On the Termination Time of the One-Sided Asymmetric Hegselmann-Krause Dynamics

In this paper, we provide a novel upper bound for the termination time of the one-dimensional asymmetric Hegselmann-Krause dynamics, when the asymmetry is one-sided. In addition to the number of agents, our upper bound depends on the ratio of asymmetry and the confidence range in the opinions of agents, and recovers the known O(n(3)) results of the symmetric case. Our proof technique relies on a novel Lyapunov-like function, which measures the spread of the opinion profile. As a by-product, we fully characterize the switching pattern in the opinions of the agents.