Stochastic Approximations and Differential Inclusions; Part II: Applications

HAL Id: hal-00242974

https://hal.archives-ouvertes.fr/hal-00242974

Preprint submitted on 6 Feb 2008

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Stochastic Approximations and Differential Inclusions;

Part II: Applications

Michel Benaïm, Josef Hofbauer, Sylvain Sorin

To cite this version:

Michel Benaïm, Josef Hofbauer, Sylvain Sorin. Stochastic Approximations and Differential Inclusions;

Part II: Applications. 2005. �hal-00242974�

Stochastic Approximations and Differential Inclusions; Part II: Applications

Michel Benaïm Josef Hofbauer Sylvain Sorin

May 2005

Cahier n°

ECOLE POLYTECHNIQUE

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

LABORATOIRE D'ECONOMETRIE

1rue Descartes F-75005 Paris (33) 1 55558215 http://ceco.polytechnique.fr/

mailto:labecox@poly.polytechnique.fr

Stochastic Approximations and Differential Inclusions; Part II:

Applications

Michel Benaïm Josef Hofbauer Sylvain Sorin

May 2005 Cahier n° 2005-011

Résumé: Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures adapatatives utilisées en théorie des jeux en particulier: approchabilité classique et généralisées, procédures de non regret (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine)

Abstract: We apply the theoretical results on ``stochastic approximations and differential inclusions'' developed in Benaïm Hofbauer and Sorin (2003) to several adaptive processes used in game theory including: classical and generalized approachability, no-regrets procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine)

Mots clés : Approximation stochastique, inclusions differentielles, systemes dynamiques multivalues, approchabilite, non regret,

Key Words : Stochastic approximation, differential inclusions, set valued dynamical systems, approachability, consistency, smooth fictitious play

Classification AMS: 91A05, 37C

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