IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v10y2020i4d10.1007_s13235-020-00367-8.html
   My bibliography  Save this article

Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games

Author

Listed:
  • Boualem Djehiche

    (KTH Royal Institute of Technology)

  • Julian Barreiro-Gomez

    (New York University Abu Dhabi
    New York University Abu Dhabi)

  • Hamidou Tembine

    (New York University Abu Dhabi
    New York University Abu Dhabi)

Abstract

In this article, a profit optimization between electricity producers is formulated and solved. The problem is described by a linear jump-diffusion system of conditional mean-field type where the conditioning is with respect to common noise and a quadratic cost functional involving the second moment, the square of the conditional expectation of the control actions of the producers. We provide semi-explicit solution of the corresponding mean-field-type game problem with common noise. The equilibrium strategies are in state-and-conditional mean-field feedback form, where the mean-field term is the conditional price given the realization of the global uncertainty. The methodology is extended to a situation of incomplete information mean-field-type game in which each producer knows its own type but not the types of the other producers. We compute the Bayesian mean-field-type equilibrium in a semi-explicit way and show that it is not ex post resilient.

Suggested Citation

  • Boualem Djehiche & Julian Barreiro-Gomez & Hamidou Tembine, 2020. "Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games," Dynamic Games and Applications, Springer, vol. 10(4), pages 798-818, December.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:4:d:10.1007_s13235-020-00367-8
    DOI: 10.1007/s13235-020-00367-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-020-00367-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-020-00367-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    2. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    3. Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    4. Bert Willems, 2002. "Modeling Cournot Competition in an Electricity Market with Transmission Constraints," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 95-125.
    5. William W. Hogan, 1997. "A Market Power Model with Strategic Interaction in Electricity Networks," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 107-141.
    6. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    7. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    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. Masaaki Fujii, 2022. "Equilibrium Pricing of Securities in the Co-Presence of Cooperative and Non-Cooperative Populations," CIRJE F-Series CIRJE-F-1201, CIRJE, Faculty of Economics, University of Tokyo.
    2. Masaaki Fujii, 2023. "Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations (Forthcoming in ESAIM: Control, Optimisation and Calculus of Variations) (Revised version of CARF-F-," CARF F-Series CARF-F-562, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Masaaki Fujii, 2022. "Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations," Papers 2209.12639, arXiv.org, revised Jun 2023.
    4. Masaaki Fujii, 2022. "Equilibrium Pricing of Securities in the Co-presence of Cooperative and Non-cooperative Populations," CARF F-Series CARF-F-545, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    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. Masahiko Hattori & Yasuhito Tanaka, 2019. "General analysis of dynamic oligopoly with sticky price," Economics Bulletin, AccessEcon, vol. 39(4), pages 2990-2998.
    2. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    3. Benchekroun, Hassan, 2008. "Comparative dynamics in a productive asset oligopoly," Journal of Economic Theory, Elsevier, vol. 138(1), pages 237-261, January.
    4. Dockner, Engelbert J. & Gaunersdorfer, Andrea, 2001. "On the profitability of horizontal mergers in industries with dynamic competition," Japan and the World Economy, Elsevier, vol. 13(3), pages 195-216, August.
    5. Santiago J. Rubio, 2002. "On The Coincidence Of The Feedback Nash And Stackelberg Equilibria In Economic Applications Of Differential Games," Working Papers. Serie AD 2002-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Caputo, Michael R. & Ling, Chen, 2013. "The intrinsic comparative dynamics of locally differentiable feedback Nash equilibria of autonomous and exponentially discounted infinite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1982-1994.
    7. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    8. Dubovik, Andrei & Parakhonyak, Alexei, 2014. "Drugs, guns, and targeted competition," Games and Economic Behavior, Elsevier, vol. 87(C), pages 497-507.
    9. Kenji Fujiwara, 2009. "Gains from Trade in a Differential Game Model of Asymmetric Oligopoly," Review of International Economics, Wiley Blackwell, vol. 17(5), pages 1066-1073, November.
    10. Bremberger, Francisca & Gasser, Stephan M. & Kremser, Thomas R. & Rammerstorfer, Margarethe, 2014. "The Impact of EU ETS Price Variations on Germany’s Electricity Production Mix," Die Unternehmung - Swiss Journal of Business Research and Practice, Nomos Verlagsgesellschaft mbH & Co. KG, vol. 68(3), pages 164-180.
    11. Kogan, Konstantin & El Ouardighi, Fouad & Herbon, Avi, 2017. "Production with learning and forgetting in a competitive environment," International Journal of Production Economics, Elsevier, vol. 189(C), pages 52-62.
    12. 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.
    13. Tyrone E. Duncan & Hamidou Tembine, 2018. "Linear–Quadratic Mean-Field-Type Games: A Direct Method," Games, MDPI, vol. 9(1), pages 1-18, February.
    14. Wirl, Franz, 2010. "Dynamic demand and noncompetitive intertemporal output adjustments," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 220-229, May.
    15. Lu, Fuxiao & Tang, Wansheng & Liu, Guowei & Zhang, Jianxiong, 2019. "Cooperative advertising: A way escaping from the prisoner’s dilemma in a supply chain with sticky price," Omega, Elsevier, vol. 86(C), pages 87-106.
    16. Robert Wilson, 2008. "Supply Function Equilibrium in a Constrained Transmission System," Operations Research, INFORMS, vol. 56(2), pages 369-382, April.
    17. C. Ling & M. R. Caputo, 2011. "A Qualitative Characterization of Symmetric Open-Loop Nash Equilibria in Discounted Infinite Horizon Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 151-174, April.
    18. Luca Grilli & Michele Bisceglia, 2020. "A dynamic private property resource game with asymmetric firms," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 109-127, June.
    19. Guido Pepermans & Bert Willems, 2005. "The Potential Impact of Cross-Ownership in Transmission: an Application to the Belgian Electricity Market," Working Papers of Department of Economics, Leuven ces0503, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    20. Jacob Engwerda, 2017. "A Numerical Algorithm to Calculate the Unique Feedback Nash Equilibrium in a Large Scalar LQ Differential Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 635-656, 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:spr:dyngam:v:10:y:2020:i:4:d:10.1007_s13235-020-00367-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.