Dresden 2011 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 19: Economic Models and Evolutionary Game Theory II (with BP, DY)
SOE 19.3: Talk
Thursday, March 17, 2011, 14:30–14:45, GÖR 226
How small are small mutation rates ? — Bin Wu1,2, •Chaitanya Gokhale1, and Arne Traulsen1 — 1Research Group for Evolutionary Theory, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany — 2Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China
In recent years numerous analytical advances have been made in the field of evolutionary game theory. Some of them consider processes in which strategies can mutate between each other. Often the assumption of small mutation rates is made to keep the analysis tractable [1,2,3]. For small mutation rates the population is monomorphic most of the time. Occasionally a mutation arises. It can either reach fixation or go extinct. The evolutionary dynamics of the process under small mutation rates can be approximated by an embedded Markov chain on the pure states. Previously it was shown that in the limit of mutation rates going to zero the embedded Markov chain is a good approximation [4]. Here we derive an upper limit until where the approximation holds good. For a coexistence game it is necessary that the mutation rate µ is less than N−1/2exp[−N] and for all other games, it is sufficient if the mutation rate is smaller than (NlnN )−1. Our results hold for a wide class of imitation processes under arbitrary selection intensity.
References: [1] Hauert C et al., Science 316, 2007. [2] Van Segbroeck S et al., Phys Rev Lett 102:058,105, 2009. [3] Sigmund K et al., Nature 466, 2010. [4] Fudenberg D, Imhof LA, J Econ Theory 131, 2006.