IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v492y2025ics0096300324007100.html
   My bibliography  Save this article

Supervised cooperation on interdependent public goods games

Author

Listed:
  • Ling, Ting
  • Li, Zhang
  • Feng, Minyu
  • Szolnoki, Attila

Abstract

It is a challenging task to reach global cooperation among self-interested agents, which often requires sophisticated design or usage of incentives. For example, we may apply supervisors or referees who are able to detect and punish selfishness. As a response, defectors may offer bribes for corrupt referees to remain hidden, hence generating a new conflict among supervisors. By using the interdependent network approach, we model the key element of the coevolution between strategy and judgment. In a game layer, agents play public goods game by using one of the two major strategies of a social dilemma. In a monitoring layer, supervisors follow the strategy change and may alter the income of competitors. Fair referees punish defectors while corrupt referees remain silent for a bribe. Importantly, there is a learning process not only among players but also among referees. Our results suggest that large fines and bribes boost the emergence of cooperation by significantly reducing the phase transition threshold between the pure defection state and the mixed solution where competing strategies coexist. Interestingly, the presence of bribes could be as harmful for defectors as the usage of harsh fines. The explanation of this system behavior is based on a strong correlation between cooperators and fair referees, which is cemented via overlapping clusters in both layers.

Suggested Citation

  • Ling, Ting & Li, Zhang & Feng, Minyu & Szolnoki, Attila, 2025. "Supervised cooperation on interdependent public goods games," Applied Mathematics and Computation, Elsevier, vol. 492(C).
  • Handle: RePEc:eee:apmaco:v:492:y:2025:i:c:s0096300324007100
    DOI: 10.1016/j.amc.2024.129249
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324007100
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2024.129249?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Gao, Shiping & Suo, Jinghui & Li, Nan, 2025. "Cooperation under endogenous punishment in the spatial public goods game," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    3. Zhang, Yuji & Zeng, Ziyan & Pi, Bin & Feng, Minyu, 2023. "An evolutionary game with revengers and sufferers on complex networks," Applied Mathematics and Computation, Elsevier, vol. 457(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. Wang, Pai & Yang, Zhihu, 2024. "The double-edged sword effect of conformity on cooperation in spatial Prisoner’s Dilemma Games with reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    6. Li, Xiaopeng & Wang, Zhonglin & Xu, Yan & Zhang, Hui & Yu, Guihai, 2024. "Asymmetrical interactions driven by strategic persistence effectively alleviate social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    7. Liu, Jiaqi & Zhang, Qianwei & Tang, Rui, 2024. "Fostering cooperative evolution through probabilistic punishment and environmental feedback in public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    8. 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).
    9. Song, Qun & Cao, Zhaoheng & Tao, Rui & Jiang, Wei & Liu, Chen & Liu, Jinzhuo, 2020. "Conditional neutral punishment promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    10. 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.
    11. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2022. "Mercenary punishment in structured populations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    12. Zhang, Yao & Hao, Qing-Yi & Qian, Jia-Li & Wu, Chao-Yun & Bi, Yan, 2024. "The influence of the heterogeneities of social institutions and individuals’ tendency to establish social institutions on cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    13. Prateek Verma & Supratim Sengupta, 2015. "Bribe and Punishment: An Evolutionary Game-Theoretic Analysis of Bribery," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-22, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2024. "Suppressing defection by increasing temptation: The impact of smart cooperators on a social dilemma situation," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    2. Wang, Chaoqian & Szolnoki, Attila, 2022. "Involution game with spatio-temporal heterogeneity of social resources," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Feng, Kehuan & Han, Songlin & Feng, Minyu & Szolnoki, Attila, 2024. "An evolutionary game with reputation-based imitation-mutation dynamics," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    4. Tian, Yue & Gao, Shun & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2024. "Particle swarm intelligence promotes cooperation by adapting interaction radii in co-evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    5. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2024. "Supporting punishment via taxation in a structured population," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    6. Chen, Qin & Pan, Qiuhui & He, Mingfeng, 2022. "The influence of quasi-cooperative strategy on social dilemma evolution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    7. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2023. "Restoring spatial cooperation with myopic agents in a three-strategy social dilemma," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    8. Bai, Pengzhou & Qiang, Bingzhuang & Zou, Kuan & Huang, Changwei, 2024. "Preferential selection based on adaptive attractiveness induce by reinforcement learning promotes cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    9. Kang, Hongwei & Li, Xin & Shen, Yong & Sun, Xingping & Chen, Qingyi, 2024. "Particle swarm optimization with historical return decay enhances cooperation in public goods games with investment risks," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    10. Pan, Na & Zeng, Ziyan & Zhang, Yuji & Feng, Minyu, 2024. "Defined benefit pension plan inhibit the emergence of cooperation in the public goods games," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    11. Quan, Ji & Yu, Junyu & Li, Xia & Wang, Xianjia, 2023. "Conditional switching between social excluders and loners promotes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    12. Lu, Shounan & Dai, Jianhua & Zhu, Ge & Guo, Li, 2023. "Investigating the effectiveness of interaction-efficiency-driven strategy updating under progressive-interaction for the evolution of the prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Shi, Zhenyu & Wei, Wei & Zheng, Hongwei & Zheng, Zhiming, 2023. "Bidirectional supervision: An effective method to suppress corruption and defection under the third party punishment mechanism of donation games," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    14. Szolnoki, Attila & Chen, Xiaojie, 2022. "Tactical cooperation of defectors in a multi-stage public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    15. Guo, Shiqiang & Wang, Juan & Zhao, Dawei & Xia, Chengyi, 2023. "Role of second-order reputation evaluation in the multi-player snowdrift game on scale-free simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    16. Zhang, Yanling & Yang, Shuo & Chen, Xiaojie & Bai, Yanbing & Xie, Guangming, 2023. "Reputation update of responders efficiently promotes the evolution of fairness in the ultimatum game," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    17. Xiong, Xiaojin & Yao, Yichao & Feng, Minyu & Chica, Manuel, 2024. "Adaptive payoff-driven interaction in networked snowdrift games," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    18. Xu, Yan & Zhao, Dawei & Chen, Jiaxing & Liu, Tao & Xia, Chengyi, 2024. "The nested structures of higher-order interactions promote the cooperation in complex social networks," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    19. Shuo Wang & Zhuang Li & Weidong Li & Hua Jiang, 2022. "Continuous Spatial Public Goods Game Based on Particle Swarm Optimization with Memory Stability," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    20. Xiaopeng Li & Zhonglin Wang & Jiuqiang Liu & Guihai Yu, 2023. "The Sense of Cooperation on Interdependent Networks Inspired by Influence-Based Self-Organization," Mathematics, MDPI, vol. 11(4), pages 1-16, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:492:y:2025:i:c:s0096300324007100. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.