IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1529-d410011.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1529/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1529/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    2. Andreas Koulouris & Ioannis Katerelos & Theodore Tsekeris, 2013. "Multi-Equilibria Regulation Agent-Based Model of Opinion Dynamics in Social Networks," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 11(1), pages 51-70.
    3. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    5. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2015. "Strategic influence in social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01158168, HAL.
    6. Phillip Monin & Richard Bookstaber, 2017. "Information Flows, the Accuracy of Opinions, and Crashes in a Dynamic Network," Staff Discussion Papers 17-01, Office of Financial Research, US Department of the Treasury.
    7. Liu, Qipeng & Wang, Xiaofan, 2013. "Social learning with bounded confidence and heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2368-2374.
    8. Ugo Bolletta & Paolo Pin, 2024. "Dynamic opinion updating with endogenous networks," Papers 2405.01341, arXiv.org.
    9. Christos Mavridis & Nikolas Tsakas, 2021. "Social Capital, Communication Channels and Opinion Formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 635-678, May.
    10. Kevin JS. Zollman, 2012. "Social network structure and the achievement of consensus," Politics, Philosophy & Economics, , vol. 11(1), pages 26-44, February.
    11. Phillip J. Monin & Richard Bookstaber, 2021. "Information flows and crashes in dynamic social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(3), pages 471-495, July.
    12. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    13. Chris Stivers & Licheng Sun, 2013. "Market Cycles and the Performance of Relative Strength Strategies," Financial Management, Financial Management Association International, vol. 42(2), pages 263-290, June.
    14. Charness, Gary & Corominas-Bosch, Margarida & Frechette, Guillaume R., 2007. "Bargaining and network structure: An experiment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 28-65, September.
    15. Bernhard Kittel & Wolfgang Luhan, 2013. "Decision making in networks: an experiment on structure effects in a group dictator game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 141-154, January.
    16. Prummer, Anja & Siedlarek, Jan-Peter, 2017. "Community leaders and the preservation of cultural traits," Journal of Economic Theory, Elsevier, vol. 168(C), pages 143-176.
    17. Javier Rivas, 2009. "Friendship selection," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 521-538, November.
    18. Krishnamurthy, Vikram & Leoff, Elisabeth & Sass, Jörn, 2018. "Filterbased stochastic volatility in continuous-time hidden Markov models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 1-21.
    19. Jeanne Hagenbach & Frédéric Koessler, 2010. "Strategic Communication Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1072-1099.
    20. Peixin (Payton) Liu & Kuan Xu & Yonggan Zhao, 2011. "Market regimes, sectorial investments, and time‐varying risk premiums," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 7(2), pages 107-133, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1529-:d:410011. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.