  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.
