Abstract
In the present study, we investigate how the initial network structure affects the evolution of cooperation in the spatial prisoner's dilemma game. Previous studies have reported that a scale-free network promotes the evolution of cooperation. However, the dependency of the shape of the degree distribution on the evolution has not been investigated systematically. In the present paper, the evolution of cooperation on scale-free networks having different power-law exponents is investigated numerically. We demonstrate that a scale-free network does not always promote the evolution of cooperation and that there exists an appropriate structure at which the cooperation becomes stronger. In addition, we consider the reason for the existence of such structure using the fixation probability.
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