Co-evolution of cooperation and limited resources on interdependent networks

摘要

In this article, based on interdependent networks, cooperation in spatial prisoner's dilemma game (PDG) with coevolving resources is studied. By means of a strategy-independent rule, limited resources can be continually re-allocated among different players in the same network or across different networks. The coevolution of dynamics is discussed respectively for two cases: game circumstances on two coupled networks are identical or asymmetry. In the first case, we obtain that the involvement of resources can be significantly beneficial for cooperative behaviors, and the heterogeneous distribution of resources can positively enhance interdependent network reciprocity. Furthermore, an optimal value (ρ ≈ 0.8) of the interdependent strength exists for cooperation, which is obviously larger than the previous results (ρ ≈ 0.5) without coevolving resources. Besides, we also find resources follow the power law distribution, where cooperators and interconnected players tend to obtain more resources. In the second case, we mainly focus on the flow of resources between networks as well as the intertwined effect of the interdependent strength and resources distribution on cooperation. Microscopic dynamical properties of the flow of resources jointly caused by various factors have been discussed. In certain conditions, instead of promoting the cooperation, the influx of resources could even be positive for defection.