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Cooperative behavior in N-person evolutionary snowdrift games with punishment

Author

Listed:
  • Xu, Meng
  • Zheng, Da-Fang
  • Xu, C.
  • Zhong, Lixin
  • Hui, P.M.

Abstract

We generalize the N-person evolutionary snowdrift game to incorporate the effects of costly punishment in a well-mixed population. A set of dynamical equations that account for the evolution of the frequencies of the three strategies under replicator dynamics is formulated. At long time, the system evolves into one of two phases with different properties consisting only of two strategies, and three-strategy coexistence is not allowed. Small cost-to-benefit ratio, big competing group size, and severe punishment tend to suppress non-cooperators, and lead to a cooperative system with a mixture of cooperators and punishers. The resulting composition depends on the initial conditions as the dynamics is frozen once non-cooperators extinct. Large cost-to-benefit ratio, small competing group size, and light punishment tend to be self-destructive for the punishers, and lead to a mixture of cooperators and non-cooperators with composition independent of initial conditions and a continual dynamics. The frozen phase and dynamical phase correspond to a line of fixed points and a single fixed point on different axes in the phase space, respectively. A simulation algorithm that mimics the replicator dynamics exactly is proposed. Results of the dynamical equations and numerical simulations are found to be in exact agreement.

Suggested Citation

  • Xu, Meng & Zheng, Da-Fang & Xu, C. & Zhong, Lixin & Hui, P.M., 2015. "Cooperative behavior in N-person evolutionary snowdrift games with punishment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 322-329.
    • Handle: RePEc:eee:phsmap:v:424:y:2015:i:c:p:322-329
    DOI: 10.1016/j.physa.2015.01.029
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    Citations

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    Cited by:

    1. Wettergren, Thomas A., 2021. "Replicator dynamics of an N-player snowdrift game with delayed payoffs," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Zhang, H.S. & Shen, X.Y. & Huang, J.P., 2016. "Pattern of trends in stock markets as revealed by the renormalization method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 340-346.
    3. Pi, Jinxiu & Yang, Guanghui & Tang, Wei & Yang, Hui, 2022. "Stochastically stable equilibria for evolutionary snowdrift games with time costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    4. Li, Kun & Mao, Yizhou & Wei, Zhenlin & Cong, Rui, 2021. "Pool-rewarding in N-person snowdrift game," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Wu, Yu’e & Zhang, Zhipeng & Wang, Xinyu & Chang, Shuhua, 2019. "Impact of probabilistic incentives on the evolution of cooperation in complex topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 307-314.
    6. Ye, Wenxing & Fan, Suohai, 2017. "Evolutionary snowdrift game with rational selection based on radical evaluation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 310-317.
    7. Pi, Jinxiu & Yang, Guanghui & Yang, Hui, 2022. "Evolutionary dynamics of cooperation in N-person snowdrift games with peer punishment and individual disguise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).

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