2024/09/03 by Ge Chen, Chen, Ge, Wei Su +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Probability (math.PR) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2409.01593
openalex publication_date 2024/09/03 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28
The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over 20 years, its convergence proof is open. Our previous paper \citeGC-WS-WM-FB:20 solves the problem for the case of uniform weighting factors greater than or equal to 1/2, but the general case remains unresolved. This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions.