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Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Bena¨ ım, Josef Hofbauer, Sylvain Sorin To cite this version: Michel Bena¨ ım, Josef Hofbauer, Sylvain Sorin. Stochastic Approximations and Differential Inclusions; Part II: Applications. CECO-886. 2005. <hal-00242974> HAL Id: hal-00242974 https://hal.archives-ouvertes.fr/hal-00242974 Submitted on 6 Feb 2008 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es.

Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

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Page 1: Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

Stochastic Approximations and Differential Inclusions;

Part II: Applications

Michel Benaım, Josef Hofbauer, Sylvain Sorin

To cite this version:

Michel Benaım, Josef Hofbauer, Sylvain Sorin. Stochastic Approximations and DifferentialInclusions; Part II: Applications. CECO-886. 2005. <hal-00242974>

HAL Id: hal-00242974

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

Submitted on 6 Feb 2008

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

Page 2: Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

Stochastic Approximations and Differential Inclusions; Part

II: Applications

Michel Benaïm Josef Hofbauer Sylvain Sorin

May 2005

Cahier n° 2005-011

ECOLE POLYTECHNIQUE CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

LABORATOIRE D'ECONOMETRIE 1rue Descartes F-75005 Paris

(33) 1 55558215 http://ceco.polytechnique.fr/

mailto:[email protected]

Page 3: Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

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

Page 4: Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

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Page 6: Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

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Page 10: Stochastic Approximations and Di erential Inclusions; Part II: … · 2017-01-29 · Stochastic Approximations and Differential Inclusions; Part II: Applications Michel Benaïm Josef

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