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Ordering structured populations in multiplayer cooperation games

Jorge Peña, Bin Wu, Arne Traulsen
doi: https://doi.org/10.1101/021550
Jorge Peña
Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 PlÖn, Germany
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  • For correspondence: pena@evolbio.mpg.de
Bin Wu
Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 PlÖn, Germany
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Arne Traulsen
Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 PlÖn, Germany
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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 𝒮2 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.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted January 12, 2016.
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Ordering structured populations in multiplayer cooperation games
Jorge Peña, Bin Wu, Arne Traulsen
bioRxiv 021550; doi: https://doi.org/10.1101/021550
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Ordering structured populations in multiplayer cooperation games
Jorge Peña, Bin Wu, Arne Traulsen
bioRxiv 021550; doi: https://doi.org/10.1101/021550

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