Cooperation dynamics on hypergraphs with punishment and Q-learning

Punishment has been proved to be a useful mechanism on pairwise interaction networks for promoting cooperation. However, these networks cannot effectively describe higher-order interactions in the multi-agent system, while hypergraph as a higher-order network has aroused extensive interests of researchers. Here, we study the evolutionary dynamics of spatial public goods game on uniform random hypergraphs with peer punishment mechanism. In that model, each agent chooses to become a cooperator, defector or punisher, and each punisher pay a cost to make each defector bear a fine. Different from the imitation rules in previous studies, we adopt self-regarding Q-learning algorithm to update agent’s strategy where agents take an action based on their historical experience to maximize their reward. Simulation results show that there is a moderate synergy factor can obtain the best result of the evolution of cooperation. For a certain relatively large synergy factor, there exists a combination of cost and fine to optimally promote cooperation. Furthermore, the theoretical analysis results are consistent with the simulation results.