Analytic study of opinion dynamics in multi-agent systems with two classes of agents

This paper describes a model for opinion dynamics in multi-agent systems composed of two classes of agents. Each class is characterized by distinctive values of the parameters that govern opinion dynamics. The proposed model is inspired by kinetic theory of gases, according to which macroscopic properties of gases are described starting from microscopic interactions among molecules. By interpreting agents as molecules of gases, and their interactions as collisions among molecules, the equations that govern kinetic theory can be reinterpreted to model opinion dynamics in multi-agent systems. A key feature of the adopted kinetic-based approach is that it allows macroscopic properties of the system to be derived analytically. In order to take into account that the considered multi-agent system is composed of two classes of agents, kinetic theory of gas mixtures, which deals with gases composed of different kinds of molecules, is adopted. Presented results show that consensus is reached after a sufficiently large number of interactions, which depends on the parameters associated with the two classes of agents.