  Recently, Antonioni and Cardillo proposed a coevolutionary model based on the
intertwining of oscillator synchronization and evolutionary game theory [Phys.
Rev. Lett. \textbf{118}, 238301 (2017)], in which each Kuramoto oscillator can
decide whether to interact-or not-with its neighbors, and all oscillators can
receive some benefits from the local synchronization but those who choose to
interact must pay a cost. Oscillators are allowed to update their strategies
according to payoff difference, wherein the strategy of an oscillator who has
obtained higher payoff is more likely to be followed. Utilizing this
coevolutionary model, we find that the global synchronization level reaches the
highest level when the average degree of the underlying interaction network is
moderate. We also study how synchronization is affected by the individual
rationality in choosing strategy.
