The Replicator Equation on Graphs The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Ohtsuki Hisashi, Martin A. Nowak. 2006. The replicator equation on graphs. Journal of Theoretical Biology 243(1): 86-97. Published Version doi:10.1016/j.jtbi.2006.06.004 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:4063696 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA The Replicator Equation on Graphs Hisashi Ohtsuki1;2;¤ & Martin A. Nowak2;3 1Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan 2Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA 3Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge MA 02138, USA ¤The author to whom correspondence should be addressed. (
[email protected]) tel: +81-92-642-2638 fax: +81-92-642-2645 Abstract : We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payo® from interaction with all their immediate neighbors. We consider three di®erent update rules, called `birth-death', `death-birth' and `imitation'. A fourth update rule, `pairwise comparison', is shown to be equivalent to birth-death updating in our model.