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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

    (CECO - Laboratoire d'econometrie de l'école polytechnique - CNRS : UMR7657 - Polytechnique - X)

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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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00242990.

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

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00242990/en/
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Related research

Keywords: Approximation stochastique; Système dynamique multivalue;

References

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  1. 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.
  2. 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.
  3. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  4. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  5. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
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Citations

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Cited by:
  1. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics.
  2. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," ESE Discussion Papers 188, Edinburgh School of Economics, University of Edinburgh.
  3. Michel Benaim & Olivier Raimond, 2007. "Simulated Annealing, Vertex-Reinforced Random Walks and Learning in Games," Levine's Bibliography 122247000000001702, UCLA Department of Economics.
  4. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2011. "Refined best reply correspondence and dynamics," Working Papers 451, Bielefeld University, Center for Mathematical Economics.
  5. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer, vol. 40(4), pages 719-733, November.
  6. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2008. "Refined best-response correspondence and dynamics," Discussion Papers 0806, Exeter University, Department of Economics.
  7. Viossat, Yannick & Sorin, Sylvain & Hofbauer, Josef, 2009. "Time average replicator and best reply dynamics," Economics Papers from University Paris Dauphine 123456789/1014, Paris Dauphine University.
  8. repec:hal:wpaper:hal-00713871 is not listed on IDEAS
  9. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
  10. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  11. Ziv Gorodeisky, 2008. "Stochastic Approximation of Discontinuous Dynamics," Discussion Paper Series dp496, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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