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Evolutionary Stability of Polymorphic Profiles in Asymmetric Games

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  • Aradhana Narang

    (Indian Institute of Technology Madras)

  • A. J. Shaiju

    (Indian Institute of Technology Madras)

Abstract

Mendoza-Palacios and Hernández-Lerma (J Differ Equ 259(11):5709–5733, 2015) have introduced the concept of a strong uninvadable profile for asymmetric games with continuous pure strategy space and proved that such a profile is Lyapunov stable for the associated replicator dynamics when the profile is monomorphic. In the present paper, we establish that a polymorphic strong uninvadable profile is necessarily monomorphic. Further, it is shown that strong unbeatability is enough to guarantee Lyapunov stability of polymorphic profiles. A stability theorem for sets of polymorphic profiles is also presented and is illustrated using examples.

Suggested Citation

  • Aradhana Narang & A. J. Shaiju, 2019. "Evolutionary Stability of Polymorphic Profiles in Asymmetric Games," Dynamic Games and Applications, Springer, vol. 9(4), pages 1126-1142, December.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:4:d:10.1007_s13235-019-00302-6
    DOI: 10.1007/s13235-019-00302-6
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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. 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.
    3. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    4. Selten, Reinhard, 1983. "Evolutionary stability in extensive two-person games," Mathematical Social Sciences, Elsevier, vol. 5(3), pages 269-363, September.
    5. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    6. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    7. Dharini Hingu & K. S. Mallikarjuna Rao & A. J. Shaiju, 2018. "Evolutionary Stability of Polymorphic Population States in Continuous Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 141-156, March.
    8. Matthijs Veelen & Peter Spreij, 2009. "Evolution in games with a continuous action space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 355-376, June.
    9. Norman, Thomas W.L., 2008. "Dynamically stable sets in infinite strategy spaces," Games and Economic Behavior, Elsevier, vol. 62(2), pages 610-627, March.
    10. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    11. Samuelson, Larry, 1991. "Limit evolutionarily stable strategies in two-player, normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 110-128, February.
    12. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 221-247, June.
    13. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
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