Opinion dynamics in multi-agent systems: selected analytic models and verifying simulations

Abstract

In this paper opinion dynamics in multi-agent systems is investigated analytically using a kinetic approach. Interactions among agents are interpreted as collisions among molecules in gases and opinion dynamics is described according to the Boltzmann equation. Starting from a microscopic description of single interactions, global properties of the opinion distribution are derived analytically. The proposed analytic model is general enough to allow reproducing features of real societies of agents, such as positive and negative influences and bounded confidence, which are typically used to study opinion distribution models. Analytic results relative to emergent and global characteristics of considered multi-agent systems are verified by simulations obtained via direct implementation of the proposed microscopic interactions rules. Simulations confirm analytic results.