A manipulator game model of urban public traffic network

Urban public traffic networks are typical complex systems. Understanding their evolution mechanism attracts much attention in recent years. Here, we propose that the evolution of urban public traffic network can be considered as a game process between two network manipulators, i.e., passengers and company, and the equilibrium solution to the game determines the steady-state behavior of the network. Both analytical solution and numerical simulations to such game model can well describe the empirical data collected from the urban public traffic systems in four Chinese cities (Beijing, Shanghai, Nanjing, and Hangzhou) and the Boston subway. Our results suggest that the manipulator game model grasps the fundamental characteristics of the evolution mechanism of the urban public traffic systems. Similar idea may be extended to other complex systems which have small number of manipulators.