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 -