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Time Average Replicator and Best Reply Dynamics

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Author Info

  • Josef Hofbauer

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

  • Sylvain Sorin

    ()
    (EC - Equipe de Combinatoire - CNRS : UMR7090 - Université Pierre et Marie Curie - Paris VI, Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Yannick Viossat

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

Abstract

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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Bibliographic Info

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, Mathematics of Operations Research, 2009, 34, 2, 263-269
Handle: RePEc:hal:journl:hal-00360767

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00360767/en/
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Related research

Keywords: replicator dynamics; best reply dynamics; logit map; perturbed differential inclusion; internally chain transitive set; attractor;

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References

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  1. 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.
  2. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
  3. 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.
  4. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  5. 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.
  6. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
  7. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," Levine's Working Paper Archive 625018000000000226, David K. Levine.
  8. Viossat, Yannick, 2007. "The Replicator Dynamics Does not Lead to Correlated Equilibria," Economics Papers from University Paris Dauphine 123456789/1061, Paris Dauphine University.
  9. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
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Citations

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Cited by:
  1. Yannick Viossat & Andriy Zapechelnyuk, 2013. "No-regret Dynamics and Fictitious Play," Post-Print hal-00713871, HAL.
  2. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
  3. van Strien, Sebastian & Sparrow, Colin, 2011. "Fictitious play in 3x3 games: Chaos and dithering behaviour," Games and Economic Behavior, Elsevier, vol. 73(1), pages 262-286, September.
  4. Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
  5. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
  6. 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.
  7. repec:hal:wpaper:hal-00713871 is not listed on IDEAS
  8. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.

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