| Lecturer: | Robert Simon |
| Room: | B404 (4th floor, Columbia House) |
| Email: | R.S.Simon@lse.ac.uk |
| Office hours: | Please see the office hours page |
See the timetable for further details: http://www.lse.ac.uk/admin/timetables/confirmed/module_sessional/ma/29.htm
Homework announcements will be made at the end of each lecture on Friday.
Lecture notes will be provided and additional notes will be
distributed from time to time.
Useful accompanying texts are:
Robert J. Aumann and Michael B. Maschler, Repeated Games with Incomplete Information, MIT Press, 1995;
Leo Breiman, Probability, SIAM, 1992.
Mathematical Game Theory has progressed rapidly in the last three decades. The techniques and results of game theory are increasingly important to economic analysis. This course is designed as an introduction to two branches of rapid growth in mathematical game theory: the theory of asymmetric information in repeated games, and Bayesian games (for example card games). For the former, we investigate the conditions sufficient for there being an equilibrium and also how incomplete information influences the payoffs of the players.
We show how the dilemmas of moral hazard can be circumvented through stochastic signalling. For the latter we look how the information structure influences the behaviour in equilibrium, including a demonstration that the equilibria of card games can be extremely complex.
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.
Pre-requisites
Past exam papers are available from the Library website and may be provided on the Course Materials page at the discretion of the lecturer. We advise all students on this course to note the following: students are advised not to rely too heavily on past exam papers when revising for their exams, as they can only offer a limited indication of what might be covered in a future exam. For further information, please see the guidance here: http://www.maths.lse.ac.uk/examinations_in_mathematics.html#past_papers