title: 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 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 nxn games in the limit of weak selection.
authors.affiliation: Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA. tibor_antal@harvard.edu
authors.forename: Tibor
authors.initials: T
authors.lastname: Antal
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
authors.forename: Hisashi
authors.initials: H
authors.lastname: Ohtsuki
authors.forename: Corina E
authors.initials: CE
authors.lastname: Tarnita
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D000818:Animals; D003198:Computer Simulation; D005716:Game Theory; D008957:Models, Genetic; D009154:Mutation; D011157:Population Dynamics; D012641:Selection, Genetic; D013269:Stochastic Processes