Abstract
We study how initial network structure affects the evolution of cooperation in a spatial prisoner's dilemma game. The network structure is characterized by various statistical properties. In those properties, we focus on the variance of degree distribution, and inquire how it affects the evolution of cooperation. Some interactions between the variance of degree distribution and other statistical properties such as degree correlation and cluster coefficient are investigated. Moreover we compare results of static networks with those of dynamical networks generated in a process of replacing links by natural selection. It is found that a scale-free network does not always promote the evolution of cooperation, and there exists an appropriate value of the variance, at which the cooperation progresses strongly. In addition, we find that the effects of degree correlation and cluster coefficient for the evolution of cooperation vary with different variances of degree distribution.
