Coevolution of synchronization and cooperation in real networks

As game theory thrives in networked interactions, we usually neglect the cost of information exchange between involved individuals. Individuals may decide (or refuse) to follow the state of their neighbors, which depends on the cost of the interactions. The payoff of a node's behavior is associated with the state difference between the node and its neighbors. Here, based on Kuramoto model, we investigate the collective behavior of different individuals in the game theory and the synchronization byproduct that is induced by the cooperation of connected nodes. Specially, we investigate the influence of network structure on the coevolutionary progress of cooperation and synchronization. We find that the networks with the higher average degree are more likely to reach synchronization in real networks. Strong synchronization is a sufficient, but not necessary condition to guarantee the cooperation. Besides, we show that synchronization is largely influenced by the average degree in both Erdos-Renyi (ER) and Barabasi-Albert (BA) networks, which is also illustrated by theoretical analysis.