Strategy abundance in evolutionary many-player games with multiple strategies

TL;DR

This paper derives a simple recursive expression for the composition of many-player, multiple-strategy systems at mutation-selection equilibrium, extending evolutionary game theory to complex multi-party interactions.

Contribution

It introduces a recursive method based on coalescence theory to analyze equilibrium compositions in multi-player, multi-strategy evolutionary systems.

Findings

Derived a simple recursive expression for equilibrium composition.

Applicable to biological and social systems with multiple strategies.

Method adaptable to various contexts like allelic polymorphisms and social dilemmas.

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.