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Effects of dynamic probabilistic punishment with environmental threshold on cooperation in spatial public goods games

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  • Li, Chanchan
  • Yang, Guanghui
  • Jia, Wensheng

Abstract

This study develops an dynamic probabilistic punishment mechanism for spatial public goods games by introducing a threshold-based regulatory framework. The mechanism dynamically adjusts punishment probability based on collective cooperation levels, mirroring how environmental agencies adjust monitoring efforts according to pollution levels. When cooperation drops below a predefined threshold, the system enters a high-alert mode with stronger punishment. When cooperation remains above the threshold, the system stays in a normal mode with weaker punishment. Through simulations, we reveal three key findings. First, higher environmental thresholds consistently lead to higher cooperation levels. Second, increasing punishment fines effectively promotes cooperative behavior. Third, in structured populations, evolutionarily stable strategies and payoff distributions tend to form clustered patterns. These results demonstrate how adaptive institutional responses can effectively address social dilemmas through self-organized behavioral regulation.

Suggested Citation

  • Li, Chanchan & Yang, Guanghui & Jia, Wensheng, 2025. "Effects of dynamic probabilistic punishment with environmental threshold on cooperation in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012159
    DOI: 10.1016/j.chaos.2025.117202
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