Continuous-time Discontinuous Equations in Bounded Confidence Opinion Dynamics

TL;DR

This paper investigates a continuous-time bounded confidence opinion dynamics model with discontinuous equations, analyzing solutions' existence, convergence to opinion clusters, and robustness to perturbations.

Contribution

It introduces a continuous-time formulation of the Hegselmann-Krause model with discontinuities and provides analysis on solution properties and stability of opinion clusters.

Findings

Solutions exist and are complete.

Opinions asymptotically cluster into stable groups.

Clusters are robust to small perturbations.

Abstract

This report studies a continuous-time version of the well-known Hegselmann-Krause model of opinion dynamics with bounded confidence. As the equations of this model have discontinuous right-hand side, we study their Krasovskii solutions. We present results about existence and completeness of solutions, and asymptotical convergence to equilibria featuring a "clusterization" of opinions. The robustness of such equilibria to small perturbations is also studied.