Geodesic
Controlling opinion dynamics and consensus and in a social network
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 4, pp. 24-39.

Voir la notice de l'article provenant de la source Math-Net.Ru

A game-theoretic model of the influence of players on the dynamics of opinions and the achieved consensus in the social network is considered. The goal of a player is to maintain the opinion of all participants in the vicinity of a predetermined value. If there are several players, then these target values are they can be different. The dynamic game belongs to the class of linear-quadratic games in discrete time. Optimal control and equilibrium are found using the Bellman equation. The solution is achieved in an analytical form. It is shown that in the model with one player, a controlled consensus is achieved in the social network. The two-player model shows that although there is no consensus in the social network, the equilibrium is completely determined by the mean value of the opinion of all participants, which converges to a certain value. The results of numerical modeling for a social network with one and two players are presented.
Keywords: opinion dynamic, consensus, linear-quadratic game, feedback Nash equilibrium
Mots-clés : social structure, Bellman equation. 
@article{MGTA_2020_12_4_a2,
     author = {Chen Wang and Vladimir V. Mazalov and Hongwei Gao},
     title = {Controlling opinion dynamics and consensus and in a social network},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {24--39},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a2/}
}
TY  - JOUR
AU  - Chen Wang
AU  - Vladimir V. Mazalov
AU  - Hongwei Gao
TI  - Controlling opinion dynamics and consensus and in a social network
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2020
SP  - 24
EP  - 39
VL  - 12
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a2/
LA  - ru
ID  - MGTA_2020_12_4_a2
ER  - 
%0 Journal Article
%A Chen Wang
%A Vladimir V. Mazalov
%A Hongwei Gao
%T Controlling opinion dynamics and consensus and in a social network
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2020
%P 24-39
%V 12
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a2/
%G ru
%F MGTA_2020_12_4_a2
Chen Wang; Vladimir V. Mazalov; Hongwei Gao. Controlling opinion dynamics and consensus and in a social network. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 4, pp. 24-39. http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a2/

[1] Rogov M.A., Sedakov A.A., “Coordinated Influence on the Opinions of Social Network Members”, Automation and Remote Control, 81:3 (2020), 528–547 | DOI | MR | Zbl | Zbl

[2] I. N. Barabanov, N. A. Korgin, D. A. Novikov, A. G. Chkhartishvili, “Dynamics models of informational control in social networks”, Autom. Remote Control, 71 (2010), 2417–2426 | DOI | MR | Zbl

[3] D. Bauso, H. Tembine, T. Basar, “Opinion dynamics in social networks through mean field games”, Control opinion, 54 (2016), 3225–3257 | MR | Zbl

[4] V. M. Bure, E. M. Parilina, A. A. Sedakov, “Consensus in a social network with two principals”, Autom. Remote Control, 78 (2017), 1489–1499 | DOI | MR | Zbl

[5] A. G. Chkhartishvili, D. A. Gubanov, D. A. Novikov, Social network: Models of information influence. Control and Confrontation, Springer, 2019

[6] E. J. Dockner, S. Jorgensen, N. V. Long, G. Sorger, Differential Games in Economics and Management Science, Cambridge University Press, 2000 | MR | Zbl

[7] S. R. Etesami, S. Bolouki, T. Basar, S. Nedic, “Evolution of Public Opinion under Conformist and Manipulative Behaviors”, IFAC PapersOnLine, 50-1 (2017), 14344–14349 | DOI

[8] N. E. Friedkin, E. C. Johnsen, “Social influence, opinions”, J. of Math. Soc., 15 (1990), 193–206 | DOI

[9] J. Ghaderi, R. Srikant, “Opinion dynamics in social networks: A local interaction game with stubborn agents”, Am. Control Conf. (ACC), 50:12 (2013), 1982–1987 | MR

[10] M. De Groot, “Reaching a consensus”, Am. Stat. Assoc., 69 (1974), 119–121

[11] R. Hegselmann, U. Krause, “Opinion dynamics driven by various ways of averaging”, Comp. econ., 25 (2005), 381–405 | DOI | Zbl

[12] V. Mazalov, E. Parilina, “Game of competition for opinion with two centers of influence”, Lecture Notes in Computer Science, 11548, 2019, 673–684 | DOI | Zbl

[13] V. V. Mazalov, E. M. Parilina, “The Euler-Equation Approach in AverageOriented Opinion Dynamics”, Mathematics, 8:3 (2020), 1–16 | DOI

[14] V. V. Mazalov, Yu. A. Dorofeeva, E. M. Parilina, “Opinion control in a team with complete and incomplete information”, Contributions to Game Theory and Management, XIII (2020), 324–334 | DOI

[15] M. U. B. Niazi, A. B. Ozguller, A. Yildiz, Consensus as a Nash Equilibrium of a Dynamic Game, 2017, arXiv: 1701.01223v1 [cs.SY]

[16] A. A. Sedakov, M. Zhen, “Opinion dynamics game in a social network with two influence nodes”, Vestn. St. Petersburg Univ. Appl. Math. Comp. Sci., 15 (2019), 118–125 | MR

[17] J. B. Stiff, P. A. Mongeau, Persuasive Communication, Guilford Press, 2003