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Fixation of Strategies for an Evolutionary Game in Finite Populations

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Abstract

A stochastic evolutionary dynamics of two strategies given by 2× 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.

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Authors and Affiliations

  1. Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, 02215, USA

    Tibor Antal

  2. Department of Plant Taxonomy and Ecology, Research Group of Ecology and Theoretical Biology, Eötvös University and HAS, Pázmány P. sétány 1/c, H-1117, Budapest, Hungary

    István Scheuring

Authors
  1. Tibor Antal
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  2. István Scheuring
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Correspondence to Tibor Antal.

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On leave from Institute for Theoretical Physics - HAS, Eötvös University, Budapest, Hungary.

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Antal, T., Scheuring, I. Fixation of Strategies for an Evolutionary Game in Finite Populations. Bull. Math. Biol. 68, 1923–1944 (2006). https://doi.org/10.1007/s11538-006-9061-4

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  • DOI: https://doi.org/10.1007/s11538-006-9061-4

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