IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i3p355-d329059.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/3/355/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/3/355/
    Download Restriction: no
    ---><---

    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. 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.
    3. Dechert, Dee, 1978. "Optimal control problems from second-order difference equations," Journal of Economic Theory, Elsevier, vol. 19(1), pages 50-63, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Javier Frutos & Guiomar Martín-Herrán, 2018. "Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games," Dynamic Games and Applications, Springer, vol. 8(3), pages 620-636, September.
    2. Bolei Di & Andrew Lamperski, 2022. "Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games," Dynamic Games and Applications, Springer, vol. 12(2), pages 394-442, June.
    3. Massol, Olivier & Rifaat, Omer, 2018. "Phasing out the U.S. Federal Helium Reserve: Policy insights from a world helium model," Resource and Energy Economics, Elsevier, vol. 54(C), pages 186-211.
    4. Colombo, Luca & Labrecciosa, Paola, 2022. "Product quality differentiation in a renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 111(C).
    5. Mathew P. Abraham & Ankur A. Kulkarni, 2018. "An Approach Based on Generalized Nash Games and Shared Constraints for Discrete Time Dynamic Games," Dynamic Games and Applications, Springer, vol. 8(4), pages 641-670, December.
    6. Ilko Vrankić & Tomislav Herceg & Mirjana Pejić Bach, 2021. "Dynamics and stability of evolutionary optimal strategies in duopoly," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 1001-1019, September.
    7. Elena M. Parilina & Puduru Viswanadha Reddy & Georges Zaccour, 2022. "Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 808-836, December.
    8. Arguedas, Carmen & Cabo, Francisco & Martín-Herrán, Guiomar, 2020. "Enforcing regulatory standards in stock pollution problems," Journal of Environmental Economics and Management, Elsevier, vol. 100(C).
    9. Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
    10. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2020. "Best response algorithms in ratio-bounded games: convergence of affine relaxations to Nash equilibria," CSEF Working Papers 593, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    11. Katarzyna Kańska & Agnieszka Wiszniewska-Matyszkiel, 2022. "Dynamic Stackelberg duopoly with sticky prices and a myopic follower," Operational Research, Springer, vol. 22(4), pages 4221-4252, September.
    12. Genc, Talat S. & De Giovanni, Pietro, 2018. "Optimal return and rebate mechanism in a closed-loop supply chain game," European Journal of Operational Research, Elsevier, vol. 269(2), pages 661-681.
    13. Crettez, Bertrand & Hayek, Naila & Zaccour, Georges, 2018. "Brand imitation: A dynamic-game approach," International Journal of Production Economics, Elsevier, vol. 205(C), pages 139-155.
    14. Carmen Arguedas & Francisco Cabo & Guiomar Martín-Herrán, 2017. "Optimal Pollution Standards and Non-compliance in a Dynamic Framework," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(3), pages 537-567, November.
    15. Lu, Lijue & Marín-Solano, Jesús & Navas, Jorge, 2019. "An analysis of efficiency of time-consistent coordination mechanisms in a model of supply chain management," European Journal of Operational Research, Elsevier, vol. 279(1), pages 211-224.
    16. Bernhard, Pierre & Deschamps, Marc & Zaccour, Georges, 2023. "Large satellite constellations and space debris: Exploratory analysis of strategic management of the space commons," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1140-1157.
    17. Elnaz Kanani Kuchesfehani & Georges Zaccour, 2015. "S-adapted Equilibria in Games Played Over Event Trees with Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 644-658, August.
    18. Utsav Sadana & Puduru Viswanadha Reddy & Tamer Başar & Georges Zaccour, 2021. "Sampled-Data Nash Equilibria in Differential Games with Impulse Controls," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 999-1022, September.
    19. Parilina, Elena M. & Zaccour, Georges, 2022. "Payment schemes for sustaining cooperation in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    20. Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:355-:d:329059. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.