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Interaction between populations promotes cooperation in voluntary prisoner's dilemma

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  • Shi, Juan
  • Hu, Die
  • Tao, Rui
  • Peng, Yunchen
  • Li, Yong
  • Liu, Jinzhuo

Abstract

The coexistence of different populations has recently been confirmed to be a simple yet effective mechanism to understand the stability of cooperation. Based on this intuition, we use the voluntary prisoner's dilemma (VPD) game as the mathematical model to explore the spatiotemporal dynamics of cooperation among different populations. By using parameter α as a key quantity that takes into account the strength of connections between populations, we observe that a fascinating spiral pattern is spontaneously formed, adding a new population always brings additional prey to cooperators in other populations, leading to competing spatial dynamics and pattern formation. Moreover, the system gradually changes from the C + D + L state to the C + D state and finally to the full C state. The inherent cyclic dominance of the strategies results in the self-organization of populations on the square lattice and ultimately effectively promotes cooperation. Our work emphasizes that the complexity of the evolutionary dynamics of structural populations is significantly increased by the simultaneous existence of different populations.

Suggested Citation

  • Shi, Juan & Hu, Die & Tao, Rui & Peng, Yunchen & Li, Yong & Liu, Jinzhuo, 2021. "Interaction between populations promotes cooperation in voluntary prisoner's dilemma," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306810
    DOI: 10.1016/j.amc.2020.125728
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    3. Li, Dandan & Zhou, Kai & Sun, Mei & Han, Dun, 2023. "Investigating the effectiveness of individuals’ historical memory for the evolution of the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Liu, Siyuan & Zhang, Chunyan & Li, Kun & Zhang, Jianlei, 2022. "Exploring the inducement for social dilemma and cooperation promotion mechanisms in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Gao, Yan & Li, Minlan & Hu, Yuanyuan & Wang, Rui-Wu & Wang, Chao, 2024. "Evolutionary dynamics in voluntary prisoner’s dilemma game with environmental feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. Peican Zhu & Xin Hou & Yangming Guo & Jiwei Xu & Jinzhuo Liu, 2021. "Investigating the effects of updating rules on cooperation by incorporating interactive diversity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(2), pages 1-8, February.
    7. Li, Xiaoyu & Jia, Danyang & Niu, Xiaotong & Liu, Chen & Zhu, Peican & Liu, Dujuan & Chu, Chen, 2022. "Ability-based asymmetrical fitness calculation promotes cooperation in spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    8. Deng, Zheng-Hong & Wang, Zi-Ren & Wang, Huan-Bo & Huang, Yijie, 2021. "Impact of informers on the evolution of cooperation in prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
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    11. Gao, Liyan & Pan, Qiuhui & He, Mingfeng, 2023. "Impact of peer pressure on the evolution of cooperation in prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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