Effects of Empty Sites on Cooperation in the Prisoner’s Dilemma Game Based on Social Diversity

We study the effects of empty sites in the prisoner’s dilemma game based on social diversity by introducing some empty sites into a square lattice. The results reveal that the empty sites dramatically enhance the cooperation level for a wide range of temptation to defection values if two types of players coexist. By calculating the chances of different type-combinations of the players located on the square lattice, we find that there is an intermediate region where five social ranks are induced to satisfy the certain rank distributions and the cooperation level is significantly enhanced. Moreover, simulation results also show that the moderate gaps among the social ranks can favor cooperation for a larger occupation density. 1. Introduction Cooperation is fundamental to biological and social systems. Thus, it is a crucial issue to find and understand what kinds of factors facilitate cooperation. Over the past decades, various versions of evolutionary games have been studied extensively to explore the possibilities for enhancing the cooperative behavior among selfish individuals. Consequently, different mechanisms, for example, kin selection [1], direct [2] and indirect [3] reciprocity, spatial reciprocity [4], voluntary participation [5], and chaotic variations to the payoffs [6], are found to urge the emergence of cooperative behavior in biological systems as well as within human societies [7]. Among all the above mechanisms, the spatial reciprocity has not become an active and important topic until Nowak and May [8] introduced their seminal theoretical mechanism about game and spatial chaos. In recent years, topological inhomogeneities have been introduced to promote the level of cooperation [9–13]. Some investigations suggested that complex networks were beneficial for the evolution of cooperation if its connectivity structure was similar to that of social networks [14–18]. Besides the topological inhomogeneities, inhomogeneities of individual personality have also been introduced [19, 20], because of the fact that inhomogeneities of individual personality are the common features of society. Several authors have reported that some distinguished players have the stronger capacities to spread their own strategies, resulting in the thriving of cooperation when the system consists of two types of players with asymmetric teaching and learning activities [21–27]. For example, Droz et al. [21] suggested that the cooperation could be greatly enhanced if there was a relevant difference of the strategy transfer capability between the influential players and