OPTIMAL CONDITION FOR ASYMPTOTIC CONSENSUS IN THE HEGSELMANN-KRAUSE MODEL WITH FINITE SPEED OF INFORMATION PROPAGATION

Jan Haskovec, Mauro Rodriguez Cartabia

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation c > 0 under minimal (i.e., necessary) assumptions on the influence function. In particular, we assume that the influence function is globally positive, which is necessary for reaching global consensus, and such that the agents move with speeds strictly less than c, which is necessary for well-posedness of solutions. From this point of view, our result is optimal. The proof is based on the fact that the state-dependent delay, induced by the finite speed of information propagation, is uniformly bounded.
Original languageEnglish (US)
JournalProceedings of the American Mathematical Society
DOIs
StatePublished - May 12 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-06-07

ASJC Scopus subject areas

  • Applied Mathematics
  • General Mathematics

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