Abstract
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.
Highlights
Cooperation behavior is ubiquitous among social individuals ranging from micro-organisms to animals and human beings [1, 2], which, seems inconsistent with the prediction of Darwinian theory [3]
Since the larger A denotes stronger interdependence heterogeneity between networks, the observations suggest the consideration of both heterogeneous coupling promotes the evolution of cooperation, which further extends the content of interdependent network reciprocity [64]
In case II, the interdependency values between each pair of players are independently taken from the uniform interval [-A, A], and the utility will be asymmetrically calculated and it is difficult to arrive at the coordination state
Summary
Cooperation behavior is ubiquitous among social individuals ranging from micro-organisms to animals and human beings [1, 2], which, seems inconsistent with the prediction of Darwinian theory [3]. To resolve this issue, evolutionary game theory has become one of key paradigms behind many scientific disciplines [4, 5]. That is to say, when players are arranged on the spatially structured topology and interact only with their direct neighbors, cooperation can survive by means of forming compact clusters, which minimizes the exploitation and protect those cooperative individuals located within the interior of such clusters [13] After this seminal discovery, the role of spatial topology and its various.
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