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Evolution of cooperation in spatial iterated Prisoner’s Dilemma games under localized extremal dynamics

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  • Wang, Zhen
  • Yu, Chao
  • Cui, Guang-Hai
  • Li, Ya-Peng
  • Li, Ming-Chu

Abstract

The spatial Iterated Prisoner’s Dilemma game has been widely studied in order to explain the evolution of cooperation. Considering the large strategy space size and infinite interaction times, it is unrealistic to adopt the common imitate-best updating rule, which assumes that the human players have much stronger abilities to recognize their neighbors’ strategies than they do in the one-shot game. In this paper, a novel localized extremal dynamic system is proposed, in which each player only needs to recognize the payoff of his neighbors and changes his strategy randomly when he receives the lowest payoff in his neighborhood. The evolution of cooperation is here explored under this updating rule for neighborhoods of different sizes, which are characterized by their corresponding radiuses r. The results show that when r=1, the system is trapped in a checkerboard-like state, where half of the players consistently use AllD-like strategies and the other half constantly change their strategies. When r=2, the system first enters an AllD-like state, from which it escapes, and finally evolves to a TFT-like state. When r is larger, the system locks in a situation with similar low average fitness as r=1. The number of active players and the ability to form clusters jointly distinguish the evolutionary processes for different values of r from each other. The current findings further provide some insight into the evolution of cooperation and collective behavior in biological and social systems.

Suggested Citation

  • Wang, Zhen & Yu, Chao & Cui, Guang-Hai & Li, Ya-Peng & Li, Ming-Chu, 2016. "Evolution of cooperation in spatial iterated Prisoner’s Dilemma games under localized extremal dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 566-575.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:566-575
    DOI: 10.1016/j.physa.2015.10.015
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    References listed on IDEAS

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    1. Chen Liu & Wen-Bo Du & Wen-Xu Wang, 2014. "Particle Swarm Optimization with Scale-Free Interactions," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-8, May.
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    3. Zhang, Jun & Fang, Yi-Ping & Du, Wen-Bo & Cao, Xian-Bin, 2011. "Promotion of cooperation in aspiration-based spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2258-2266.
    4. A. Szolnoki & M. Perc, 2009. "Promoting cooperation in social dilemmas via simple coevolutionary rules," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(3), pages 337-344, February.
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    Cited by:

    1. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    2. Chen, Wei & Wang, Jianwei & Yu, Fengyuan & Xu, Wenshu & Dai, Wenhui, 2024. "Heterogeneous interaction radius based on emotional dynamics can promote cooperation in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    3. Li, Bing & Zhao, Xiaowei & Xia, Haoxiang, 2019. "Promotion of cooperation by Hybrid Migration mechanisms in the Spatial Prisoner’s Dilemma Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 1-8.
    4. Han, Xu & Zhao, Xiaowei & Xia, Haoxiang, 2021. "Evolution of cooperation through aspiration-based adjustment of interaction range in spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    5. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.

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