Skip to main content
SpringerLink
Log in

Modeling and Simulation of Impact and Control in Social Networks

  • Conference paper
  • First Online:
Modeling and Simulation of Social-Behavioral Phenomena in Creative Societies (MSBC 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1079))

Abstract

The problems of analysis and prediction in social networks are interpreted for the domain of marketing (other applications are also possible). Algorithms of determination of the strong subgroups and satellites for a network are implemented using the programming language R and tested on model examples. An original algorithm of calculation of the final opinions is proposed, implemented in R and also tested on the model examples. The main idea is that all control efforts in marketing (and other problem domains) should be directed only to the members of strong subgroups because they and only they determine the final opinions of all members of the network. Based on this idea, two problems of the opinions control on networks are studied. First, a static game in normal form where the players maximize the final opinions of all members of a target audience by means of the marketing impact to the initial opinions of some members of the strong subgroups. Second, a dynamic (difference) 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. In both cases we received the analytical solutions and conducted their comparative analysis. More complicated versions of the models are studied numerically on the base of the method of qualitatively representative scenarios in computer simulation.

The work is supported by the Russian Science Foundation, project #17-19-01038.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. French, J.R.: A formal theory of social power. Psychol. Rev. 63, 181–194 (1956)

    Article  Google Scholar 

  2. Harary, F.: A criterion for unanimity in French’s theory of social power, in studies in social power, pp. 168–182. Institute of Sociological Research, Michigan (1959)

    Google Scholar 

  3. De Groot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69, 118–121 (1974)

    Article  MATH  Google Scholar 

  4. Golub, B., Jackson, M.: Naive learning in social networks and the wisdom of crowds. Am. Econ. J.: Microecon. 2(1), 112–149 (2010)

    Google Scholar 

  5. Hegselman, R., Krause, U.: Opinion dynamics and bounded confidence models: analysis and simulation. J. Artif. Soc. Soc. Simul. 5(3) (2002)

    Google Scholar 

  6. Krause, U.: A discrete nonlinear and non-autonomous model of consensus formation. In: Communications in Difference Equations. Amsterdam: Gordon and Breach Publishers, pp. 227–236 (2000)

    Chapter  Google Scholar 

  7. Berger, R.J.: A necessary and sufficient conditions for reaching a consensus using De Groot’s method. J. Am. Stat. Assoc. 76, 415–419 (1981)

    Article  MATH  Google Scholar 

  8. Chatterjee, S., Seneta, E.: Toward consensus: some convergence theorems on repeated averaging. J. Appl. Probab. 14, 159–164 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  9. De Marzo, P., Vayanos, D., Zwiebel, J.: Persuasion bias, social influence and unidimensional opinions. Quart. J. Econ. 118(3), 909–968 (2003)

    Article  MATH  Google Scholar 

  10. Zhang, D., Gatica-Perez, D., Bengio, S., Roy, D.: Learning influence among interactive markov chains. In: Neural Information Processing Systems (NIPS), pp. 132–141 (2005)

    Google Scholar 

  11. Saul, L.K., Jordan, M.I.: Mixed memory markov models: decomposing complex stochastic processes as mixtures of simpler ones. Mach. Learn. 37(1), 75–87 (1999)

    Article  MATH  Google Scholar 

  12. Oliver, N., Rosario, B., Pentland, A.: Graphical models for recognizing human interactions. In: Neural Information Processing Systems (NIPS), pp. 924–930 (1998)

    Google Scholar 

  13. Howard, A., Jebara, T.: Dynamical systems trees. In: Uncertainty in Artificial Intelligence, pp. 260–267 (2003)

    Google Scholar 

  14. Jackson, M.: Social and Economic Networks. Princeton University Press, Princeton (2008)

    Book  MATH  Google Scholar 

  15. Jackson, M., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  16. Chwe, M.S.: Communication and coordination in social networks. Rev. Econ. Stud. 67, 1–16 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Buttle, F.A.: Word-of-mouth: understanding and managing referral marketing. J. Strategic Mark. 6, 241–254 (1998)

    Article  Google Scholar 

  18. Godes, D., Mayzlin, D.: Using online conversations to study word of mouth communication. Mark. Sci. 23, 545–560 (2004)

    Article  Google Scholar 

  19. Goldenberg, J., Libai, B., Muller, E.: Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark. Lett. 2, 11–34 (2001)

    Google Scholar 

  20. Masuda, N., Kawamura, Y., Kori, H.: Analysis of relative influence of nodes in directed networks. Phys. Rev. E80, 046114 (2009)

    Google Scholar 

  21. Newman, M.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Robins, G., Pattison, P., Elliot, P.: Network models for social influence processes. Psychometrica 66(2), 161–190 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Watts, D.: The, “New” Science of Networks. Ann. Rev. Sociol. 30, 243–270 (2004)

    Article  Google Scholar 

  24. Chkhartishvili, A., Gubanov, D., Novikov, D.: Social Networks: Models of Information Influence, Control, and Confrontation. Springer, Heielberg (2019). https://doi.org/10.1007/978-3-030-05429-8

    Book  Google Scholar 

  25. Sedakov, A., Zhen, M.: Opinion dynamics game in a social network with two influence nodes. Appl. Math. Inform. Control process. 15(1), 118–125 (2019). Vestnik SPbGU

