Dresden 2009 – scientific programme

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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme

AGSOE 9: Economic Models and Evolutionary Game Theory I

AGSOE 9.3: Talk

Tuesday, March 24, 2009, 15:00–15:30, BAR 205

Fixation times in evolutionary games under weak selection — •Philipp M. Altrock and Arne Traulsen — Max-Planck-Institut für Evolutionsbiologie, Plön, Deutschland

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 [1].

We show analytically that these times depend on the payoff matrix of the game in an amazingly simple way under weak selection [2]: The payoff difference Δ π is a linear function of the number of A individuals i, Δ 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.

[1] T. Antal and I. Scheuring. Fixation of strategies for an evolutionary game in finite populations. Bull. Math. Biol., 36(12):1923–1944 2006.

[2] P. M. Altrock. and A. Traulsen. Fixation times in evolutionary games under weak selection. New J. Physics, in press 2008.