Regensburg 2010 – scientific programme

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BP: Fachverband Biologische Physik

BP 10: Evolutionary Game Theory I (joint SOE, BP)

BP 10.4: Talk

Tuesday, March 23, 2010, 10:30–10:45, H44

Evolutionary games in the multiverse — •Chaitanya S. Gokhale and Arne Traulsen — Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players. As long as we have only two strategies, many results from two player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions do no longer hold. For two player games with any number of strategies there can be at most one isolated internal equilibrium. We show that for any number of players d with any number of strategies n, there can be at most (d−1)ⁿ⁻¹ isolated internal equilibria. Thus, multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied for specific cases, e.g. public goods games or multiplayer stag hunts.