Year: 2009
Type: article
Abstract: 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.
Source: New Journal of Physics
Authors: Philipp M Altrock, Arne Traulsen
Language: English
Subfield: Sociology and Political Science
Field: Social Sciences
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $919
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2048924536