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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
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    2. 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.
    3. 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.
    4. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    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, January.
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    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, 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.
    3. 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.
    4. 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.

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