Evolutionary Stability of Polymorphic Profiles in Asymmetric Games

被引：13

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.

引用

页码：1126 / 1142

页数：17

共 35 条

[11] Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space [J].

Cressman, Ross .

INTERNATIONAL JOURNAL OF GAME THEORY, 2009, 38 (02) :221-247

[12] Evolutionary and dynamic stability in continuous population games [J].

Eshel, I ;

Sansone, E .

JOURNAL OF MATHEMATICAL BIOLOGY, 2003, 46 (05) :445-459

[13] Asymptotic stability of strongly uninvadable sets [J].

Hingu, Dharini .

ANNALS OF OPERATIONS RESEARCH, 2020, 287 (02) :737-749

[14] On superiority and weak stability of population states in evolutionary games [J].

Hingu, Dharini ;

Rao, K. S. ;

Shaiju, A. J. .

ANNALS OF OPERATIONS RESEARCH, 2020, 287 (02) :751-760

[15] Evolutionary Stability of Polymorphic Population States in Continuous Games [J].

Hingu, Dharini ;

Rao, K. S. Mallikarjuna ;

Shaiju, A. J. .

DYNAMIC GAMES AND APPLICATIONS, 2018, 8 (01) :141-156

[16] EVOLUTIONARY STABLE STRATEGIES AND GAME DYNAMICS [J].

HOFBAUER, J ;

SCHUSTER, P ;

SIGMUND, K .

JOURNAL OF THEORETICAL BIOLOGY, 1979, 81 (03) :609-612

[17]

Maynard Smith J., 1982, pi

[18] Stability of the replicator dynamics for games in metric spaces [J].

Mendoza-Palacios, Saul ;

Hernández-Lerma, Onésimo .

Journal of Dynamics and Games, 2017, 4 (04) :319-333

[19] Evolutionary dynamics on measurable strategy spaces: Asymmetric games [J].

Mendoza-Palacios, Saul ;

Hernandez-Lerma, Onesimo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (11) :5709-5733

[20] Dynamically stable sets in infinite strategy spaces [J].

Norman, Thomas W. L. .

GAMES AND ECONOMIC BEHAVIOR, 2008, 62 (02) :610-627

← 1 2 3 4 →