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Evolution and Correlated Equilibrium

  • Lars Koch

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    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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    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

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    1. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    2. J. Hofbauer & J. Weibull, 2010. "Evolutionary Selection against dominated strategies," Levine's Working Paper Archive 444, David K. Levine.
    3. George J. Mailath & Larry Samuelson & Avner Shaked, . ""Correlated Equilibria and Local Interactions''," CARESS Working Papres 95-16, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    4. 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.
    5. R. J. Aumann & J. H. Dreze, 2005. "When All is Said and Done, How Should You Play and What Should You Expect?," Discussion Paper Series dp387, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer, vol. 29(4), pages 571-595.
    7. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, vol. 59(2), pages 397-407, May.
    8. 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.
    9. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    10. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
    11. Lenzo, Justin & Sarver, Todd, 2006. "Correlated equilibrium in evolutionary models with subpopulations," Games and Economic Behavior, Elsevier, vol. 56(2), pages 271-284, August.
    12. Yannick Viossat, 2004. "Replicator Dynamics and Correlated Equilibrium," Working Papers hal-00242953, HAL.
    13. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
    14. Cripps, Martin, 1991. "Correlated equilibria and evolutionary stability," Journal of Economic Theory, Elsevier, vol. 55(2), pages 428-434, December.
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