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Type: Journal article
Title: Mixing times in evolutionary game dynamics
Author: Black, A.
Traulsen, A.
Galla, T.
Citation: Physical Review Letters, 2012; 109(2):1-5
Publisher: American Physical Soc
Issue Date: 2012
ISSN: 0031-9007
Statement of
Andrew J. Black, Arne Traulsen and Tobias Galla
Abstract: Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics. However, many biological arguments focus on stationary distributions in a mutation-selection equilibrium. Here, we address the mixing time required to reach stationarity in the presence of mutation. We show that mixing times in evolutionary games have the opposite behavior from fixation times when the intensity of selection increases: in coordination games with bistabilities, the fixation time decreases, but the mixing time increases. In coexistence games with metastable states, the fixation time increases, but the mixing time decreases. Our results are based on simulations and the Wentzel-Kramers-Brillouin approximation of the master equation.
Keywords: Mutation; Game Theory; Models, Genetic; Time Factors; Biological Evolution
Rights: ©2012 American Physical Society
RMID: 0020120704
DOI: 10.1103/PhysRevLett.109.028101
Appears in Collections:Mathematical Sciences publications

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