Eur. Phys. J. B (2014) 87: 19
https://doi.org/10.1140/epjb/e2013-40797-3

Regular Article

Cooperation within triplets in the rock-paper-scissors game

Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro, 8400 Bariloche, Río Negro, Argentina

^a e-mail: damian.g.h.l@gmail.com

Received: 28 August 2013
Received in final form: 30 November 2013
Published online: 22 January 2014

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.