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Anomalous finite-size effects in the Battle of the Sexes

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  • J. Cremer
  • T. Reichenbach
  • E. Frey

Abstract

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • J. Cremer & T. Reichenbach & E. Frey, 2008. "Anomalous finite-size effects in the Battle of the Sexes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 373-380, June.
  • Handle: RePEc:spr:eurphb:v:63:y:2008:i:3:p:373-380
    DOI: 10.1140/epjb/e2008-00036-x
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    Cited by:

    1. Alessandra F. Lütz & Annette Cazaubiel & Jeferson J. Arenzon, 2017. "Cyclic Competition and Percolation in Grouping Predator-Prey Populations," Games, MDPI, vol. 8(1), pages 1-9, February.
    2. Frey, Erwin, 2010. "Evolutionary game theory: Theoretical concepts and applications to microbial communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4265-4298.

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