, Chapter 8
12 Wednesday, 11 March 2020 Fairness in Coalitional Games Shapley (1953) Homework #6 (due: 20 March 2020)
13 Tuesday, 17 March 2020 Hedonic Games Bogomolnaia & Jackson (2002)
14 Wednesday, 18 March 2020 Matching Gale & Shapley (1962)