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).
|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
|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
|6||Wednesday, 19 February 2020||Bayesian Games||Essentials, Chapter 7
|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
|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)|