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

Author

Listed:
  • M. T. Agieva

    (Faculty of Technology and Pedagogics, Ingush State University, 386132 Nazran, Russia)

  • A. V. Korolev

    (Department of Mathematics, Higher School of Economics, St. Petersburg Branch, 190121 St. Petersburg, Russia)

  • G. A. Ougolnitsky

    (I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 344090 Rostov-on-Don, Russia)

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.

Suggested Citation

  • M. T. Agieva & A. V. Korolev & G. A. Ougolnitsky, 2020. "Modeling and Simulation of Impact and Control in Social Networks with Application to Marketing," Mathematics, MDPI, vol. 8(9), pages 1-28, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1529-:d:410011
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    References listed on IDEAS

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    1. Garry Robins & Philippa Pattison & Peter Elliott, 2001. "Network models for social influence processes," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 161-189, June.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. Michael Suk-Young Chwe, 2000. "Communication and Coordination in Social Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 1-16.
    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    6. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    7. David Godes & Dina Mayzlin, 2004. "Using Online Conversations to Study Word-of-Mouth Communication," Marketing Science, INFORMS, vol. 23(4), pages 545-560, June.
    8. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 909-968.
    9. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
    10. Weber, Gerhard-Wilhelm & Defterli, Ozlem & Alparslan Gök, SIrma Zeynep & Kropat, Erik, 2011. "Modeling, inference and optimization of regulatory networks based on time series data," European Journal of Operational Research, Elsevier, vol. 211(1), pages 1-14, May.
    11. Timmermann, Allan, 2000. "Moments of Markov switching models," Journal of Econometrics, Elsevier, vol. 96(1), pages 75-111, May.
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