No abstract

The problems of social networks analysis and calculation of the resulting opinions of network agents are considered. Algorithms for identifying strong subgroups and satellites as well as for calculating some quantitative characteristics of a network are implemented by the R programming language and tested on model examples. A new algorithm for calculating the resulting opinions of agents is developed by the R toolkit and tested on model examples. It is important that control actions that exert impact to the opinions should be applied exclusively to the members of strong subgroups (opinion leaders of a target audience), since they fully determine the stable resulting opinions of all network members. This approach allows saving control resources without significantly affecting its efficiency. Much attention is paid to the original models of optimal control (single subject) and conflict control (several competing subjects) under the assumption that the members of strong subgroups (opinion leaders) are already identified at the previous stage of network analysis. Models of optimal opinion control on networks are constructed and investigated by computer simulations using the author’s method of qualitatively representative scenarios. Differential game-based models of opinion control on networks with budget constraints in the form of equalities and inequalities are constructed and analytically investigated. All used notions, approaches and results of this paper are interpreted in terms of marketing problems.

This paper is dedicated to the models of regional sustainable management on networks. The main objective of the paper is to propose a synthesis of the network models of influence and control with the models of sustainable management for the solution of the problems of regional sustainable management with consideration of the structural aspects. The respective formal setups are presented and interpreted for the problem domain of regional development.

Difference and differential Stackelberg games of opinion control on marketing networks are considered. The principal allocates financial resources to the firms for marketing purposes. It is supposed that the structure of a target audience described by a weighted directed graph is already determined in the stage of network analysis, and marketing control actions are applied only to the members of strong subgroups (opinion leaders). Conditions of homeostasis (phase constraints) which reflect the requirements of sustainable management are introduced additionally. The Stackelberg equilibria are found analytically. It is shown that the interests of the principal and the firms are completely compatible.

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 in uence digraph, and the control impact is exerted only to the members of those subgroups because they determine all stable nal opinions. An agent's opinion is interpreted as his expenses for buying goods (services) of a rm. The following problem of opinion control is being studied. A dynamic (di erence) 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.