Anomalous finite-size effects in the Battle of the Sexes
Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
Corresponding author: a firstname.lastname@example.org
Revised: 13 November 2007
Published online: 30 January 2008
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.
PACS: 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.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008