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Stochastic Approximations and Differential Inclusions

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Author Info
Michel Benaïm (Université de Neûchatel -)
Josef Hofbauer (University College of London -)
Sylvain Sorin (LEEP - Laboratoire d'econometrie de l'école polytechnique - CNRS : UMR7657 - Polytechnique - X)

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Abstract

L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème de Benaim et Hirsch sur l'ensemble limite est étendu a ce cas. On étudie en détail les ensembles ICT et les attracteurs. On donne des applications a des questions de théorie des jeux, en particulier concernant le théorème d'approchabilite de Blackwell et la convergence de "fictitious play".

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File URL: http://hal.archives-ouvertes.fr/docs/00/24/29/90/PDF/2005-06-07-954.pdf
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Paper provided by HAL in its series Working Papers with number hal-00242990_v1.

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Date of creation: 2003
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Handle: RePEc:hal:wpaper:hal-00242990_v1

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Related research
Keywords: Approximation stochastique; Système dynamique multivalue;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics. [Downloadable!]
  2. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October. [Downloadable!] (restricted)
  3. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November. [Downloadable!] (restricted)
  4. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January. [Downloadable!] (restricted)
  5. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics. [Downloadable!]
    Other versions:
  2. Ziv Gorodeisky, 2008. "Stochastic Approximation of Discontinuous Dynamics," Discussion Paper Series dp496, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  3. Michel Benaim & Olivier Raimond, 2007. "Simulated Annealing, Vertex-Reinforced Random Walks and Learning in Games," Levine's Bibliography 122247000000001702, UCLA Department of Economics. [Downloadable!]
  4. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974_v1, HAL. [Downloadable!]
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