title: Strategy abundance in evolutionary many-player games with multiple strategies.
abstract: Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several parties determines evolutionary success. Rather than pair-wise interactions, in this case we must take into account the interactions between many players, which are inherently more complicated than the usual two-player games, but can still yield simple results. In this manuscript we derive the composition of a many-player multiple strategy system in the mutation-selection equilibrium. This results in a simple expression which can be obtained by recursions using coalescence theory. This approach can be modified to suit a variety of contexts, e.g. to find the equilibrium frequencies of a finite number of alleles in a polymorphism or that of different strategies in a social dilemma in a cultural context.
authors.affiliation: Research Group for Evolutionary Theory, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany. gokhale@evolbio.mpg.de
authors.forename: Chaitanya S
authors.initials: CS
authors.lastname: Gokhale
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D008957:Models, Genetic; D009154:Mutation; D012641:Selection, Genetic