Evolutionary stability on graphs

JOURNAL OF THEORETICAL BIOLOGY

卷:251

Article

Ohtsuki, Hisashi¹  Nowak, Martin A.^1,2,3 

[1] Harvard Univ, Program Evolut Dynam, Cambridge, MA 02138 USA

[2] Harvard Univ, Dept Organ & Evolut Biol, Cambridge, MA 02138 USA

[3] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

关键词: evolutionary game theory;    evolutionary graph theory;    ESS;    structured population;    spatial games;   

DOI  :  10.1016/j.jtbi.2008.01.005

来源: Elsevier

【 摘 要 】

Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BID), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. (c) 2008 Elsevier Ltd. All rights reserved.

【 授权许可】

Free