# Berlin 2008 – wissenschaftliches Programm

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# SYDN: Symposium Game theory in dynamical systems

## SYDN 1: Game theory in dynamical systems

### SYDN 1.4: Vortrag

### Freitag, 29. Februar 2008, 11:20–11:35, H 0105

**Anomalous finite-size effects in the Battle of the Sexes** — •Jonas Cremer, Tobias Reichenbach, and Erwin Frey — Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians Universität München

We investigate finite-size fluctuations in Dawkins Battle of the Sexes. This game describes mating behavior of males and females, where males can be either philanderer or faithful, females are fast or coy. The replicator dynamics is cyclic with a deterministic drift towards coexistence of all four strategies. In contrast to this behavior, we show that finite-size fluctuations unavoidably lead to extinction of two strategies in the population [1]. The typical time until extinction occurs, however, strongly prolongs with increasing system size. During this emerging time window, a quasi-stationary probability distribution forms that is non-Gaussian in the vicinity of the coexistence state. As we show, this behavior originates in a vanishing linear deterministic drift near the coexistence fixed point. We provide an analytical approach for this distribution and the mean extinction time.

[1] Jonas Cremer, Tobias Reichenbach, and Erwin Frey, submittted to EPJB, arxiv.org/abs/0709.0225