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Algorithme de fictitious play et cycles

Published online by Cambridge University Press:  17 August 2016

Richard Baron ,
Jacques Durieu  and
Philippe Solal
Richard Baron
Affiliation:
Université de Saint-Étienne
Jacques Durieu
Affiliation:
Université de Saint-Étienne
Philippe Solal
Affiliation:
Université de Saint-Étienne
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Résumé

Fudenberg et Kreps (1993), Young (1993), et Sela et Herreiner (1999) ont souligné l'insuffisance du critère de convergence en croyances du processus de Fictitious Play dans un cadre d'apprentissage des équilibres de Nash. En conséquence, nous choisissons d'étudier la convergence en straté gies du processus de Fictitious Play dans des jeux de coordination 2x2. Notre propos est de montrer que la convergence en stratégies de ce processus dépend de manière cruciale de la forme des croyances initiales des joueurs. Premièrement, lorsque les croyances initiales forment un profil de stratégies pures, nous établissons que la convergence en stratégies est certaine pour n'importe quelle catégorie de jeux de coordination. Deuxièmement, si les croyances initiales forment un profil de stratégies mixtes, le processus de Fictitious Play converge pour certaines catégories de jeux de coordination. Ainsi, nous caractérisons complètement les conditions assurant la convergence en stratégies.

Summary

Summary

Fudenberg and Kreps (1993), Young (1993), and Sela and Herreiner (1999) suggest that the convergence in beliefs of the Fictitious Play process is not an appopriate notion of what it means to learn an equilibrium. Consequently, we consider the convergence in strategies in two Fictitious Player coordination games. We distinguish two cases according to the initial beliefs of the players. First, if the initial beliefs of the players consist of a pair of pure strategies, we show that the Fictitious Play process converges in strategies in every coordination game. Second, if the initial beliefs of the players consist of a pair of completely mixed strategies, we show that the Fictitious Play process converges in strategies in some categories of coordination games. In this way, we give a complete characterization of the conditions which ensure the convergence in strategies of the Fictitious Play process.

Keywords

ApprentissageCroyancesEquilibre de NashFictitious PlayC72D83BeliefsFictitious PlayLearningNash equilibriumC72D83
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 69 , Issue 2 , 2003 , pp. 167 - 180
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 2003 

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Footnotes

*

Les auteurs remercient Fabien Feschet pour sa suggestion concernant la preuve de la proposition 1 ainsi qu'un rapporteur anonyme pour ses commentaires.

Universitéde Saint-Étienne. CREUSET. 6, rue basse des rives. 42100 Saint-Étienne, France, e-mail: [email protected]. e-mail: [email protected]. e-mail: [email protected].

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