Opinion clusters in a modified Hegselmann-Krause model with heterogeneous bounded confidences and stubbornness

In opinion dynamics with continuous opinion, bounded confidence is a critical parameter. Agents can interact with each other only when the opinion difference between them is less than the bounded confidence. Larger bounded confidence always leads to fewer opinion clusters. Stubbornness characterizing the insistence of an agent on her own opinion is thought to only affect the transition time. In this work, a modified Hegselmann-Krause model with heterogeneous population is investigated, where agents in different/same subpopulation have different/same bounded confidence and stubbornness. We find that, due to the interaction among subpopulations, increasing the stubbornness of agents in the subpopulation with the largest bounded confidence favors fewer opinion clusters and the expansion of the largest cluster. We also find that increasing the bounded confidence of a subpopulation leads to fewer clusters and a larger largest cluster provided that all the others have large bounded confidence. While one subpopulation is with a small bounded confidence, there exist an optimal bounded confidence of another subpopulation for the smallest number of opinion clusters and that for the largest size of the largest cluster. (C) 2019 Elsevier B.V. All rights reserved.