How the weak and strong links affect the evolution of prisoner's dilemma game

The complex interactions between individuals are intertwined with time in multilayer networks. In this paper, we propose a prisoner's dilemma game on a two-layered network, including the weak-link layer and the strong-link layer. Based on the mean-field theory and numerical simulations, we show that if the players update their strategies primarily depending on the information received in the weak-link layer, i.e. the weak relations have the dominate influences on the individuals' strategies choice, the cooperation becomes the most abundant strategy. More comparative analysis of the different structures on the strong-link layer indicates that a higher connectivity heterogeneity of the strong-link layer could be conducive to promote the individuals' cooperation behavior. In the situation while the relation between the players' connections in the strong-link layer and their activity rates in the weak-link layer is negative correlated, i.e. ones' connections increase with the decrease of their activity rates, the propensity for cooperation can be greatly enhanced. (paper)