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

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.

Citation
Haskovec, J., & Rodriguez Cartabia, M. (2023). Optimal condition for asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation. Proceedings of the American Mathematical Society. Portico. https://doi.org/10.1090/proc/16482

Publisher
American Mathematical Society (AMS)

Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI
10.1090/proc/16482

arXiv
2303.07140

Additional Links
https://www.ams.org/proc/0000-000-00/S0002-9939-2023-16482-5/

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2023-06-06 06:56:37
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