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The evolution of cooperation in the Prisoner’s Dilemma and the Snowdrift game based on Particle Swarm Optimization

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  • Wang, Xianjia
  • Lv, Shaojie
  • Quan, Ji

Abstract

This paper studies the evolution of cooperation in the Prisoner’s Dilemma (PD) and the Snowdrift (SD) game on a square lattice. Each player interacting with their neighbors can adopt mixed strategies describing an individual’s propensity to cooperate. Particle Swarm Optimization (PSO) is introduced into strategy update rules to investigate the evolution of cooperation. In the evolutionary game, each player updates its strategy according to the best strategy in all its past actions and the currently best strategy of its neighbors. The simulation results show that the PSO mechanism for strategy updating can promote the evolution of cooperation and sustain cooperation even under unfavorable conditions in both games. However, the spatial structure plays different roles in these two social dilemmas, which presents different characteristics of macroscopic cooperation pattern. Our research provides insights into the evolution of cooperation in both the Prisoner’s Dilemma and the Snowdrift game and maybe helpful in understanding the ubiquity of cooperation in natural and social systems.

Suggested Citation

  • Wang, Xianjia & Lv, Shaojie & Quan, Ji, 2017. "The evolution of cooperation in the Prisoner’s Dilemma and the Snowdrift game based on Particle Swarm Optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 286-295.
    • Handle: RePEc:eee:phsmap:v:482:y:2017:i:c:p:286-295
    DOI: 10.1016/j.physa.2017.04.080
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    Cited by:

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    3. Gu, Cuiling & Wang, Xianjia & Ding, Rui & Zhao, Jinhua & Liu, Yang, 2022. "Evolutionary dynamics of multi-player snowdrift games based on the Wright-Fisher process," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Quan, Ji & Yang, Xiukang & Wang, Xianjia, 2018. "Spatial public goods game with continuous contributions based on Particle Swarm Optimization learning and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 973-983.
    5. Li, Cong & Xu, Hedong & Fan, Suohai, 2021. "Evolutionary compromise game on assortative mixing networks," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    6. Lv, Shaojie & Song, Feifei, 2022. "Particle swarm intelligence and the evolution of cooperation in the spatial public goods game with punishment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    7. Wang, Jianwei & Xu, Wenshu & Zhang, Xingjian & Zhao, Nianxuan & Yu, Fengyuan, 2023. "Redistribution based on willingness to cooperate promotes cooperation while intensifying equality in heterogeneous populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    8. Wang, Xianjia & Yang, Zhipeng & Liu, Yanli & Chen, Guici, 2023. "A reinforcement learning-based strategy updating model for the cooperative evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
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    11. Wang, Xianjia & Chen, Wenman, 2020. "Evolutionary dynamics in spatial threshold public goods game with the asymmetric return rate mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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