How the intimate relationship affects the individuals' behaviors in a two-layer network

Abstract

Game theories could help us to understand the origin of the emergence and persistence of cooperation among selfish individuals. Considering the intimate relationship among individuals, we study the prisoner's dilemma (PD) game in a two-layer network. Firstly, we calculate the closeness between any two players according to their connectivity. Further, we define and obtain one's comprehensive income index according to the different income values obtained by individuals in the two-layer network. Then, we formulate the mechanism of individual strategy change. Finally, we analyze the influence of different parameters on individual strategy change through numerical simulation results. Our results show that the heterogeneous network structure is more conducted to cooperation, but it takes a long time for the whole system to reach a stable state. With the increase of the measure coefficient θ, when the two-layer networks are, respectively, the BA scale-free network and ER random network, the final increase rate of cooperator's density in the whole system is the fastest.