The evolutionary ultimatum game on multiplex networks

As a comprehensive theoretical framework to investigate the strategic choice in complex systems, evolutionary games on multilayer networks or networks of networks have recently gained increasing attention. Previous works have been devoted to investigate the evolutionary game on multilayer networks, but concentrated mainly on the evolution of cooperation. Thus, the purpose of this paper is to explore the evolution of fairness in the ultimatum game which is played on multiplex networks. It is found that the largest supra-Laplacian eigenvalue of the multiplex network almost determines the critical division of offers, once beyond which the costly punishment will emerge within the game and the whole network system is not fair. Considerable numerical experiments on computer-generated multiplex networks support the theoretical analysis findings. Furthermore, the number of layers of multiplex also affect the evolutionary results of the game, and by choosing appropriate interlayer connection strength players can avoid overly lavish while the system is still fair.