Evolutionary dynamics of the cooperation clusters on interdependent networks

Abstract

In this article, the evolutionary dynamics of cooperation (defection) clusters on interdependent networks is studied. The emergence of spatial structures and distributions of strategy clusters have important influence on the cooperative behaviors. Different from the existing works, we focus on the effect of the structure of interdependent networks on the dynamics of strategy clusters. In order to reveal the co-evolution of game strategies and interdependent structure, the interdependent strength is taken as a kind of limited resources, which can be reallocated among players along with the game process but keep the total quantity unchanged. Through quantitative and qualitative analysis, we find that cooperation clusters are considerably affected by the overall interdependent strength of dynamical system as well as the strategy distributions on two layers. Furthermore, the size of the largest cooperation cluster is related to the kind of strategy pairs. By studying the interdependent strength among clusters, we find that larger clusters have stronger resource concentration ability. At the same time, players with more resources tend to be more cooperative. We also discuss the related microscopic system properties and demonstrate the related discussion by various analysis tools.