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Stochastic Approximations and Differential Inclusions

  • Michel Benaïm


    (Université de Neûchatel)

  • Josef Hofbauer

    (University College of London [London])

  • Sylvain Sorin

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

The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Bena\"{\i}m and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to Blackwell's approachability theorem and the convergence of fictitious play.

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

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Date of creation: 2003
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Handle: RePEc:hal:wpaper:hal-00242990
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  1. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  2. Itzhak Gilboa & Akihiko Matsui, 1991. "Social Stability and Equilibrium," Post-Print hal-00753235, HAL.
  3. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  4. 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.
  5. 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.
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