# Berlin 2008 – wissenschaftliches Programm

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# SYDN: Symposium Game theory in dynamical systems

## SYDN 1: Game theory in dynamical systems

### SYDN 1.5: Vortrag

### Freitag, 29. Februar 2008, 11:35–11:50, H 0105

**Evolutionary game dynamics: From infinite to finite populations and back** — •Arne Traulsen — Max-Planck-Institute for Evolutionary Biology, Plön, Germany

Evolutionary game dynamics is traditionally considered in infinite populations, based on the replicator dynamics. These nonlinear differential equations have given rise to a wealth of beautiful mathematical results. In finite populations, surprising effects arise from the interplay of stochasticity and weak selection. For example, the 1/3-rule connects the position of an unstable equilibrium in coordination games with the fixation probabilities under weak selection. Cooperation in group structured populations is only nontrivial for a finite number of finite groups. Costly punishment of uncooperative individuals does not emerge in infinite populations, but can dominate when the population is finite. In the appropriate limits, the usual results of the replicator dynamics can be reproduced, with added insight on the system parameters.