Opinion dynamics in bounded confidence models with manipulative agents: Moving the Overton window

This paper focuses on the opinion dynamics under the influence of manipulative agents. This type of agents is characterized by the fact that their opinions follow a trajectory that does not respond to the dynamics of the model, although it does influence the rest of the normal agents. Simulation has been implemented to study how one manipulative group modifies the natural dynamics of some opinion models of bounded confidence. It is studied what strategies based on the number of manipulative agents and their common opinion trajectory can be carried out by a manipulative group to influence normal agents and attract them to their opinions. In certain weighted models, some effects are observed in which normal agents move in the opposite direction to the manipulator group. Moreover, the conditions which ensure the influence of a manipulative group on a group of normal agents over time are also established for the Hegselmann–Krause model. •Manipulators in discrete time models of opinion dynamics with bounded confidence.•Analysis of interactions between manipulative groups and normal groups of agents.•Opinion dynamics simulations with one manipulative group of agents.•Simulations for Hegselmann–Krause, Deffuant–Weisbuch and Weighted HK models.