The evolutionary fairness dynamics on multiplex networks with information reliability and time delays

Abstract

This paper studies the fairness behavior of an ultimatum game played on multiplex networks from the perspective of stability and consensus, which enables us to gain more insights into large-scale complex systems, ranging from biology to behavioral sciences to economics, regarding the evolution of fairness and cooperative behavior. In addition to existing works, a more realistic and challenging scenario is considered, where the credit and response capacity of each player are not assumed identical, and the possible distortion or delay in the information transmission is taken into account. The conditions for the system to asymptotically achieve fairness in two cases are rigorously derived which show an inversely proportional relationship between the largest eigenvalue of the normalized supra-Laplacian matrix and the critical offer division ratio, and reveal the effect of information reliability and time delay on the convergence property of the overall system. The results of theoretical analysis are verified via extensive numerical examples in which an indicator called the fairness index is used to measure the evolution of fairness.