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The impact of adaptive trust reinforcement in a multi-state Public Goods Game

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  • Moussa, Fatima Zahra
  • Zine-Dine, Khalid

Abstract

The Public Goods Game (PGG) is a foundational framework for studying the emergence and sustainability of cooperation among self-interested agents. However, its conventional binary structure – where individuals either contribute their full endowment or nothing – oversimplifies the range of cooperative behaviors observed in real-world settings, where partial contributions are common. In this study, we introduce a multi-state extension of the PGG, denoted PGGM, in which agents choose from M discrete contribution levels, allowing for a more nuanced representation of cooperative strategies.

Suggested Citation

  • Moussa, Fatima Zahra & Zine-Dine, Khalid, 2026. "The impact of adaptive trust reinforcement in a multi-state Public Goods Game," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017382
    DOI: 10.1016/j.chaos.2025.117725
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    References listed on IDEAS

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    1. Cao, Xian-Bin & Du, Wen-Bo & Rong, Zhi-Hai, 2010. "The evolutionary public goods game on scale-free networks with heterogeneous investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1273-1280.
    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. Julian Vicens & Nereida Bueno-Guerra & Mario Gutiérrez-Roig & Carlos Gracia-Lázaro & Jesús Gómez-Gardeñes & Josep Perelló & Angel Sánchez & Yamir Moreno & Jordi Duch, 2018. "Resource heterogeneity leads to unjust effort distribution in climate change mitigation," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-17, October.
    4. Fischbacher, Urs & Gachter, Simon & Fehr, Ernst, 2001. "Are people conditionally cooperative? Evidence from a public goods experiment," Economics Letters, Elsevier, vol. 71(3), pages 397-404, June.
    5. Flores, Lucas S. & Han, The Anh, 2024. "Evolution of commitment in the spatial public goods game through institutional incentives," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    6. Lv, Shaojie & Wang, Xianjia, 2020. "The impact of heterogeneous investments on the evolution of cooperation in public goods game with exclusion," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    7. Elinor Ostrom, 2000. "Collective Action and the Evolution of Social Norms," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 137-158, Summer.
    8. 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.
    9. Shen, Yong & Deng, Zixuan & Kang, Hongwei & Sun, Xingping & Chen, Qingyi, 2025. "The impact of tax-based rewards and mercenary punishment on public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    10. Zhang, Lan & Xie, Yuan & Huang, Changwei & Li, Haihong & Dai, Qionglin, 2020. "Heterogeneous investments induced by historical payoffs promote cooperation in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    11. Zhang, Yali & Lu, Yikang & Jin, Haoyu & Dong, Yuting & Du, Chunpeng & Shi, Lei, 2024. "The impact of dynamic reward on cooperation in the spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    12. Andreoni, James, 1995. "Cooperation in Public-Goods Experiments: Kindness or Confusion?," American Economic Review, American Economic Association, vol. 85(4), pages 891-904, September.
    13. Ding, Rui & Wang, Xianjia & Zhao, Jinhua & Gu, Cuiling, 2025. "Effects of punishment driven by inequity aversion on promoting cooperation in public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    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).
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