Modeling and Simulation of Impact and Control in Social Networks with Application to Marketing.

Mathematics. 2020. Vol. 8. No. 9. P. 1–25.

Agieva M. T., Korolev A. V., Ougolnitsky G. A.

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.

Keywords: computer simulation, analysis of social networks, difference games, optimal control theory