Static and dynamic game theoretic models of opinion control in marketing networks

In this paper we consider game theoretic models of control on networks with application to marketing. We suppose that all strong subgroups are determined in the stage of analysis of the influence digraph, and the control impact is exerted only to the members of those subgroups because they determine all stable final opinions. An agent's opinion is interpreted as his expenses for buying goods (services) of a firm. The following problem of opinion control is being studied. A dynamic (difference) game in normal form where the players solve the problem of maximization of the sum of opinions of the members of a target audience by means of the closed-loop strategies of impact to the current opinions of the members of strong subgroups. We received the analytical solutions and conducted their comparative analysis.