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We prove that asymptotic global consensus is always reached in theHegselmann-Krause model with finite speed of information propagation$\mathfrak{c}>0$ under minimal (i.e., necessary) assumptions on the influencefunction. In particular, we assume that the influence function is globallypositive, which is necessary for reaching global consensus, and such that theagents move with speeds strictly less than $\mathfrak{c}$, which is necessaryfor well-posedness of solutions. From this point of view, our result isoptimal. The proof is based on the fact that the state-dependent delay, inducedby the finite speed of information propagation, is uniformly bounded.

Optimal condition for asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation