Preferential selection based on degree difference in the spatial prisoner's dilemma games

Strategy evolution in spatial evolutionary games is generally implemented through imitation processes between individuals. In most previous studies, it is assumed that individuals pick up one of their neighbors randomly to learn from. However, by considering the heterogeneity of individuals' influence in the real society, preferential selection is more realistic. Here, we introduce a preferential selection mechanism based on degree difference into spatial prisoner's dilemma games on Erdös-Rényi networks and Barabási-Albert scale-free networks and investigate the effects of the preferential selection on cooperation. The results show that, when the individuals prefer to choose the neighbors who have small degree difference with themselves to imitate, cooperation is hurt by the preferential selection. In contrast, when the individuals prefer to choose those large degree difference neighbors to learn from, there exists optimal preference strength resulting in the maximal cooperation level no matter what the network structure is. In addition, we investigate the robustness of the results against variations of the noise, the average degree and the size of network in the model, and find that the qualitative features of the results are unchanged