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Asymptotic stability of strongly uninvadable sets

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  • Dharini Hingu

    (Indian Institute of Technology, Madras)

Abstract

In this article, we study in detail asymptotic stability of strongly uninvadable faces generated by finite Borel sets in a continuous strategy space of an evolutionary game. It is proved that such a face is an asymptotically stable set for the associated replicator dynamics. This result is illustrated using examples.

Suggested Citation

  • Dharini Hingu, 2020. "Asymptotic stability of strongly uninvadable sets," Annals of Operations Research, Springer, vol. 287(2), pages 737-749, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-017-2695-9
    DOI: 10.1007/s10479-017-2695-9
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    References listed on IDEAS

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    1. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
    2. Norman, Thomas W.L., 2008. "Dynamically stable sets in infinite strategy spaces," Games and Economic Behavior, Elsevier, vol. 62(2), pages 610-627, March.
    3. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    4. Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
    5. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.
    6. Lahkar, Ratul & Riedel, Frank, 2015. "The logit dynamic for games with continuous strategy sets," Games and Economic Behavior, Elsevier, vol. 91(C), pages 268-282.
    7. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
    8. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
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