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The replicator dynamics does not lead to correlated equilibria

Author

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  • Yannick Viossat

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

It is shown that, under the replicator dynamics, all strategies played in correlated equilibrium may be eliminated, so that only strategies with zero marginal probability in all correlated equilibria survive. This occurs in particular in a family of 4×4 games built by adding a strategy to a Rock-Paper-Scissors game.

Suggested Citation

  • Yannick Viossat, 2007. "The replicator dynamics does not lead to correlated equilibria," Post-Print hal-00664293, HAL.
    • Handle: RePEc:hal:journl:hal-00664293
    DOI: 10.1016/j.geb.2006.09.001
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    Citations

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    Cited by:

    1. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best-Reply Dynamics," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 263-269, May.
    2. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    3. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    4. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    5. Yannick Viossat, 2011. "Deterministic monotone dynamics and dominated strategies," Working Papers hal-00636620, HAL.
    6. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
    7. Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
    8. Yannick Viossat, 2014. "Game Dynamics and Nash Equilibria," Post-Print hal-00756096, HAL.
    9. Koch, Lars P., 2008. "Evolution and Correlated Equilibrium," Bonn Econ Discussion Papers 14/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
    10. Galit Askenazi-Golan & Domenico Mergoni Cecchelli & Edward Plumb, 2024. "Reinforcement Learning, Collusion, and the Folk Theorem," Papers 2411.12725, arXiv.org.
    11. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.

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