Hegselmann–Krause model with environmental noise
- Authors: Li Chen, Paul Nikolaev, David J. Prömel
- Preprint year: 2023
- First public date: 2023-01-10
- arXiv: 2301.03955
- Status: Published
- Publication type: Journal article
- Publication year: 2025
- Journal: Transactions of the American Mathematical Society 378(1) (2025)
- DOI: 10.1090/tran/9289
Abstract
We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle system with a non-Lipschitz continuous interaction force, perturbed by idiosyncratic and environmental noises. Sending the number of agents to infinity, we derive a McKean-Vlasov stochastic differential equation as the limiting dynamic, by establishing propagation of chaos for regularized versions of the noisy opinion dynamics. To that end, we prove the existence of a unique strong solution to the McKean-Vlasov stochastic differential equation as well as well-posedness of the associated non-local, non-linear stochastic Fokker-Planck equation.