IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v184y2024ics0960077924005551.html

Threshold-initiated spatial public goods games

Author

Listed:
  • Wang, Weijie
  • Xu, Zhehang
  • Hua, Shijia
  • Cui, Longqing
  • Zhang, Jianlin
  • Meng, Fanyuan

Abstract

The Public Goods Game (PGG) encounters hurdles when donations are scarce, resulting in failed game initiations. To investigate such phenomena, we propose a threshold-based spatial PGG model operating on a lattice with periodic boundaries. Players strategically choose between cooperation (C) and defection (D), with PGG initiation determined by a cooperative contribution threshold. Additionally, we introduce an adjustment factor for player reputation, reflecting how individual strategy choices and responses from interacting partners influence reputation changes. We hypothesize that within non-initiated PGG, defectors’ reputations decrease, while within initiated PGG, defectors are evaluated and penalized by cooperators. Our findings reveal that higher initiation thresholds can enhance final cooperation levels. Moreover, the inclusion of the reputation adjustment factor acts as a catalyst for cooperative behavior. Interestingly, greater uncertainty in strategy adoption is associated with increased cooperative levels under higher initiation thresholds. This study adds new insights into the evolution of cooperation in the context of spatial structure.

Suggested Citation

  • Wang, Weijie & Xu, Zhehang & Hua, Shijia & Cui, Longqing & Zhang, Jianlin & Meng, Fanyuan, 2024. "Threshold-initiated spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005551
    DOI: 10.1016/j.chaos.2024.115003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924005551
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115003?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Xu, Zhixiong & Xu, Zhehang & Zhang, Wei & Han, Xiao-Pu & Meng, Fanyuan, 2024. "Memory-based spatial evolutionary prisoner’s dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Zhou, Tianwei & Ding, Shuai & Fan, Wenjuan & Wang, Hao, 2016. "An improved public goods game model with reputation effect on the spatial lattices," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 130-135.
    3. Zhang, Haifeng & Shi, Dongmei & Liu, Runran & Wang, Binghong, 2012. "Dynamic allocation of investments promotes cooperation in spatial public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2617-2622.
    4. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    5. Zhao, Jinqiu & Luo, Chao, 2019. "The effect of preferential teaching and memory on cooperation clusters in interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. Cheng, Fei & Chen, Tong & Chen, Qiao, 2020. "Rewards based on public loyalty program promote cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    7. 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.
    8. Yang, Luhe & Zhang, Lianzhong, 2021. "Environmental feedback in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
    10. Quan, Ji & Tang, Caixia & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Reputation evaluation with tolerance and reputation-dependent imitation on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    11. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    12. Zhu, Peican & Wang, Xiaoyu & Jia, Danyang & Guo, Yangming & Li, Shudong & Chu, Chen, 2020. "Investigating the co-evolution of node reputation and edge-strategy in prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    13. Jeff Gore & Hyun Youk & Alexander van Oudenaarden, 2009. "Snowdrift game dynamics and facultative cheating in yeast," Nature, Nature, vol. 459(7244), pages 253-256, May.
    14. Sun, Xingping & Li, Mingyuan & Kang, Hongwei & Shen, Yong & Chen, Qingyi, 2023. "Combined effect of pure punishment and reward in the public goods game," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    15. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2021. "Effect of reputation-based heterogeneous investment on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    16. Dominic D. P. Johnson & Pavel Stopka & Stephen Knights, 2003. "The puzzle of human cooperation," Nature, Nature, vol. 421(6926), pages 911-912, February.
    17. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "The interplay of behaviors and attitudes in public goods game considering environmental investment," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xu, Zhehang & Liu, Xu & Wang, Hainan & Cui, Longqing & Han, Xiao-Pu & Meng, Fanyuan, 2024. "Free-rider or contributor: A dilemma in spatial threshold public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    2. Li, Xiaopeng & Zhang, Xiuli & Wang, Zhonglin & Pang, Yicheng, 2025. "Dynamic asymmetric reflective decision-making supports the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    3. Wang, Hainan & Zhang, Jiliang & Luo, Qiyao & Han, Xiao-Pu & Cui, Longqing & Wu, Ruirui & Gong, Lei & Liu, Yanni & Meng, Fanyuan, 2025. "Evolutionary dynamics of threshold public goods games on random hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    4. Li, Ming & Huo, Liang'an, 2025. "Effect of time-varying validity of individual interaction on co-evolution of awareness and epidemics in a multiplex high-order network," Applied Mathematics and Computation, Elsevier, vol. 499(C).
    5. Liu, Xu & Wang, Chongkai & Cui, Longqing & Xu, Zhehang & Liu, Yanni & Han, Xiao-Pu & Meng, Fanyuan, 2025. "Enhancing cooperation by balancing the contributions of early and late movers in spatial threshold public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).

