Impact of binary social status with hierarchical punishment on the evolution of cooperation in the spatial prisoner’s dilemma game

Abstract Since ancient times, people have lived in a hierarchical society. In this paper, we consider a simple hierarchical society with disadvantaged group and powerful group(i.e. the binary social status). The ability for powerful group is reflected to be a punisher, and this privilege cannot be imitated by the disadvantaged agent. On this base, the theory of asymmetric evolutionary game with hierarchical punishment is extend. And its impact on the evolution of cooperation is studied. The simulation results show that the hierarchical punishment with square lattices connection can promote the cooperation. Specifically, there is a reverse phenomenon of the cooperation for different social fines with the increasing temptation. Interestingly, the living cooperators survive not only by forming clusters, but also by attaching to the punishers. There is an optimal initial fraction of the powerful group for the excitation of cooperation. The cooperation on the island of powerful agents reveal that the influence range of the punitive right is limited, but the powerful agent squint towards this special right. Taken together, we deeply study the mechanism of the hierarchical punishment to the cooperation. The new recognitions may provide some novel perspectives for engineering better social systems.