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, 7 February 2017||Introduction||Essentials, Chapters 1 & 2|
|2||Thursday, 9 February 2017||Nash Equilibria||Essentials, Chapters 1 & 2
|Homework #1 (due: 15 February 2017)|
|3||Tuesday, 14 February 2017||Congestion Games||Rosenthal (1973)|
|4||Thursday, 16 February 2017||More Solution Concepts||Essentials, Chapter 3||Homework #2 (due: 22 February 2017)|
|5||Tuesday, 21 February 2017||Zero-Sum Games||Essentials, Chapter 3
|6||Thursday, 23 February 2017||Bayesian Games||Essentials, Chapter 7
|Homework #3 (due: 1 March 2017)|
|7||Tuesday, 28 February 2017||Extensive Games||Essentials, Chapter 4|
|8||Thursday, 2 March 2017||Imperfect-Information Games||Essentials, Chapter 5
|Homework #4 (due: 8 March 2017)|
|9||Tuesday, 7 March 2017||Auctions||McAfee & McMillan (1987)|
|10||Thursday, 9 March 2017||More Mechanism Design||Nisan (2007) [Chapter 9]||Homework #5 (due: 15 March 2017)|
|11||Tuesday, 14 March 2017||Stability in Coalitional Games||Essentials, Chapter 8
|12||Thursday, 16 March 2017||Fairness in Coalitional Games||Shapley (1953)|
|13||Tuesday, 21 March 2017||Hedonic Games||Bogomolnaia & Jackson (2002)||Homework #6 (due: 29 March 2017)|
|14||Thursday, 23 March 2017||Matching||Gale & Shapley (1962)|