  We studied synchronization between prisoner's dilemma games with voluntary
participation in two Newman-Watts small-world networks. It was found that there
are three kinds of synchronization: partial phase synchronization, total phase
synchronization and complete synchronization, for varied coupling factors.
Besides, two games can reach complete synchronization for the large enough
coupling factor. We also discussed the effect of coupling factor on the
amplitude of oscillation of $cooperator$ density.
