Advertisement

Game of Competition for Opinion with Two Centers of Influence

  • Vladimir Mazalov
  • Elena ParilinaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

The paper considers the model of opinion dynamics in the network having a star structure. An opinion about an event is distributed among network agents restricted by the network structure. The agent in the center of the star is influenced by all other agents with equal intensity. The agents located in non-center nodes are influenced only by the agent located in the center of the star. Additionally, it is assumed that there are two players who are not located in the considered network but they influence the agents’ opinions with some intensities which are strategies of the players. The goal of any player is to make opinions of the network agents be closer to the initially given value as much as possible in a finite time interval. The game of competition for opinion is linear-quadratic and is solved using the Euler-equation approach. The Nash equilibrium in open-loop strategies is found. A numerical simulation demonstrates theoretical results.

Keywords

Opinion dynamics Consensus Game of competition for opinion 

References

  1. 1.
    Avrachenkov, K.E., Kondratev, A.Y., Mazalov, V.V.: Cooperative game theory approaches for network partitioning. In: Cao, Y., Chen, J. (eds.) COCOON 2017. LNCS, vol. 10392, pp. 591–602. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-62389-4_49CrossRefGoogle Scholar
  2. 2.
    Barabanov, I.N., Korgin, N.A., Novikov, D.A., Chkhartishvili, A.G.: Dynamic models of informational control in social networks. Autom. Remote Control. 71(11), 2417–2426 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bauso, D., Cannon, M.: Consensus in opinion dynamics as a repeated game. Automatica 90, 204–211 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bauso, D., Tembine, H., Basar, T.: Opinion dynamics in social networks through mean field games. SIAM J. Control Optim. 54(6), 3225–3257 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bure, V.M., Ekimov, A.V., Svirkin, M.V.: A simulation model of forming profile opinions within the collective. Vestn. Saint Petersburg Univ. Appl. Math. Comput. Sci. Control Process. 3, 93–98 (2014)Google Scholar
  6. 6.
    Bure, V.M., Parilina, E.M., Sedakov, A.A.: Consensus in a social network with two principals. Autom. Remote Control 78(8), 1489–1499 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Chkhartishvili, A.G., Gubanov, D.A., Novikov, D.A.: Social Networks: Models of Information Influence, Control and Confrontation. Springer, Switzerland (2019).  https://doi.org/10.1007/978-3-030-05429-8CrossRefGoogle Scholar
  8. 8.
    DeGroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)CrossRefGoogle Scholar
  9. 9.
    Engwerda, J.: LQ Dynamic Optimization and Differential Games. Wiley, New York (2005)Google Scholar
  10. 10.
    Engwerda, J.: Algorithms for computing Nash equilibria in deterministic LQ games. Comput. Manage. Sci. 4(2), 113–140 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Haurie, A., Krawczyk, J.B., Zaccour, G.: Games and Dynamic Games. World Scientific Publishing, Singapore (2012)CrossRefGoogle Scholar
  12. 12.
    González-Sánchez, D., Hernandez-Lerma, O.: Discrete-Time Stochastic Control and Dynamic Potential Games. The Euler-Equation Approach. Springer International Publishing, Heidelberg (2013).  https://doi.org/10.1007/978-3-319-01059-5CrossRefzbMATHGoogle Scholar
  13. 13.
    Gubanov, D.A., Novikov, D.A., Chkhartishvili, A.G.: Sotsial’nye seti: modeli informatsionnogo vliyaniya, upravleniya i protivoborstva (Social Networks: Models of Informational Influence, Control and Confrontation). Fizmatlit, Moscow (2010)Google Scholar
  14. 14.
    Gubanov, D.A., Novikov, D.A., Chkhartishvili, A.G.: Informational influence and informational control models in social networks. Autom. Remote Control 72(7), 1557–1567 (2011)CrossRefGoogle Scholar
  15. 15.
    Mazalov, V.V.: Mathematical Game Theory and Applications. Wiley, New York (2014). Wiley Desktop EditionszbMATHGoogle Scholar
  16. 16.
    Mazalov, V.V.: Comparing game-theoretic and maximum likelihood approaches for network partitioning. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds.) Transactions on Computational Collective Intelligence XXXI. LNCS, vol. 11290, pp. 37–46. Springer, Heidelberg (2018).  https://doi.org/10.1007/978-3-662-58464-4_4CrossRefGoogle Scholar
  17. 17.
    Parilina, E., Sedakov, A.: Stable cooperation in a game with a major player. Int. Game Theory Rev. 18(2), 1640005 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Rogov, M.A., Sedakov, A.A.: Coordinated influence on the beliefs of social network members. Math. Game Theory Appl. 10(4), 30–58 (2018)zbMATHGoogle Scholar
  19. 19.
    Sedakov, A., Zhen, M.: Opinion dynamics game in a social network with two influence nodes. Vestn. Saint Petersburg Univ. Appl. Math. Comput. Sci. Control Process. 15(1), 118–125 (2019)Google Scholar
  20. 20.
    Smyrnakis, M., Bauso, D., Hamidou, T.: An evolutionary game perspective on quantised consensus in opinion dynamics. PLoS ONE 14(1), e0209212 (2019)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Applied Mathematical ResearchKarelian Research Center, Russian Academy of SciencesPetrozavodskRussia
  2. 2.Saint Petersburg State UniversitySaint PetersburgRussia

Personalised recommendations