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Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players

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  • Hendrik Richter

    (Faculty of Engineering, HTWK Leipzig University of Applied Sciences, D-04251 Leipzig, Germany)

Abstract

We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with N ≤ 14 vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of a certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices.

Suggested Citation

  • Hendrik Richter, 2020. "Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players," Games, MDPI, vol. 11(1), pages 1-18, February.
    • Handle: RePEc:gam:jgames:v:11:y:2020:i:1:p:12-:d:321595
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    References listed on IDEAS

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    1. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    2. Yunming Xiao & Bin Wu, 2019. "Close spatial arrangement of mutants favors and disfavors fixation," PLOS Computational Biology, Public Library of Science, vol. 15(9), pages 1-20, September.
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    4. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    5. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    6. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    7. Swami Iyer & Timothy Killingback, 2016. "Evolution of Cooperation in Social Dilemmas on Complex Networks," PLOS Computational Biology, Public Library of Science, vol. 12(2), pages 1-25, February.
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