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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's (1983) (selten1983evolutionary) notion of limit ESS. We demonstrate 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, we present a novel definition that solves this issue and has appealing properties.

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  • Heller, Yuval, 2013. "Stability and trembles in extensive-form games," MPRA Paper 48160, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:48160
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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.
    2. Heller, Yuval, 2015. "Three steps ahead," Theoretical Economics, Econometric Society, vol. 10(1), January.
    3. Bhaskar V., 1996. "On the neutral stability of mixed strategies in asymmetric contests," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 56-57, February.
    4. Selten, Reinhard, 1983. "Evolutionary stability in extensive two-person games," Mathematical Social Sciences, Elsevier, vol. 5(3), pages 269-363, September.
    5. Bolton, Gary E., 1997. "The rationality of splitting equally," Journal of Economic Behavior & Organization, Elsevier, vol. 32(3), pages 365-381, March.
    6. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    7. Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
    8. Kim, Yong-Gwan, 1994. "Evolutionarily stable strategies in the repeated prisoner's dilemma," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 167-197, December.
    9. Bhaskar, V., 1998. "Noisy Communication and the Evolution of Cooperation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 110-131, September.
    10. Sandholm, William 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, 2020. "Observations on Cooperation," Papers 2006.15310, arXiv.org.
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, Open Access Journal, vol. 9(2), pages 1-67, May.
    4. Heller, Yuval & Mohlin, Erik, 2015. "Stable Observable Behavior," MPRA Paper 63013, University Library of Munich, Germany.

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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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