2008/12/04 by Philipp M. Altrock, Arne Traulsen · 125 citations
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · Social Sciences · #Artificial intelligence #Computer science #Evolution and Genetic Dynamics #Evolutionarily stable strategy #Evolutionary Game Theory and Cooperation #Evolutionary dynamics #Evolutionary game theory #Fixation (population genetics) #Game Theory and Applications #Game theory #Mathematical economics #Mathematics #Normal-form game #Physics #Population #Repeated game #Selection (genetic algorithm) #Simple (philosophy) #Statistical physics #Stochastic game #q-bio.PE
paper · pdf · doi:10.1088/1367-2630/11/1/013012
published in New Journal of Physics 11(1), 013012 (IOP Publishing) · Forthcoming in New Journal of Physics
arxiv created 2008/12/04 · openalex publication_date 2009/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In evolutionary game dynamics, reproductive success increases with the performance in an evolutionary game.If strategy A performs better than strategy B, strategy A will spread in the population.Under stochastic dynamics, a single mutant will sooner or later take over the entire population or go extinct.We analyze the mean exit times (or average fixation times) associated with this process.We show analytically that these times depend on the payoff matrix of the game in an amazingly simple way under weak selection, i.e. strong stochasticity: the payoff difference π is a linear function of the number of A individuals i, π = u i + v.The unconditional mean exit time depends only on the constant term v. Given that a single A mutant takes over the population, the corresponding conditional mean exit time depends only on the density dependent term u.We demonstrate this finding for two commonly applied microscopic evolutionary processes.