Evolutionary Stability of Polymorphic Profiles in Asymmetric Games

被引：10
作者：
Narang, Aradhana [1 ]
Shaiju, A. J. [1 ]
机构：
[1] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India
来源：
DYNAMIC GAMES AND APPLICATIONS | 2019年 / 9卷 / 04期
关键词：
Asymmetric evolutionary games; Replicator dynamics; Games with continuous strategy space; Uninvadable profiles and sets; Lyapunov and asymptotic stability; STABLE STRATEGIES; DYNAMICS; SELECTION; STATES; SETS;
D O I：
10.1007/s13235-019-00302-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Mendoza-Palacios and Hernandez-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.
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页码：1126 / 1142
页数：17
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