Social hierarchy is important that cannot 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 Barabási–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.

社会等级制度很重要，在人类的社会经济活动和动物界中不可忽视。在这里，我们将这个因素纳入进化博弈中，以了解它可能对合作成果产生什么影响。那么，两个参与者之间概率策略的采用不仅取决于他们的收益，还取决于他们的等级差异-高级别的参与者比低级别的伙伴更有可能重现其策略。通过模拟具有三个层次分布的囚徒困境博弈的演化，我们发现在所有情况下合作水平都得到了提高，而在统一情况下合作水平是最佳的。增强归因于以下事实：等级制度的存在促进了以高级参与者为核心的合作集群的形成。这种机制在Barabási-Albert无标度网络上仍然有效，特别是当中心的社会地位较高时，合作增强最大。我们还研究了两层模型，其中揭示了类似的合作促进，并提供了一些理论分析。我们的发现可能部分解释了为什么社会等级制度在这个星球上如此普遍。