    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. Xie, Kai & Liu, Xingwen & Wang, Huazhang & Jiang, Yulian, 2023. "Multi-heterogeneity public goods evolutionary game on lattice," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Qian, Jia-Li & Zhou, Yin-Xiang & Hao, Qing-Yi, 2024. "The emergence of cooperative behavior based on random payoff and heterogeneity of concerning social image," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Sun, Xingping & Zhu, Haoran & Kang, Hongwei & Bi, Yanzheng & Shen, Yong & Chen, Qingyi, 2025. "The impact of memory reputation-induced tax and reward allocation on spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    4. Kang, Hongwei & Jiang, Chao & Shen, Yong & Sun, Xingping & Chen, Qingyi, 2025. "Neighbor-aware reinforcement learning fosters cooperation in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    5. Xie, Kai & Szolnoki, Attila, 2025. "Reputation in public goods cooperation under double Q-learning protocol," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    6. Xie, Kai & Liu, Tingjin, 2024. "The regulation of good and evi promotes cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    7. Zhang, Yao & Hao, Qing-Yi & Qian, Jia-Li & Wu, Chao-Yun & Guo, Ning & Ling, Xiang, 2024. "The cooperative evolution in the spatial prisoner's dilemma game with the local loyalty of two-strategy," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    8. Zhang, Gui & Xiong, Xiaojin & Pi, Bin & Feng, Minyu & Perc, Matjaž, 2025. "Spatial public goods games with queueing and reputation," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    9. Yunsheng Deng & Jihui Zhang, 2022. "The choice-decision based on memory and payoff favors cooperation in stag hunt game on interdependent networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-13, February.
    10. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2024. "Supporting punishment via taxation in a structured population," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. Zhang, Mengshu & Ren, Tianyu & Zeng, Xiao-Jun & Li, Jia, 2024. "Promoting cooperation through dynamic trustworthiness in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    12. Xiang Wei & Peng Xu & Shuiting Du & Guanghui Yan & Huayan Pei, 2021. "Reputational preference-based payoff punishment promotes cooperation in spatial social dilemmas," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(10), pages 1-7, October.
    13. Yu, Fengyuan & Wang, Jianwei & Chen, Wei & He, Jialu, 2023. "Increased cooperation potential and risk under suppressed strategy differentiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    14. Zou, Kuan & Han, Wenchen & Zhang, Lan & Huang, Changwei, 2024. "The spatial public goods game on hypergraphs with heterogeneous investment," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    15. Zhu, Xiaochen, 2023. "The dynamic edge environment under interactive diversity is a double-edged sword," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    16. Quan, Ji & Yang, Haoliang & Wang, Xianjia, 2025. "Cooperation dynamics in a two-state spatial prisoner's dilemma game with reputation-driven transitions," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    17. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2023. "Group-size dependent synergy in heterogeneous populations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    18. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2021. "Effect of reputation-based heterogeneous investment on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Gao, Hongyu & Wang, Juan & Zhang, Fan & Li, Xiaopeng & Xia, Chengyi, 2021. "Cooperation dynamics based on reputation in the mixed population with two species of strategists," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    20. Yang, Qianxi & Yang, Yanlong, 2024. "A social monitoring mechanism for third-party judges promotes cooperation in evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 483(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:chsofr:v:184:y:2024:i:c:s0960077924005551. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.