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Course Description

Learning in games

Bernard Walliser

Ecole Nationale des Ponts et Chaussées

Ecole des Hautes Etudes en Sciences Sociales

walliser@mail.enpc.fr

http://ceco.polytechnique.fr/CHERCHEURS/WALLISER/

In game theory, an equilibrium notion was first defined from the modeller’s point of view: an equilibrium state appears as a fixed point without making explicit the process by which it is reached by the players. Later, the ‘eductive’ justifications of equilibria tried to infer the equilibrium notions from the sole reasoning of hyper-rational players. More recently, the ‘evolutionist’ justifications of equilibria sustain an equilibrium notion as the result of a dynamic process followed by boundedly rational players. The dynamic process was first of a biological nature (the replicator dynamics), but is more and more grounded on various learning mechanisms.

The course describes the main learning processes studied in (static or dynamic) game theory and the collective results they achieve.

Lecture 1. A taxonomy of learning processes in game theory

Required readings:

J. Lesourne, A. Orléan, B. Walliser (2005): Evolutionary microeconomics, Springer, to appear, chapter 3: Game Situations.

Fudenberg, D.-Levine, D. (1998): The theory of learning in games, MIT Press, chapter 1 :introduction.

Lecture 2. Belief-based learning in games

Required readings:

Fudenberg, D.-Levine, D. (1998): The theory of learning in games, MIT Press, chapters 2,3,4 :fictitious play Young, P. (1993) 

The evolution of conventions, Econometrica, 61 :57-84.

Lecture 3. Reinforcement learning in normal form games

Required readings:

J.-F.Laslier-R., Topol, B. Walliser (2001): A behavioral learning process in games, Games and Economic Behavior, 37 Weibull,J. (1995) Evolutionary game theory, MIT Press, introduction.

Lecture 4. Reinforcement learning in extensive form games

Required readings:

Laslier J.F. & Walliser, B. A Reinforcement Learning Process in Extensive Form Games. International Journal of Game Theory, 33:219-227

Sutton, R.S., Barto, A.G. (1998): Reinforcement learning, MIT Press, part 1:the problem

Small Group Sessions

Small groups will be devoted to an extended discussion of the main lectures and to the examination of experiments especially devoted to learning in games.

Assignments

Students who take the course for credit have to write a short paper (5-6 pages) proposing an original learning process (which can be applied in games) and indicating how it could be studied in a theoretical way (asymptotic convergence) and in an experimental way (type of application).

Bernard Walliser

Bernard Walliser has an engineering background from Ecole Polytechnique and Ecole Nationale des Ponts et Chaussées, in Paris. He moved to economics and received his PHD in Economics at University Paris 1. Recently, he chaired an interdisciplinary research group on ‘cognitive economics’ (2000-2004). He belongs now to the research laboratory ‘Paris-Jourdan Sciences Economiques’. His research interests are in cognitive economics (influence of agents’ beliefs and reasoning on economic phenomena) and economic methodology (especially models). He is a professor at Ecole Nationale des Ponts et Chaussées and research director at Ecole des Hautes Etudes en Sciences Sociales.