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The Euler-Equation Approach in Average-Oriented Opinion Dynamics

Author

Listed:
  • Vladimir Mazalov

    (Institute of Applied Mathematical Research, Karelian Research Center of the Russian Academy of Sciences, 11, Pushkinskaya str., 185910 Petrozavodsk, Russia
    School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    Institute of Applied Mathematics of Shandong, Qingdao 266071, China
    These authors contributed equally to this work.)

  • Elena Parilina

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    Institute of Applied Mathematics of Shandong, Qingdao 266071, China
    Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 Saint Petersburg, Russia
    These authors contributed equally to this work.)

Abstract

We consider the models of average-oriented opinion dynamics. An opinion about an event is distributed among the agents of a social network. There are an optimization problem and two game-theoretical models when players as centers of influence aim to make the opinions of the agents closer to the target ones in a finite time horizon minimizing their costs. The optimization problem and the games of competition for the agents’ opinion are linear-quadratic and solved using the Euler-equation approach. The optimal strategies for optimization problem and the Nash equilibria in the open-loop strategies for the games are found. Numerical simulations demonstrate theoretical results.

Suggested Citation

  • Vladimir Mazalov & Elena Parilina, 2020. "The Euler-Equation Approach in Average-Oriented Opinion Dynamics," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:355-:d:329059
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    References listed on IDEAS

    as
    1. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Games and Dynamic Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8442, February.
    2. Dechert, Dee, 1978. "Optimal control problems from second-order difference equations," Journal of Economic Theory, Elsevier, vol. 19(1), pages 50-63, October.
    3. Elena Parilina & Artem Sedakov, 2016. "Stable Cooperation in a Game with a Major Player," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-20, June.
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    Cited by:

    1. Hui Jiang & Vladimir V. Mazalov & Hongwei Gao & Chen Wang, 2023. "Opinion Dynamics Control in a Social Network with a Communication Structure," Dynamic Games and Applications, Springer, vol. 13(1), pages 412-434, March.
    2. Kareeva, Yulia & Sedakov, Artem & Zhen, Mengke, 2023. "Influence in social networks with stubborn agents: From competition to bargaining," Applied Mathematics and Computation, Elsevier, vol. 444(C).

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