Edvin Wedin

Peter Hegarty, Anders Martinsson, Edvin Wedin

We consider the Hegselmann-Krause dynamics on a one-dimensional torus and provide the first proof of convergence of this system. The proof requires only fairly minor modifications of existing methods for proving convergence in Euclidean space.

Edvin Wedin, Peter Hegarty

Let f_{k}(n) be the maximum number of time steps taken to reach equilibrium by a system of n agents obeying the k-dimensional Hegselmann-Krause bounded confidence dynamics. Previously, it was known that Ω(n) = f_{1}(n) = O(n^3). Here we show that f_{1}(n) = Ω(n^2), which matches the best-known lower bound in all dimensions k >= 2.