Social hierarchy promotes the cooperation prevalence

Social hierarchy is important that can not be ignored in human socioeconomic activities and in the animal world. Here we incorporate this factor into the evolutionary game to see what impact it could have on the cooperation outcome. The probabilistic strategy adoption between two players is then not only determined by their payoffs, but also by their hierarchy difference -- players in the high rank are more likely to reproduce their strategies than the peers in the low rank. Through simulating the evolution of Prisoners' dilemma game with three hierarchical distributions, we find that the levels of cooperation are enhanced in all cases, and the enhancement is optimal in the uniform case. The enhancement is due to the fact that the presence of hierarchy facilitates the formation of cooperation clusters with high-rank players acting as the nucleation cores. This mechanism remains valid on Barab\'asi-Albert scale-free networks, in particular the cooperation enhancement is maximal when the hubs are of higher social ranks. We also study a two-hierarchy model, where similar cooperation promotion is revealed and some theoretical analyses are provided. Our finding may partially explain why the social hierarchy is so ubiquitous on this planet.