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Evolution and Correlated Equilibrium

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  • Lars Koch

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    Abstract

    We show that a set of outcomes outside the convex hull of Nash equilibria can be asymptotically stable with respect to convex monotonic evolutionary dynamics. Boundedly rational agents receive signals and condition the choice of strategies on the signals. A set of conditional strategies is asymptotically stable only if it represents a strict (correlated-)equilibrium set. There are correlated equilibria that cannot be represented by an asymptotically stable signal contingent strategy. For generic games it is shown that if signals are endogenous but no player has an incentive to manipulate the signal generating process and if the signal contingent strategy is asymptotically stable, then and only then, the outcome must be a strict Nash equilibrium.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse14_2008.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse14_2008.

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    Length: 30
    Date of creation: Jun 2008
    Date of revision:
    Handle: RePEc:bon:bonedp:bgse14_2008

    Contact details of provider:
    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: Dynamic Stability; Noncooperative Games; Correlated Equilibrium; Evolution;

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    1. George J. Mailath & Larry Samuelson & Avner Shaked, . "Correlated Equilibria and Local Interactions," Penn CARESS Working Papers 65b8832286a695ab9adcaad9f, Penn Economics Department.
    2. Lenzo, Justin & Sarver, Todd, 2006. "Correlated equilibrium in evolutionary models with subpopulations," Games and Economic Behavior, Elsevier, vol. 56(2), pages 271-284, August.
    3. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    4. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
    5. Yannick Viossat, 2004. "Replicator Dynamics and Correlated Equilibrium," Working Papers hal-00242953, HAL.
    6. Cripps, Martin, 1991. "Correlated equilibria and evolutionary stability," Journal of Economic Theory, Elsevier, vol. 55(2), pages 428-434, December.
    7. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
    8. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
    9. Viossat, Yannick, 2007. "The Replicator Dynamics Does not Lead to Correlated Equilibria," Economics Papers from University Paris Dauphine 123456789/1061, Paris Dauphine University.
    10. AUMANN, Robert J. & DREZE, Jacques H., 2005. "When all is said and done, how should you play and what should you expect ?," CORE Discussion Papers 2005021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    12. Swinkels, Jeroen M., 1992. "Evolution and strategic stability: From maynard smith to kohlberg and mertens," Journal of Economic Theory, Elsevier, vol. 57(2), pages 333-342, August.
    13. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
    14. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer, vol. 29(4), pages 571-595.
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