Regensburg 2010 – scientific programme

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BP: Fachverband Biologische Physik

BP 11: Evolutionary Game Theory II (joint SOE, BP)

BP 11.4: Talk

Tuesday, March 23, 2010, 12:00–12:15, H44

Deterministic evolutionary game dynamics in finite populations — •Philipp M. Altrock and Arne Traulsen — MPI f. Evolutionary Biology, Plön, Germany

Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic only in infinitely large populations. Here, we introduce a new microscopic birth–death process that has a fully deterministic strong selection limit in well–mixed populations of any size. Additionally, under weak selection, from this new process the frequency dependent Moran process is recovered. This makes it a natural extension of the usual evolutionary dynamics under weak selection. We analytically find simple expressions for the fixation probabilities and average fixation times of the new process in evolutionary games with two players and two strategies. For cyclic games with two players and three strategies, we show that the resulting deterministic dynamics crucially depends on the initial condition in a non–trivial way.

[1] Goel & Richter-Dyn, Stochastic Models in Biology, Academic Press, NY, (1974).

[2] Altrock & Traulsen, Phys. Rev. E 80, 011909 (2009).