A Particle Method for Continuous Hegselmann-Krause Opinion Dynamics

We derive a differential-integral equation akin to the Hegselmann -Krause model of opinion dynamics [R. Hegselmann and U. Krause, JASSS, vol. 5, 2002], and propose a particle method for solving the equation. Numerical experiments show second-order weak convergence of the method. We also show that our differential-integral equation can equivalently be stated as a system of differential equations. An integration-by-parts argument that would typically yield an energy dissipation inequality in physical problems yields a concentration inequality here, showing that a natural measure of concentration increases monotonically.