Controlling opinions in the SCARDO-model of opinion dynamics with two-element opinion alphabet and single type of native agents: analytical solution

This paper investigates a control problem whereby a concerned person attempts to change individuals' opinions by using a group of social bots – stubborn agents that can influence other, native, agents via direct conversations. The control problem is formulated in terms of the mean field approximation for the SCARDO-model, built for the case of a social system with a modular network structure, heterogeneous levels of agent activity and content personalization. We focus on, perhaps, the simplest case of the two-element opinion alphabet, in which there are only two possible opinions (interpretation – elections in a two-party system) and one type of non-bot agents. We derive a precise analytical solution to the control problem and demonstrate that depending on the model parameters, there can be either one optimal control strategy or infinitely many. At the same time, in the case when there is only one optimal control trajectory, it should be organized as follows: all social bots should broadcast the same opinion, and the switch to a different opinion can occur no more than once, only for some parameter configurations. The theoretical results obtained are complemented by insightful examples with data from the online network VKontakte.