Geodesic
Opinion dynamics game in a social network with two influence nodes
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 1, pp. 118-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider an opinion dynamics game in a social network with two influence nodes. Pursuing certain goals, the influence nodes affect other members of the network by the selection of their levels of influence. Considering this model as a 2-person non-cooperative dynamic game and choosing Nash equilibrium as its solution, we find the equilibrium levels of influence for both influence nodes at any game stage. We also perform the numerical simulation for both low and high levels of players' influence on agents.
Keywords: social network, opinion dynamics, equilibrium.
Mots-clés : influence 
@article{VSPUI_2019_15_1_a8,
     author = {A. A. Sedakov and M. Zhen},
     title = {Opinion dynamics game in a social network with two influence nodes},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {118--125},
     year = {2019},
     volume = {15},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a8/}
}
TY  - JOUR
AU  - A. A. Sedakov
AU  - M. Zhen
TI  - Opinion dynamics game in a social network with two influence nodes
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2019
SP  - 118
EP  - 125
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a8/
LA  - en
ID  - VSPUI_2019_15_1_a8
ER  - 
%0 Journal Article
%A A. A. Sedakov
%A M. Zhen
%T Opinion dynamics game in a social network with two influence nodes
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2019
%P 118-125
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a8/
%G en
%F VSPUI_2019_15_1_a8
A. A. Sedakov; M. Zhen. Opinion dynamics game in a social network with two influence nodes. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 1, pp. 118-125. http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a8/

[1] DeGroot M. H., “Reaching a Consensus”, Journal of the American Statistical Association, 69:345 (1974), 118–12 | DOI

[2] Friedkin N. E., Johnsen E. C., “Social influence and opinions”, Journal of Mathematical Sociology, 15:3–4 (1990), 193–206 | DOI

[3] Friedkin N. E., Johnsen E. C., “Social influence networks and opinion change”, Advances in Group Processes, 16 (1999), 1–29 | MR

[4] Bauso D., Cannon M., “Consensus in opinion dynamics as a repeated game”, Automatica, 90 (2018), 204–211 | DOI | MR | Zbl

[5] Bindel D., Kleinberg J., Oren S., How bad is forming your own opinion?, Games and Economic Behavior, 92 (2015), 248–26 | DOI | MR

[6] Acemoglu D., Ozdaglar A., “Opinion dynamics and learning in social networks”, Dynamic Games and Applications, 1:1 (2011), 3–49 | DOI | MR | Zbl

[7] Buechel B., Hellmann T., Klößner S., “Opinion dynamics and wisdom under conformity”, Journal of Economic Dynamics and Control, 52 (2015), 240–25 | DOI | MR

[8] Dandekar P., Goel A., Lee D. T., “Biased assimilation, homophily, and the dynamics of polarization”, Proceedings of the National Academy of Sciences, 110:15 (2013), 5791–5796 | DOI | MR | Zbl

[9] Hegselmann R., Krause U., “Opinion dynamics and bounded confidence models, analysis, and simulation”, Journal of Artificial Societies and Social Simulation, 5:3 (2002), 615–645

[10] Ghaderi J., Srikant R., “Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate.”, Automatica, 50:12 (2014), 3209–3215 | DOI | MR | Zbl

[11] Golub B., Jackson M. O., “Naive learning in social networks and the wisdom of crowds”, American Economic Journal: Microeconomics, 2:1 (2010), 112–49 | DOI

[12] Bure V., Parilina E., Sedakov A., “Consensus in social networks with heterogeneous agents and two centers of influence”, Stability and Control Processes in memory of V. I. Zubov (SCP), 2015 Intern. Conference, 2015, 233–236

[13] Bure V., Parilina E., Sedakov A., “Consensus in a social network with two principals”, Automation and Remote Control, 78:8 (2017), 1489–1499 | DOI | MR | Zbl

[14] Barabanov I. N., Korgin N. A., Novikov D. A., Chkhartishvili A. G., “Dynamic models of informational control in social networks”, Automation and Remote Control, 71:11 (2010), 2417–2426 | DOI | MR | Zbl

[15] Gubanov D. A., Novikov D. A., Chkhartishvili A. G., “Informational influence and informational control models in social networks”, Automation and Remote Control, 72:7 (2011), 1557–1597 | DOI | MR

[16] Etesami S. R., Ba{ş}ar T., “Game-theoretic analysis of the Hegselmann—Krause model for opinion dynamics in finite dimensions”, IEEE Transactions on Automatic Control, 60:7 (2015), 1886–1897 | DOI | MR | Zbl

[17] Krawczyk J. B., Tidball M., “A discrete-time dynamic game of seasonal water allocation”, Journal of Optimization Theory and Applications, 128:2 (2006), 411–429 | DOI | MR | Zbl

[18] Niazi M. U. B., Özgüler A. B., Y{\i}ld{\i}z A., “Consensus as a Nash equilibrium of a dynamic game”, 12th Intern. Conference on Signal-Image Technology $\$ Internet-Based Systems, 2016, 365–372

[19] Ba{ş}ar T., Olsder G. J., Dynamic noncooperative game theory, 2nd ed., Academic Press, New York, 1999, 511 pp. | MR

[20] Haurie A., Krawczyk J., Zaccour G., Games and dynamic games, World Scientific Press, Singapore, 2012, 488 pp. | MR | Zbl