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Stability and trembles in extensive-form games

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  • Heller, Yuval

Abstract

A leading solution concept in the evolutionary study of extensive-form games is Selten (1983) notion of limit ESS. This note demonstrates that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, I present a novel definition that solves this issue and has appealing properties.

Suggested Citation

  • Heller, Yuval, 2014. "Stability and trembles in extensive-form games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 132-136.
    • Handle: RePEc:eee:gamebe:v:84:y:2014:i:c:p:132-136
    DOI: 10.1016/j.geb.2013.12.011
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    References listed on IDEAS

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    1. Bomze Immanuel M. & Weibull Jorgen W., 1995. "Does Neutral Stability Imply Lyapunov Stability?," Games and Economic Behavior, Elsevier, vol. 11(2), pages 173-192, November.
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    9. Bhaskar, V., 1998. "Noisy Communication and the Evolution of Cooperation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 110-131, September.
    10. , H., 2010. "Local stability under evolutionary game dynamics," Theoretical Economics, Econometric Society, vol. 5(1), January.
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    Cited by:

    1. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    2. Yuval Heller & Erik Mohlin, 2018. "Observations on Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2253-2282.
    3. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    4. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    5. Heller, Yuval & Mohlin, Erik, 2015. "Stable Observable Behavior," MPRA Paper 63013, University Library of Munich, Germany.
    6. Heller, Yuval & Kuzmics, Christoph, 2020. "Communication, Renegotiation and Coordination with Private Values (Extended Version)," MPRA Paper 102926, University Library of Munich, Germany, revised 26 Jul 2021.

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    More about this item

    Keywords

    Limit ESS; Evolutionary stability; Extensive-form games;
    All these keywords.

    JEL classification:

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

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