title: Ordering structured populations in multiplayer cooperation games.
abstract: Spatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure S1 is greater than population structure S1 in the containment or the volume order, then S1 can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany pena@evolbio.mpg.de.
authors.forename: Jorge
authors.initials: J
authors.lastname: Peña
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany.
authors.forename: Bin
authors.initials: B
authors.lastname: Wu
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany.
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D008954:Models, Biological; D011157:Population Dynamics
keywords: computational geometry; evolutionary game theory; order theory; spatial structure; stochastic orders
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