TY - JOUR
T1 - OPTIMAL CONDITION FOR ASYMPTOTIC CONSENSUS IN THE HEGSELMANN-KRAUSE MODEL WITH FINITE SPEED OF INFORMATION PROPAGATION
AU - Haskovec, Jan
AU - Cartabia, Mauro Rodriguez
N1 - KAUST Repository Item: Exported on 2023-06-07
PY - 2023/5/12
Y1 - 2023/5/12
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/690394
UR - https://www.ams.org/proc/0000-000-00/S0002-9939-2023-16482-5/
U2 - 10.1090/proc/16482
DO - 10.1090/proc/16482
M3 - Article
SN - 1088-6826
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
ER -