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On the dynamic foundation of evolutionary stability in continuous models

Author

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  • Oechssler, Jörg
  • Riedel, Frank

Abstract

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games.

Suggested Citation

  • Oechssler, Jörg & Riedel, Frank, 2000. "On the dynamic foundation of evolutionary stability in continuous models," SFB 373 Discussion Papers 2000,73, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200073
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    References listed on IDEAS

    as
    1. Bester, Helmut & Guth, Werner, 1998. "Is altruism evolutionarily stable?," Journal of Economic Behavior & Organization, Elsevier, vol. 34(2), pages 193-209, February.
    2. J. Maynard Smith, 2010. "The Theory of Games and Evolution of Animal Conflicts," Levine's Working Paper Archive 448, David K. Levine.
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    More about this item

    Keywords

    replicator dynamics; evolutionary stability; ESS; CSS;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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