Coevolution of agent’s behavior and noise parameters in majority vote game on multilayer networks

Abstract

In many real-world systems, agents’ behaviors are usually coupled with environmental changes. To model their coevolutionary process, we study a non-equilibrium model known as majority vote model coupled with reaction-diffusion processes on a two-layer multiplex network. The dynamics of the noise parameter in noise layer is related to the voting behavior and represents the increase and decrease of social tension in the context of social dynamics. We perform Monte Carlo simulations and finite-size scaling analysis in order to investigate the statistical behavior of the model. It is interesting to find that our coupling mechanism induces a continuous order–disorder phase transition on random regular graphs, but the critical phenomenon disappears on square lattices. Besides, switching from one sign of the spontaneous magnetization to the opposite is also observed near the critical region. Given specific parameters, the system may self-organize to a critical state from any initial conditions. In addition, a mean-field method is developed to study the properties of the phase transition analytically and the solutions are in good agreement with our numerical results qualitatively.