Effects of higher-order interactions on the evolution of cooperative behavior in hyperbolic scale-free network

This study proposes an innovative hypergraph model to explore the effects of higher-order interactions on the evolution of cooperative behavior in a hyperbolic scale-free network. By adjusting the heterogeneity coefficient and clustering coefficient of the hyperbolic scale-free network, four distinct network structures with notable differences can be obtained. We then map pairwise and three-way interactions to 2-hyperedges and 3-hyperedges, constructing a hypergraph model with higher-order interactions. Our findings reveal that when the proportion of three-way interactions exceeds a critical threshold, cooperative tendencies exhibit explosive growth, leading to a bistable phenomenon of coexisting cooperation and defection. The system's average degree significantly influences the critical mass of initial cooperators needed to maintain stable cooperative behavior. The network structure shows complex, non-linear effects on cooperation. In low-conditions, increasing heterogeneity acts to suppress the appearance of bistable phenomena, while in high clustering conditions, it acts to promote. Increasing clustering tends to suppress the appearance of bistable phenomena in both low and high heterogeneity conditions. Furthermore, the effects of heterogeneity, clustering, and noise factors on cooperation are non-monotonic, exhibiting inverted U-shaped patterns with critical transition points. These findings provide new theoretical perspectives for understanding diverse cooperation patterns in real-world scenarios and suggest the need for dynamic, context-specific approaches when designing strategies to promote cooperation.