Evolutionary Games on Weighted Newman–Watts Small-World Networks

Abstract

We investigate the evolutionary prisoner's dilemma game (PDG) on weighted Newman–Watts (NW) networks. In weighted NW networks, the link weight wij is assigned to the link between the nodes i and j as: wij = (κi · κj)β, where κi(κj) is the degree of node i(j) and β represents the strength of the correlations. Obviously, the link weight can be tuned by only one parameter β. We focus on the cooperative behavior and wealth distribution in the system. Simulation results show that the cooperator frequency is promoted by a large range of β and there is a minimal cooperation frequency around β = – 1. Moreover, we also employ the Gini coefficient to study the wealth distribution in the population. Numerical results show that the Gini coefficient reaches its minimum when β ≈ – 1. Our work may be helpful in understanding the emergence of cooperation and unequal wealth distribution in society.