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Time Average Replicator and Best Reply Dynamics

  • Josef Hofbauer

    ()

    (Department of Mathematics, University of Vienna - Universität Wien)

  • Sylvain Sorin

    ()

    (Equipe combinatoire et optimisation - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique, Department of Economics, Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique)

  • Yannick Viossat

    ()

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS - Centre National de la Recherche Scientifique - Université Paris IX - Paris Dauphine)

Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.

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Paper provided by HAL in its series Post-Print with number hal-00360767.

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Date of creation: May 2009
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Publication status: Published in Mathematics of Operations Research, INFORMS, 2009, 34 (2), pp.263-269. <10.1287/moor.1080.0359>
Handle: RePEc:hal:journl:hal-00360767
DOI: 10.1287/moor.1080.0359
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00360767
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  1. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  2. Yannick Viossat, 2007. "The replicator dynamics does not lead to correlated equilibria," Post-Print hal-00664293, HAL.
  3. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
  4. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  5. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
  6. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
  7. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
  8. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
  9. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
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