The evolution of cooperation and global synchronization in the evolutionary Kuramoto dilemma combined with the prisoner's dilemma

Abstract

In this work, we have studied the evolution of the cooperation and the global synchronization on the Kuramoto model upon random networks with two games, in which one is the evolutionary Kuramoto dilemma and the other is the weak prisoner's dilemma. Agents can gain their payoffs from these two games synchronously. In the evolutionary Kuramoto game, cooperators prefer the formation of local synchronization but pay less cooperative cost. Cooperators in weak prisoner's dilemma can form cooperator clusters because of the network reciprocity. Combining these two games shows a mutual promotion effect upon the order of the global synchronization but a competition effect on the cooperation level. The global synchronization begins to rise only when most agents choose cooperation. It is manifested by the fact that the optimal coupling strength for the highest cooperation level is smaller than that for the highest synchronization level. The high cooperation cost makes defection the most advantageous strategy when the coupling strength reaches rather high, which diminishes the effect of cooperator clusters, and ultimately results in the absence of both cooperators and global synchronization. When agents have more neighbors in the random network, it is observed that cooperation is consistently hindered unless the coupling strength is relatively small. Additionally, there is always an optimal average degree that allows for global synchronization.