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Cooperation within triplets in the rock-paper-scissors game

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  • Damián G. Hernández
  • Damián H. Zanette

Abstract

We study a population involved in a cyclic game of three strategies – the rock-paper-scissors game – whose agents interact through groups of three individuals (triplets), considering the possibility that two weak agents cooperate and beat a strong one. In a wide range of parameters the system presents a stable heteroclinic cycle, which implies that in a finite population some of the strategies become extinct and others survive. We find that the cooperation within triplets only benefits the survival of the strategy if the cooperation probability is above a certain threshold. We study the survival probabilities of the different strategies as a function of the cooperation parameters through a analytic approximation and compare with simulations, obtaining a good agreement. Results are generalizable to other systems with heteroclinic cycles. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Damián G. Hernández & Damián H. Zanette, 2014. "Cooperation within triplets in the rock-paper-scissors game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-7, January.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:1:p:1-7:10.1140/epjb/e2013-40797-3
    DOI: 10.1140/epjb/e2013-40797-3
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    1. Jeffrey Johnson, 2008. "Multidimensional Events in Multilevel Systems," Springer Books, in: Sergio Albeverio & Denise Andrey & Paolo Giordano & Alberto Vancheri (ed.), The Dynamics of Complex Urban Systems, pages 311-334, Springer.
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      Statistical and Nonlinear Physics;

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