Mutation-selection equilibrium in games with multiple strategies
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 finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process and the frequency dependent Wright-Fisher process in well-mixed populations. We find surprisingly simple conditions that specify whether a strategy is more abundant than the average, 1/n, 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 by n games in the limit of weak selection.Keywords
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