Effect of Growing Size of Interaction Neighbors on the Evolution of Cooperation in Spatial Snowdrift Game

In this paper, we study the influence of the size of interaction neighbors (k) on the evolution of cooperation in the spatial snowdrift game. At first, we consider the effects of noise K and cost-to-benefit ratio r, the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio. For a lower r, the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise. However, for a higher r, the defectors account for the majority of the game and dominate the game if the noise is large enough. Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail. We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r. In the case of lower r, the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4, while for higher r the cooperation is improved for a growing size of neighborhood. At last, based on the above discussions, we explore the cluster-forming mechanism among the cooperators. The current results are beneficial to further understand the evolution of cooperation in many natural, social and biological system