Bounded confidence dynamics and graph control: Enforcing consensus

Guan Lin Li, Sebastien Motsch, Dylan Weber

Research output: Contribution to journalArticlepeer-review

Abstract

A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics which we name the No one left behind dynamics is the introduction of a local control on the agents which preserves the connectivity of the interaction network. We rigorously demonstrate that these dynamics result in unconditional convergence to a consensus. The qualitative nature of our argument prevents us quantifying how fast a consensus emerges, however we present numerical evidence that sharp convergence rates would be challenging to obtain for such dynamics. Finally, we propose a relaxed version of the control. The dynamics that result maintain many of the qualitative features of the bounded confidence dynamics yet ultimately still converge to a consensus as the control still maintains connectivity of the interaction network.

Original languageEnglish (US)
Pages (from-to)489-517
Number of pages29
JournalNetworks and Heterogeneous Media
Volume15
Issue number3
DOIs
StatePublished - Sep 1 2020

Keywords

  • Agent-based models
  • Complex networks
  • Connectivity
  • Directed graphs
  • Distributed control
  • Opinion dynamics

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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