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

Chanchan Li, Guanghui Yang and Wensheng Jia

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

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.

Keywords: Spatial public goods game; Dynamic probabilistic punishment; Environmental threshold; Cooperation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012159

DOI: 10.1016/j.chaos.2025.117202

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