Spatial public goods game on hypergraphs with particle swarm intelligence

Particle swarm optimization (PSO) has emerged as a powerful tool in evolutionary game theory, particularly for enhancing cooperation in spatial public goods games (PGGs). While existing research often focuses on one-on-one pairwise interactions, the role of PSO in fostering cooperation under many-body interactions on hypergraphs remains unexplored. Here, we extend spatial PGGs to uniform random hypergraphs (URHs) with tunable group sizes and integrate the PSO algorithm into evolutionary dynamics for agents to adapt their strategies. We consider two scenarios for the PSO, one in which cognitive component and social learning are interdependent, and the other where they are independent. We find that in the former case, PSO can promote cooperation over a larger parameter range compared to the Fermi strategy updating rule. Moreover, larger groups are more effective in promoting cooperation on URHs, enabling the population to reach a high level of cooperation. Notably, combining smaller self-cognitive adjustments with larger social influences can significantly enhance cooperation. Furthermore, in the independent case where the constraint between individual and social learning weights is relaxed, cooperation could be optimized with environment-dependent parameter settings. In particular, individual learning buffers cooperators in harsh environments, while social learning accelerates cooperation in favorable conditions. Our research underscores the effectiveness of PSO in addressing social dilemmas and advances the understanding of the interaction between individual learning and social learning in complex networked systems.