Opinion dynamics of modified Hegselmann–Krause model in a group-based population with heterogeneous bounded confidence

Continuous opinion dynamics in a group-based population with heterogeneous bounded confidences is considered in this paper. A slightly modified Hegselmann–Krause model is proposed, and agents are classified into three categories: open-minded-, moderate-minded-, and closed-minded-agents, while the whole population is divided into three subgroups accordingly. We study how agents of each category and the population size can affect opinion dynamics. It is observed that the number of final opinion clusters is dominated by the closed-minded agents; open-minded agents cannot contribute to forming opinion consensus and the existence of open-minded agents may diversify the final opinions instead; for the fixed population size and proportion of closed-minded agents, the relative size of the largest final opinion cluster varies along concave-parabola-like curve as the proportion of open-minded agents increases, and there is a tipping point when the number of open-minded agents is almost equal to that of moderate-minded agents; for the fixed proportion of the three categories in the population, as the population size becomes larger, the number of final opinion clusters will reach a plateau. Some of the results are different from the previous studies.