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.

15 pages, 6 figures, Journal of Theoretical Biology (2011)

References in corpus (6)

• Phase transitions and volunteering in spatial public goods games
• Human strategy updating in evolutionary games
• Evolutionary games in the multiverse
• Evolutionary game dynamics in phenotype space
• Mutation-selection equilibrium in games with multiple strategies
• Strategy abundance in 2x2 games for arbitrary mutation rates

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• Stationary frequencies and mixing times for neutral drift processes with spatial structure
• Stationary Stability for Evolutionary Dynamics in Finite Populations