Co-evolution of synchronization and cooperation with multi-agent Q-learning

Cooperation is a widespread phenomenon in human society and plays a significant role in achieving synchronization of various systems. However, there has been limited progress in studying the co-evolution of synchronization and cooperation. In this manuscript, we investigate how reinforcement learning affects the evolution of synchronization and cooperation. Namely, the payoff of an agent depends not only on the cooperation dynamic but also on the synchronization dynamic. Agents have the option to either cooperate or defect. While cooperation promotes synchronization among agents, defection does not. We report that the dynamic feature, which indicates the action switching frequency of the agent during interactions, promotes synchronization. We also find that cooperation and synchronization are mutually reinforcing. Furthermore, we thoroughly analyze the potential reasons for synchronization promotion due to the dynamic feature from both macro- and microperspectives. Additionally, we conduct experiments to illustrate the differences in the synchronization-promoting effects of cooperation and dynamic features.