F10.05: Game Theory

Dries Vermeulen (UM)

Aims/Description

This course will be based on the book Game Theory, A Multi-Leveled Approach by Hans Peters (Springer, 2008; ISBN 978-3-540-69290-4). It aims at providing students with a broad basis in game theory and treats most of the standard topics in a thorough way. These topics include: zero- and non-zerosum games, games in extensive form, games with incomplete information, refinements of equilibrium concepts, evolutionary games and repeated games, bargaining, cooperative games with transferable utility and solution concepts.

As in previous years, we may deviate from the program below if there are special requests by students.

Credits

6 ECTS

Time Schedule

Blocks 1 & 2
10, 17, 24 September and 1, 8 October 2010
29 October and 5, 12, 19, 26 November 2010
There will be 10 weeks of 2 hour lectures in total.

Prerequisites

A basic knowledge of mathematics/calculus is sufficient, but some experience with mathematical reasoning is indispensable. Although the course starts from scratch and can be taken without prior knowledge of game theory, it is very helpful if students have some acquaintance with the field, preferably on the level of standard micro-economic texts such as Mas-Colell, Green, and Whinston, or Jehle and Reny.

Examination

The evaluation will be based on home assignments (50%) and a written exam (50%) right after the end of the course.

Course Outline

Topic 1. Introduction, Examples, Cooperative vs. non-cooperative models, zero-sum games (chaps. 1,2,12)

Topic 2. Zero-sum games (chaps. 2,12)

Topic 3. Games in strategic form, Nash equilibrium, refinements (chaps. 3,13)

Topic 4. Games in strategic form, Nash equilibrium, refinements (chaps. 3,13)

Topic 5. Games in extensive form (chaps. 4,5,14)

Topic 6. Games in extensive form (chaps. 4,5,14)

Topic 7. Evolutionary games (chaps. 8, 15)

Topic 8. Evolutionary games (chaps. 8, 15), repeated games (chap. 7)

Topic 9. Cooperative games and bargaining (chaps. 9,16,17,19,21)

Topic 11. Cooperative games and bargaining (chaps. 9,16,17,19,21)

Topic 12. Cooperative games and bargaining (chaps. 9,16,17,19,21)

Literature

For the first part there is a textbook available. For the second part a reader will be composed.

Note: For the first meeting (September 11) students may prepare by starting to read the textbook, in particular Chapters 1 and 2.

Additional topics

Auction design: revenue equivalence, Green-Laffont, VCG mechanism.
Congestion games: Monderer-Shapley potential games, Tardos-Roughgarden.
Topics from learning theories (H. P. Young and others).