Mutation-selection equilibrium in games with multiple strategies

TL;DR

This paper analyzes the mutation-selection equilibrium in multi-strategy evolutionary games, providing simple conditions to determine strategy abundance across different mutation rates in large populations.

Contribution

It introduces a comprehensive analysis of stochastic evolutionary dynamics in multi-strategy games, deriving conditions for strategy abundance under varying mutation rates.

Findings

Conditions for strategy abundance depend on mutation rate

Results apply to Moran, Wright-Fisher, and Pairwise Comparison processes

Complete characterization of n-strategy games under weak selection

Abstract

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n*n games in the limit of weak selection.