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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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