Work

Threshold-based punishment mechanism in evolutionary public goods games on random hypergraphs

Year: 2025

Type: article

Abstract: Free-rider behaviors severely hinder the maintenance of cooperation in public goods games, yet existing mechanisms for curbing such behaviors often overlook the punishment triggered by higher-order interactions. To address this gap, we introduce an evolutionary public goods game on hypergraphs, where individuals interact through hyperedges (groups) and a conditional punishment mechanism is activated when the number of defectors within a group exceeds a predefined threshold $\phi$. Once triggered, defectors retain only a fraction $\beta$ of their original payoff, while cooperators benefit from the redistributed penalties. We derive exact theoretical critical points for reduced synergy factors governing the emergence and saturation of cooperation on uniform random hypergraphs. Specifically, lower thresholds enable cooperation to emerge at a critical reduced synergy factor inversely proportional to the group size $g$ and punishment intensity $\beta$. Conversely, higher thresholds impede cooperation by raising both critical points to 1. Furthermore, introducing heterogeneity in group size, threshold, or punishment intensity amplifies cooperation compared to homogeneous settings. By integrating higher-order interactions, threshold-based punishment, and structural heterogeneity into a unified analytical framework, this work provides new insights for designing robust cooperation-promoting mechanisms in complex systems beyond pairwise networks.

Source: Chaos Solitons & Fractals

DOI: 10.1016/j.chaos.2025.117031

Authors: Jiliang Zhang, Yuhang Wang, Yinzuo Zhou, Yi-Cheng Zhang, Fanyuan Meng

Institutions: Hangzhou Normal University, Beihang University

Language: English

Topic: Evolutionary Game Theory and Cooperation

Subfield: Sociology and Political Science

Field: Social Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,970