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Evolutionary Stability of Polymorphic Profiles in Asymmetric Games

  • Aradhana NarangEmail author
  • A. J. Shaiju
Article

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.

Keywords

Asymmetric evolutionary games Replicator dynamics Games with continuous strategy space Uninvadable profiles and sets Lyapunov and asymptotic stability 

Mathematics Subject Classification

91A22 91A10 34A34 34G20 34D20 34D05 92D25 

Notes

Acknowledgements

The authors would like to thank two anonymous reviewers for valuable suggestions to improve the manuscript.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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