Opinion Dynamics in Multiagent Systems with Optimal Choice of Opinion Verification Moments
Doklady Mathematics - 2024
Tóm tắt
A model of opinion dynamics in a social network that is a multiagent system with a finite number of agents is considered. There is a center influencing the agents’ opinions by applying control, which is an influence level at every time. The center’s costs are represented by a linear-quadratic function of a state variable (agents’ opinions) and its controls. The center of influence aims to choose a finite number of opinion verification moments to compare the agents’ opinions with the target one. A solution method for this dynamic problem on a finite time interval is proposed and implemented. In numerical simulation, we show how to find optimal opinion verification moments and the corresponding optimal state trajectories and controls.
Từ khóa
Tài liệu tham khảo
G. Albi, L. Pareschi, and M. Zanella, “On the optimal control of opinion dynamics on evolving networks,” in System Modeling and Optimization, Ed. by L. Bociu, J. A. Désidéri, and A. Habbal (Springer, Cham, 2015). pp. 58–67.
D. Arthur, R. Motwani, A. Sharma, and Y. Xu, “Pricing strategies for viral marketing on social networks,” in Internet and Network Economics, Ed. by S. Leonardi (Springer, Heidelberg, 2009), pp. 101–112.
D. Dechert, “Optimal control problems from second-order difference equations,” J. Econ. Theory 19 (1), 50–63 (1978).
J. Gao and E. M. Parilina, “Average-oriented opinion dynamics with the last moment of observation,” Control Processes Stability 8 (1), 505–509 (2021).
J. Gao and E. M. Parilina, “Opinion control problem with average-oriented opinion dynamics and limited observation moments,” Contrib. Game Theory Manage. 14, 103–112 (2021).
D. González-Sánchez and O. Hernández-Lerma, Discrete-Time Stochastic Control and Dynamic Potential Games: The Euler-Equation Approach (Springer Science/Business Media, 2013).
D. González-Sánchez and O. Hernández-Lerma, “On the Euler equation approach to discrete-time nonstationary optimal control problems,” J. Dyn. Games 1 (1), 57 (2014).
H. Jiang, V. V. Mazalov, H. Gao, and C. Wang, “Opinion dynamics control in a social network with a communication structure,” Dyn. Games Appl. 13, 412–434 (2023).
Y. Liang and B. Wang, “Robust mean field social optimal control with applications to opinion dynamics,” in 2019 IEEE 15th International Conference on Control and Automation (ICCA), 2019, pp. 1079–1084.
V. Mazalov and E. M. Parilina, “The Euler-equation approach in average-oriented opinion dynamics,” Mathematics 8 (3), 355 (2020).
M. A. Rogov and A. A. Sedakov, “Coordinated influence on the opinions of social network members,” Autom. Remote Control 81 (3), 528–547 (2020).
J. Veetaseveera, V. S. Varma, and I.-C. Morarescu, “A dynamic game formulation for control of opinion dynamics over social networks,” in Network Games, Control and Optimization, Ed. by S. Lasaulce, P. Mertikopoulos, and A. Orda (Springer, Cham, 2021), pp. 252–260.
M. Wang, D. Liang, and Z. Xu, “Consensus achievement strategy of opinion dynamics based on deep reinforcement learning with time constraint,” J. Oper. Res. Soc. 73 (3), 1–15 (2021).