Multiagent Opinion Dynamics of Bounded Confidence with Nonlocal Aggregative Interaction

Abstract

In this paper, we propose nonlocal aggregative opinion interactions for a bounded-confidence opinion model to demonstrate the fluctuation mechanism, and then study this opinion fluctuation mechanism by both theoretical analyses and numerical simulations. In this proposed agent-based opinion model, there are stubborn agents and regular agents: while each stubborn agent never changes its opinion, a regular agent updates his/her opinion based on selected agents' opinion values and his/her confidence bound. At first, we show that the global fluctuation for opinions of regular agents occurs almost surely if and only if the confidence bound of regular agents is larger than a critical value. Next, we give an estimated probability bound of the local fluctuation for regular agent opinions when the confidence bound is sufficiently small. Finally, we provide upper and lower bounds on the fluctuation strength and the regular agent opinion mean in the case when the global fluctuation occurs almost surely.