An overview of kinetic approaches to study consensus formation

This paper discusses some recent results in the study of opinion dynamics and consensus formation in multi-agent systems. While results in these fields are typically obtained by simulation, the adoption of the approach inspired by kinetic theory of gases allows deriving analytic results. More precisely, analytic relationships between the parameters of the model and the asymptotic characteristics of the systems can be analytically determined. Various models inspired from kinetic theory of gases have been studied. For instance, different microscopic phenomena can be investigated, such as compromise and diffusions, and both deterministic and stochastic parameters have been used to model such phenomena. Recently, models inspired from kinetic theory of gas mixtures have also been introduced in the context of opinion dynamics. Such models allow studying multi-agent systems in which different classes of agents coexist. Agents belonging to different classes may be associated with different features, such as the initial distribution of the opinion and the propensity of agents to change their opinions when interacting with other agents. A discussion on the features of different models is presented in this paper.