Dr Robert Simon COL 4.07

This course is available on the MSc in Applicable Mathematics. This course is available with permission as an outside option to students on other programmes where regulations permit.

Students should have taken MA402 (Game Theory I) or an equivalent course in game theory. A background in algebra, topology, or probability theory would be desirable. Some degree of mathematical maturity is expected.

The techniques and results of game theory are increasingly important to economic analysis. This course focuses on the problems of information incompleteness and information asymmetry. This is a relatively new but rapidly expanding area of game theory with connections to several areas of economic theory, for example conflict resolution, auctions, principal-agent problems, and the logic of knowledge. The course is divided into three parts, I Basic Results, II Repeated Games, III Bayesian Games. For the first part we cover the Min-max Theorem and Nash's Theorem of Equilibrium Existence, Extensive Form and Discounted Games. For the second part we cover Zero-sum Games with Vector Payoffs, The Value of the Zero-sum Repeated Game of Incomplete Information on One Side, Non-Zero-Sum Games with Incomplete Information on One Side, Incomplete Information on Two Sides, and Variations of Repeated Games of Incomplete Information. For the third part we cover Common Knowledge, Belief Spaces, Zero-Sum Bayesian Games, Locally Finite Games, Non-Zero-Sum Bayesian Games, Ergodic Theory and Ergodic Games, and Open Problems of Bayesian Games.  In order to understand the third part, some functional analysis and measure theory are included in the course.  This includes the difference between Lebesgue and conventional integration and the difference between strong and weak topologies.

20 hours of lectures and 9 hours of seminars in the LT. 2 hours of lectures and 1 hour of seminars in the ST.

Weekly exercises are set and marked.

A full set of lecture notes will be provided. Useful accompanying texts are Robert J. Aumann and Michael B. Maschler, Repeated Games with Incomplete Information, MIT Press, 1995; L. Breiman, Probability; K. Border, Fixed Point Theorems with Applications to Economics and Game Theory; R Myserson, Game Theory, Analysis of Conflict, Harvard University Press; D Fudenberg & J Tirole, Game Theory, MIT Press.

Exam (100%, duration: 2 hours) in the main exam period.