Recent advances in opinion modeling: control and social influence

Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella
(1/7/2016 Active particles. Vol. 1. Advances in theory, models, and applications, 49–98, Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, Cham, 2017. arxiv: 1607.05853)

We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social aspects, like conviction and number of connections in social networks, which modify the agents' role in the opinion exchange process.