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Threshold-initiated spatial public goods games

Author

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  • 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
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    References listed on IDEAS

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    1. 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).
    2. 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).
    3. 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).
    4. 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).
    5. 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).
    6. Pi, Jinxiu & Wang, Chun & Cai, Jin & Tang, Wei, 2026. "Reputation-based strategy persistence and environmental feedback promote cooperation in spatial snowdrift games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).

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