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Evolutionary Dynamics May Eliminate All Strategies Used in 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
We show on a 4x4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard regularity conditions. For the replicator dynamics and the best-response dynamics, elimination of all strategies used in correlated equilibrium is shown to be robust to the addition of mixed strategies as new pure strategies.

Suggested Citation

  • Yannick Viossat, 2008. "Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria," Post-Print hal-00360756, HAL.
    • Handle: RePEc:hal:journl:hal-00360756
    DOI: 10.1016/j.mathsocsci.2007.12.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-00360756
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    References listed on IDEAS

    as
    1. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, vol. 59(2), pages 397-407, May.
    2. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    3. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287, World Scientific Publishing Co. Pte. Ltd..
    4. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    5. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    6. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "Regret-Based Continuous-Time Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 5, pages 99-124, World Scientific Publishing Co. Pte. Ltd..
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    9. Myerson, Roger B., 1994. "Communication, correlated equilibria and incentive compatibility," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 24, pages 827-847, Elsevier.
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    11. 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.
    12. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
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    15. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
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    24. Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
    25. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
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    Citations

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    Cited by:

    1. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    2. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
    3. 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.
    4. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    5. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    6. Yannick Viossat, 2011. "Deterministic monotone dynamics and dominated strategies," Working Papers hal-00636620, HAL.
    7. Yannick Viossat, 2014. "Game Dynamics and Nash Equilibria," Post-Print hal-00756096, HAL.

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    More about this item

    Keywords

    Correlated equilibrium; Evolutionary dynamics; Elimination; As-if rationality;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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