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.
Prerequisites: I will expect what sometimes is called mathematical maturity, meaning that you should have some experience with 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 classical papers.
|1||Tuesday, 5 February 2019||Introduction||Essentials, Chapters 1 & 2||IPD Tournament (due: 8 February 2019)|
|2||Thursday, 7 February 2019||Nash Equilibria||Essentials, Chapters 1 & 2
|Homework #1 (due: 12 February 2019)|
|3||Tuesday, 12 February 2019||Congestion Games||Rosenthal (1973)|
|4||Thursday, 14 February 2019||More Solution Concepts||Essentials, Chapter 3||Homework #2 (due: 19 February 2019)|
|5||Tuesday, 19 February 2019||Zero-Sum Games||Essentials, Chapter 3
|6||Thursday, 21 February 2019||Bayesian Games||Essentials, Chapter 7
|Homework #3 (due: 26 February 2019)|
|7||Tuesday, 26 February 2019||Extensive Games||Essentials, Chapter 4|
|8||Thursday, 28 February 2019||Imperfect-Information Games||Essentials, Chapter 5
|Homework #4 (due: 5 March 2019)|
|9||Tuesday, 5 March 2019||Auctions||McAfee & McMillan (1987)|
|10||Thursday, 7 March 2019||More Mechanism Design||Nisan (2007) [Chapter 9]||Homework #5 (due: 12 March 2019)|
|11||Tuesday, 12 March 2019||Stability in Coalitional Games||Essentials, Chapter 8|
|12||Thursday, 14 March 2019||Fairness in Coalitional Games||Shapley (1953)|
|13||Tuesday, 19 March 2019||Hedonic Games||Bogomolnaia & Jackson (2002)||Homework #6 (due: 25 March 2019)|
|14||Thursday, 21 March 2019||Matching||Gale & Shapley (1962)|