    MathSciNet  Google Scholar 

  26. Zhen, M.: Stackelberg equilibrium in opinion dynamics game in social network with two influence nodes. In: Petrosyan, L., Zenkevich, N. (eds.) Contributions to Game Theory and Management. Vol. XII. Collected papers presented on the Twelfth International Conference Game Theory and Management, pp. 366–386. SPb., Saint Petersburg State University (2019)

    Google Scholar 

  27. Alparslan-Gok, S.Z., Defterli, O., Kropat, E., Weber, G.-W.: Modeling, inference and optimization of regulatory networks based on time series data. Eur. J. Oper. Res. 211(1), 1–14 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Alparslan-Gok, S.Z., Soyler, B., Weber, G.-W.: A new mathematical approach in environmental and life sciences: gene-environment networks and their dynamics. Environ. Model. Assess. 14(2), 267–288 (2009)

    Article  Google Scholar 

  29. Belen, S., Kropat, E., Weber, G.-W.: Dynamical gene-environment networks under ellipsoidal uncertainty: set-theoretic regression analysis based on ellipsoidal OR. In: Dynamics, Games and Science I: DYNA 2008, Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, 8–12 September, pp. 545-571 (2008)

    Google Scholar 

  30. Kropat, E., Weber, G.-W., Akteke-Ozturk, B.: Eco-finance networks under uncertainty. In: Herskovits, J., Canelas, A., Cortes, H., Aroztegui, M. (eds.) Proceedings of the International Conference on Engineering Optimization, Rio de Janeiro, Brazil (2008)

    Google Scholar 

  31. Liu, Y.J., Zeng, C.M., Luo, Y.Q.: Dynamics of a new rumor propagation model with the spread of truth. Appl. Math. 9, 536–549 (2018)

    Article  Google Scholar 

  32. Hamilton, J.D.: A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  33. Timmermann, A.: Moments of Markov switching models. J. Econ. 96, 75–111 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  34. Savku, E., Weber, G.-W.: A stochastic maximum principle for a markov regime-switching jump-diffusion model with delay and an application to finance. J. Optim. Theory Appl. 179(2), 696–721 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  35. Kropat, E., Meyer-Nieberg, S., Weber, G.-W.: Singularly perturbed diffusion-advection-reaction processes on extremely large three-dimensional curvilinear networks with a periodic microstructure: efficient solution strategies based on homogenization theory. Numer. Algebra 6(2), 183–219 (2016)

    MathSciNet  MATH  Google Scholar 

  36. Kropat, E., Meyer-Nieberg, S., Weber, G.-W.: Bridging the gap between variational homogenization results and two-scale asymptotic averaging techniques on periodic network structures. Numer. Algebra 7(3), 223–250 (2017)

    MathSciNet  MATH  Google Scholar 

  37. Kropat, E., Ozmen, A., Weber, G.-W.: Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty. Optimization 66(12), 2135–2155 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  38. Alparslan-Gok, S.Z., Aydogan, T., Ergun, S., Weber, G.-W.: Performance analysis of a cooperative flow game algorithm in ad hoc networks and a comparison to Dijkstra’s algorithm. J. Ind. Manage. Optim. 15(3), 1085–1100 (2019)

    MATH  MathSciNet  Google Scholar 

  39. Agieva, M.T., Ougolnitsky, G.A.: Regional sustainable management problems on networks. In: Russkova, E. (ed.) Proceedings of the International Scientific Conference “Competitive, Sustainable and Secure Development of the Regional Economy: Response to Global Challenges” (CSSDRE 2018). Advances in Economics, Business and Management Research (AEBMR), vol. 39, pp. 6–9. Atlantis Press (2018). https://doi.org/10.2991/cssdre-18.2018.2

  40. Kabacoff, R.: R in Action: Data analysis and graphics with R. Manning Publications, Shelter Island (2011)

    Google Scholar 

  41. Ougolnitsky, G.A., Usov, A.B.: Computer simulations as a solution method for differential games. In: Pfeffer, M.D., Bachmaier, E. (eds.) Computer Simulations: Advances in Research and Applications, pp. 63–106. Nova Science Publishers, New York (2018)

    Google Scholar 

  42. Roberts, F.: Discrete Mathematical Models with Applications to Social, Biological and Environmental Problems. Prentice-Hall, Upper Saddle River (1976)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ingush State University, Nazran, Russian Federation

    M. T. Agieva

  2. Saint Petersburg Higher School of Economics, Saint Petersburg, Russian Federation

    A. V. Korolev

  3. Southern Federal University, Rostov-on-Don, Russian Federation

    G. A. Ougolnitsky

Authors
  1. M. T. Agieva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Korolev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. A. Ougolnitsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Ougolnitsky .

Editor information

Editors and Affiliations

  1. Information Science Department, University of Arkansas at Little Rock, Little Rock, AR, USA

    Nitin Agarwal

  2. Vilnius University, Vilnius, Lithuania

    Leonidas Sakalauskas

  3. Faculty of Engineering Management, Poznan University of Technology, Poznan, Poland

    Gerhard-Wilhelm Weber

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Agieva, M.T., Korolev, A.V., Ougolnitsky, G.A. (2019). Modeling and Simulation of Impact and Control in Social Networks. In: Agarwal, N., Sakalauskas, L., Weber, GW. (eds) Modeling and Simulation of Social-Behavioral Phenomena in Creative Societies. MSBC 2019. Communications in Computer and Information Science, vol 1079. Springer, Cham. https://doi.org/10.1007/978-3-030-29862-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-29862-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29861-6

  • Online ISBN: 978-3-030-29862-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation