An analytic study of opinion dynamics in multi-agent systems with additive random noise

In this paper we analytically derive macroscopic properties of the temporal evolution of opinion distribution in multi-agent systems under the influence of additive random noise. Proper rules which describe how the opinion of agents are updated after their interactions are given. Such rules involve a deterministic part, related to compromise, and a stochastic part, in terms of an additive random noise. Starting from the microscopic interaction rules among agents, macroscopic properties of the system are derived using an approach based on kinetic theory of gases. In particular, the stationary profiles of opinion distribution are derived analytically. In the last part of the paper, some illustrative examples of stationary profiles are presented