Strategy abundance in 2x2 games for arbitrary mutation rates
Abstract
We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A and B, under mutation and selection. The game dynamical interaction between the two strategies is given by the 2x2 payoff matrix [(a,b), (c,d)]. It has previously been shown that A is more abundant than B, if (N-2)a+Nb>Nc+(N-2)d. This result has been derived for particular stochastic processes that operate either in the limit of asymptotically small mutation rates or in the limit of weak selection. Here we show that this result holds in fact for a wide class of stochastic birth-death processes for arbitrary mutation rate and for any intensity of selection.
Cite
@article{arxiv.0809.2804,
title = {Strategy abundance in 2x2 games for arbitrary mutation rates},
author = {Tibor Antal and Martin A. Nowak and Arne Traulsen},
journal= {arXiv preprint arXiv:0809.2804},
year = {2009}
}
Comments
version 2 is the final published version that contains minor changes in response to referee comments