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The Evolution of Cooperation in Multigames with Uniform Random Hypergraphs

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  • Haozheng Xu

    (School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Yiwen Zhang

    (School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Xing Jin

    (School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China
    Experimental Center of Data Science and Intelligent Decision-Making, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Jingrui Wang

    (School of Network Security, Changchun University, Changchun 130022, China)

  • Zhen Wang

    (School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China
    Experimental Center of Data Science and Intelligent Decision-Making, Hangzhou Dianzi University, Hangzhou 310018, China
    Zhuoyue Honors College, Hangzhou Dianzi University, Hangzhou 310018, China)

Abstract

How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common in human society and a person can participate in multiple groups, this paper studies an evolutionary multigame with high-order interaction properties. For this purpose, a uniform random hypergraph is adopted as the network structure, allowing players to interact with all nodes in the same hyperedge. First, we investigate the effect of the multigame payoff matrix differences on the evolution of cooperation and find that increasing the differences in the payoff matrix promotes cooperation on the hypergraph network. Second, we discover that an increase in the average hyperdegree of the hypergraph network promotes network reciprocity, wherein high-hyperdegree nodes influence surrounding nodes to form a cooperator cluster. Conversely, groups with a low hyperdegree are more susceptible to betrayal, leading to a decline in cooperation.

Suggested Citation

  • Haozheng Xu & Yiwen Zhang & Xing Jin & Jingrui Wang & Zhen Wang, 2023. "The Evolution of Cooperation in Multigames with Uniform Random Hypergraphs," Mathematics, MDPI, vol. 11(11), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2409-:d:1153212
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    References listed on IDEAS

    as
    1. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    2. Francisco C. Santos & Marta D. Santos & Jorge M. Pacheco, 2008. "Social diversity promotes the emergence of cooperation in public goods games," Nature, Nature, vol. 454(7201), pages 213-216, July.
    3. repec:hhs:iuiwop:487 is not listed on IDEAS
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    Cited by:

    1. Zhang, Huizhen & An, Tianbo & Yan, Pingping & Hu, Kaipeng & An, Jinjin & Shi, Lijuan & Zhao, Jian & Wang, Jingrui, 2024. "Exploring cooperative evolution with tunable payoff’s loners using reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Wang, Jingrui & Zhang, Huizhen & Jin, Xing & Ma, Leyu & Chen, Yueren & Wang, Chao & Zhao, Jian & An, Tianbo, 2023. "Subsidy policy with punishment mechanism can promote voluntary vaccination behaviors in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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