Opinion Control Problem with Average-Oriented Opinion Dynamics and Limited Observation Moments

Jingjing Gao; Elena Parilina

doi:10.21638/11701/spbu31.2021.09

Authors

Jingjing Gao St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia https://orcid.org/0000-0001-7575-7110
Elena Parilina St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia https://orcid.org/0000-0003-3976-7180

DOI:

https://doi.org/10.21638/11701/spbu31.2021.09

Abstract

In the paper, we propose a model of opinion dynamics in the presence of a center of influence. The center aims in distributing the opinion closer to the target one minimizing the costs. We consider the case when the center takes into account only some fixed number of observations from the opinion trajectory and taking into account the difference between the agent's opinion and the socially desired opinion in these periods. The dynamics of the state variable is given by a linear difference equation. The player's cost is a linear quadratic function with respect to the state variables and the player's strategy. The Euler equation method is used to find the center's optimal strategy. Numerical simulations of the theoretical results are given.

Keywords:

opinion dynamics, social network, linear-quadratic games, Eulerequation approach

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References

Bure, V. M., Parilina, E. M., and Sedakov, A. A. (2017). Consensus in a social network with two principals. Autom. Remote Control, 78(8), 1489–1499

Dechert, D. (1978). Optimal control problems from second-order difference equations. J. Econ. Theory, 19(1), 50–63

DeGroot, Morris H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118–121

González-Sánchez, D. and Hernández-Lerma, O. (2013). Discrete-time stochastic control and dynamic potential games: the Euler-Equation approach. Chap. 2. Springer International Publishing: Cham, Switzerland

González-Sánchez, D. and Hernández-Lerma, O. (2014). On the Euler equation approach to discrete-time nonstationary optimal control problems. J. Dyn. Games, 1(1), 57

Mazalov, V. and Parilina, E. (2019). Game of competition for opinion with two centers of influence. In Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings, Russia, July 8–12, 2019 (Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 673–684. Springer: Cham, Switzerland

Mazalov, V. and Parilina, E. (2020). The Euler-Equation Approach in Average-Oriented Opinion Dynamics. Mathematics, 8(3), 355

Rogov, M. A. and Sedakov, A. A. (2020). Coordinated Influence on the Opinions of Social Network Members. Autom Remote Control 81, 528–547

Sedakov, A. A. and Zhen, M. (2019). Opinion dynamics game in a social network with two influence nodes. Vestn. St. Petersburg Univ. Appl. Math. Comput. Sci. Control Process, 15(1), 118–125