Dynamic Cooperative Game Theoretic Models of Opinion Control

In this paper we consider dynamic cooperative game theoretic models of control on networks. 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. We show that due to the model assumptions the characteristic functions by Neumann-Morgenstern, Petrosyan-Zaccour, and Gromova-Petrosyan coincide. We find Shapley value for this common characteristic function, prove its time inconsistency, and built an imputation distribution procedure. We compared the components of Shapley value with players’ payoffs for different forms of non-cooperative behavior.