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Cooperation in changing environments: Irreversibility in the transition to cooperation in complex networks

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  • Gracia-Lázaro, Carlos
  • Floría, Luis M.
  • Gómez-Gardeñes, Jesús
  • Moreno, Yamir

Abstract

In the framework of the evolutionary dynamics of the Prisoner’s Dilemma game on complex networks, we investigate the possibility that the average level of cooperation shows hysteresis under quasi-static variations of a model parameter (the “temptation to defect”). Under the “discrete replicator” strategy updating rule, for both Erdös–Rényi and Barabási–Albert graphs we observe cooperation hysteresis cycles provided one reaches tipping point values of the parameter; otherwise, perfect reversibility is obtained. The selective fixation of cooperation at certain nodes and its organization in cooperator clusters, that are surrounded by fluctuating strategists, allows the rationalization of the “lagging behind” behavior observed.

Suggested Citation

  • Gracia-Lázaro, Carlos & Floría, Luis M. & Gómez-Gardeñes, Jesús & Moreno, Yamir, 2013. "Cooperation in changing environments: Irreversibility in the transition to cooperation in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 188-193.
    • Handle: RePEc:eee:chsofr:v:56:y:2013:i:c:p:188-193
    DOI: 10.1016/j.chaos.2013.08.008
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    References listed on IDEAS

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    1. Szolnoki, Attila & Perc, Matjaž & Danku, Zsuzsa, 2008. "Towards effective payoffs in the prisoner’s dilemma game on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2075-2082.
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    1. Li, Ya & Lan, Xin & Deng, Xinyang & Sadiq, Rehan & Deng, Yong, 2014. "Comprehensive consideration of strategy updating promotes cooperation in the prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 284-292.
    2. Xie, Qian & Si, Gangquan & Zhang, Yanbin & Yuan, Yiwei & Yao, Rui, 2016. "Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 35-49.
    3. Deng, Xinyang & Zhang, Zhipeng & Deng, Yong & Liu, Qi & Chang, Shuhua, 2016. "Self-adaptive win-stay-lose-shift reference selection mechanism promotes cooperation on a square lattice," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 322-331.

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