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Social hierarchy is important that can not be ignored in human socioeconomicactivities and in the animal world. Here we incorporate this factor into theevolutionary game to see what impact it could have on the cooperation outcome.The probabilistic strategy adoption between two players is then not onlydetermined by their payoffs, but also by their hierarchy difference -- playersin the high rank are more likely to reproduce their strategies than the peersin the low rank. Through simulating the evolution of Prisoners' dilemma gamewith three hierarchical distributions, we find that the levels of cooperationare 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 facilitatesthe formation of cooperation clusters with high-rank players acting as thenucleation cores. This mechanism remains valid on Barab\'asi-Albert scale-freenetworks, in particular the cooperation enhancement is maximal when the hubsare of higher social ranks. We also study a two-hierarchy model, where similarcooperation promotion is revealed and some theoretical analyses are provided.Our finding may partially explain why the social hierarchy is so ubiquitous onthis planet.

Social hierarchy promotes the cooperation prevalence