Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner's Dilemma Game

In the research realm of game theory, interdependent networks have extended the content of spatial reciprocity, which needs the suitable coupling between networks. However, thus far, the vast majority of existing works just assume that the coupling strength between networks is symmetric. This hypothesis, to some extent, seems inconsistent with the ubiquitous observation of heterogeneity. Here, we study how the heterogeneous coupling strength, which characterizes the interdependency of utility between corresponding players of both networks, affects the evolution of cooperation in the prisoner's dilemma game with two types of coupling schemes (symmetric and asymmetric ones). Compared with the traditional case, we show that heterogeneous coupling greatly promotes the collective cooperation. The symmetric scheme seems much better than the asymmetric case. Moreover, the role of varying amplitude of coupling strength is also studied on these two interdependent ways. Current findings are helpful for us to understand the evolution of cooperation within many real-world systems, in particular for the interconnected and interrelated systems.