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Local stability under evolutionary game dynamics

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  • Sandholm, William H.

    () (Department of Economics, University of Wisconsin)

Abstract

We prove that any regular ESS is asymptotically stable under any impartial pairwise comparison dynamic, including the Smith dynamic; under any separable excess payoff dynamic, including the BNN dynamic; and under the best response dynamic. Combined with existing results for imitative dynamics, our analysis validates the use of ESS as a blanket sufficient condition for local stability under evolutionary game dynamics.

Suggested Citation

  • Sandholm, William H., 2010. "Local stability under evolutionary game dynamics," Theoretical Economics, Econometric Society, vol. 5(1), January.
  • Handle: RePEc:the:publsh:505
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    Citations

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    Cited by:

    1. Heller, Yuval, 2014. "Stability and trembles in extensive-form games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 132-136.
    2. Nesrine Ben Khalifa & Rachid El-Azouzi & Yezekael Hayel & Issam Mabrouki, 2017. "Evolutionary Games in Interacting Communities," Dynamic Games and Applications, Springer, vol. 7(2), pages 131-156, June.
    3. Heller, Yuval & Mohlin, Erik, 2015. "Stable Observable Behavior," MPRA Paper 63013, University Library of Munich, Germany.
    4. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    5. Sirghi Nicoleta, 2013. "The Theory Of The Firm And The Evolutionary Games," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 533-542, July.
    6. Heller, Yuval & Mohlin, Erik, 2014. "Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli," MPRA Paper 58255, University Library of Munich, Germany.
    7. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.
    8. Heller, Yuval, 2013. "Language, Meaning, and Games: Comment," MPRA Paper 49375, University Library of Munich, Germany.

    More about this item

    Keywords

    Evolutionary game dynamics; ESS;

    JEL classification:

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

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