The European Physical Journal B

, Volume 63, Issue 3, pp 373–380 | Cite as

Anomalous finite-size effects in the Battle of the Sexes

  • J. CremerEmail author
  • T. Reichenbach
  • E. Frey
Topical issue dedicated to ECCS2007 - Dresden


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.


87.23.-n Ecology and evolution 05.40.-a Nonlinear dynamics and chaos 02.50.Ey Stochastic processes 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.) 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of PhysicsLudwig-Maximilians-Universität MünchenMünchenGermany

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