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Evolutionary Stability of Polymorphic Profiles in Asymmetric Games

Aradhana Narang () and A. J. Shaiju
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Aradhana Narang: Indian Institute of Technology Madras
A. J. Shaiju: Indian Institute of Technology Madras

Dynamic Games and Applications, 2019, vol. 9, issue 4, No 12, 1126-1142

Abstract: 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; 91A22; 91A10; 34A34; 34G20; 34D20; 34D05; 92D25 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13235-019-00302-6

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Handle: RePEc:spr:dyngam:v:9:y:2019:i:4:d:10.1007_s13235-019-00302-6