Abstract: Online social media are nowadays an integral part of people's everyday life that can influence our behaviour and opinions. Despite recent advances, the changing role of traditional media and the emerging role of "influencers" are still not well understood, and the implications of their strategies in the attention economy even less so. In this talk, we will propose a novel agent-based model (ABM) that aims to model how individuals (agents) change their opinions (states) under the impact of media and influencers. We will show the rich behavior of this ABM in different regimes and how different opinion formations can emerge, e.g. fragmentation. In the limit of infinite number of agents, we will derive a corresponding mean-field model given by a PDE. Based on the mean-field model, we will show how strategies of influencers can impact the overall opinion distribution and that optimal control strategies allow other influencers (or media) to counteract such attempts and prevent further fragmentation of the opinion landscape.
