The impact of dynamic hyperedge activation mechanism on the evolution of cooperation on hypergraphs

Extensive studies have been conducted on the activation mechanisms of game groups in complex networks characterized by pairwise interactions. However, these studies are insufficient to accurately capture the higher-order interaction scenarios in real-world systems. Therefore, we propose a continuous-strategy public goods game implemented on uniformly random hypergraphs, where the hyperedge activation function is determined by the hyperedge investment (denoted by α) and the baseline activation probability (denoted by β). Subsequently, the groups are categorized into three types (moderate, radical, and conservative) based on the value of the shape parameter δ in the hyperedge activation function. Additionally, the particle swarm optimization algorithm is adopted to update the strategies of agents. Simulation results demonstrate that the introduction of the hyperedge activation mechanism improves the cooperation level compared with the baseline model in which all hyperedges are consistently activated. Notably, when the group is radical, the cooperation level exhibits a non-monotonic relationship with the baseline activation probability β when reduced synergy factor r is small; when the group is conservative, the cooperation level demonstrates a non-monotonic relationship with the shape parameter δ at intermediate values of r. Moreover, we find that the individual learning weight in the particle swarm optimization algorithm exerts a non-monotonic influence on the cooperation level under certain parameter combinations.