Geodesic
Optimal control in a multiagent opinion dynamic system
Contributions to game theory and management, Tome 15 (2022), pp. 51-59.

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

The paper considers a multiagent system of opinion dynamics modeling a finite social network opinion transformation. In the system, there is an influencer or a player who is interested in making the agents' opinions in the system close to the target opinion. We assume that the player can influence the system only at a limited number of time periods. The player minimizes his costs by selecting moments to control the multiagent system at these moments, while at any time period he observes the agents' opinions. The optimization problem is solved using the Euler-equation approach. The numerical simulations represent the proposed method of finding the optimal solution of the problem.
Keywords: multiagent system, opinion dynamics, linear-quadratic games, Euler-equation approach. 
@article{CGTM_2022_15_a5,
     author = {Jingjing Gao and Elena Parilina},
     title = {Optimal control in a multiagent opinion dynamic system},
     journal = {Contributions to game theory and management},
     pages = {51--59},
     publisher = {mathdoc},
     volume = {15},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2022_15_a5/}
}
TY  - JOUR
AU  - Jingjing Gao
AU  - Elena Parilina
TI  - Optimal control in a multiagent opinion dynamic system
JO  - Contributions to game theory and management
PY  - 2022
SP  - 51
EP  - 59
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2022_15_a5/
LA  - en
ID  - CGTM_2022_15_a5
ER  - 
%0 Journal Article
%A Jingjing Gao
%A Elena Parilina
%T Optimal control in a multiagent opinion dynamic system
%J Contributions to game theory and management
%D 2022
%P 51-59
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2022_15_a5/
%G en
%F CGTM_2022_15_a5
Jingjing Gao; Elena Parilina. Optimal control in a multiagent opinion dynamic system. Contributions to game theory and management, Tome 15 (2022), pp. 51-59. http://geodesic.mathdoc.fr/item/CGTM_2022_15_a5/

[1] Bauso, D. Tembine, H. and Basar, T., “Opinion Dynamics in Social Networks through Mean-Field Games”, SIAM J. Con. Opt., 54:6 (2016), 3225–3257 | DOI | MR | Zbl

[2] Dechert, D., “Optimal control problems from second-order difference equations”, J. Econ. Theory, 19:1 (1978), 50–63 | DOI | MR | Zbl

[3] Deffuant, G., Neau, D., Amblard, F. and Weisbuch, G., “Mixing beliefs among interacting agents”, Advances in Complex Systems, 3:01n04 (2000), 87–98 | DOI

[4] DeGroot, M. H., “Reaching a consensus”, J. Ame. Sta. Ass., 69:345 (1974), 118–121 | DOI | Zbl

[5] Elliott, R., Li, X. and Ni, Y. H., “Discrete time mean-field stochastic linear-quadratic optimal control problems”, Automatica, 49:11 (2013), 3222–3233 | DOI | MR | Zbl

[6] Friedkin, N. E. and Johnsen, E. C., “Social influence and opinions”, J. Mat. Soc., 15:3–4 (1990), 193–206 | DOI

[7] Gao, J. and Parilina, E., “Average-oriented opinion dynamics with the last moment of observation”, Control Processes and Stability, 8:1 (2021), 505–509 (in Russian)

[8] Gao, J. and Parilina, E. M., “Opinion Control Problem with Average-Oriented Opinion Dynamics and Limited Observation Moments”, Contributions to Game Theory and Management, 14 (2021), 103–112 | DOI | MR

[9] González-Sánchez, D. and Hernández-Lerma, O., Discrete–time stochastic control and dynamic potential games: the Euler–Equation approach, Chap. 2, Springer International Publishing, Cham, Switzerland, 2013 | MR

[10] González-Sánchez, D. and Hernández-Lerma, O., “On the Euler equation approach to discrete–time nonstationary optimal control problems”, J. Dyn. Games, 1:1 (2014), 57 | DOI | MR

[11] Hegselmann, R. and Krause, U., “Opinion dynamics and bounded confidence models, analysis, and simulation”, J. art. soc. soc. simu., 5:3 (2002)

[12] Ignaciuk, P. and Bartoszewicz, A., “Linear-quadratic optimal control strategy for periodic-review inventory systems”, Automatica, 46:12 (2010), 1982–1993 | DOI | MR | Zbl

[13] Liu, X., Li, Y. and Zhang, W., “Stochastic linear quadratic optimal control with constraint for discrete-time systems”, App. Math. Comp., 228 (2014), 264–270 | DOI | MR | Zbl

[14] Mazalov, V. and Parilina, E., “The Euler-Equation Approach in Average-Oriented Opinion Dynamics”, Mathematics, 8:3 (2020), 355 | DOI

[15] Ni, Y. H. Elliott, R. and Li, X., “Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case”, Automatica, 57 (2015), 65–77 | DOI | MR | Zbl

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

[17] Sedakov, A. A. and Zhen, M., “Opinion dynamics game in a social network with two influence nodes”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 15:1 (2019), 118–125 | DOI | MR

[18] Sznajd-Weron, K. and Sznajd, J., “Opinion evolution in closed community”, Int. J. Mod. Phy. C, 11:06 (2000), 1157–1165 | DOI