Controlling opinion dynamics and consensus and in a social network

A game-theoretic model of the influence of players on the dynamics of opinions and the achieved consensus in the social network is considered. The goal of a player is to maintain the opinion of all participants in the vicinity of a predetermined value. If there are several players, then these target values are they can be different. The dynamic game belongs to the class of linear-quadratic games in discrete time. Optimal control and equilibrium are found using the Bellman equation. The solution is achieved in an analytical form. It is shown that in the model with one player, a controlled consensus is achieved in the social network. The two-player model shows that although there is no consensus in the social network, the equilibrium is completely determined by the mean value of the opinion of all participants, which converges to a certain value. The results of numerical modeling for a social network with one and two players are presented.