Convergence properties of the heterogeneous Deffuant-Weisbuch model

TitleConvergence properties of the heterogeneous Deffuant-Weisbuch model
Publication TypeJournal Article
Year of Publication2020
AuthorsChen G, Su W, Mei W, Bullo F
Volume 114
Start Page108825
Date Published04/2020
KeywordsBounded confidence model, consensus, Deffuant model, Gossip model, opinion dynamics

The Deffuant–Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence properties, easy to observe numerically, are only conjectures.

This paper solves the convergence problem for the heterogeneous DW model with the weighting factor not less than . We establish that, for any positive confidence bounds and initial values, the opinion of each agent will converge to a limit value almost surely, and the convergence rate is exponential in mean square. Moreover, we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents. Finally, we provide some sufficient conditions for the heterogeneous DW model to reach consensus.

Refereed DesignationRefereed