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Dynamic Properties of Evolutionary Multi-player Games in Finite Populations
Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany
* Author to whom correspondence should be addressed.
Received: 11 February 2013; in revised form: 11 April 2013 / Accepted: 22 April 2013 / Published: 6 May 2013
Abstract: William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.
Keywords: multi-player games; finite population; fixation probability; fixation time; average abundance
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Cite This Article
MDPI and ACS Style
Wu, B.; Traulsen, A.; Gokhale, C.S. Dynamic Properties of Evolutionary Multi-player Games in Finite Populations. Games 2013, 4, 182-199.
Wu B, Traulsen A, Gokhale CS. Dynamic Properties of Evolutionary Multi-player Games in Finite Populations. Games. 2013; 4(2):182-199.
Wu, Bin; Traulsen, Arne; Gokhale, Chaitanya S. 2013. "Dynamic Properties of Evolutionary Multi-player Games in Finite Populations." Games 4, no. 2: 182-199.