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A Mean-Field Game Approach to Price Formation

Author

Listed:
  • Diogo A. Gomes

    (King Abdullah University of Science and Technology (KAUST))

  • João Saúde

    (Carnegie Mellon University)

Abstract

Here, we introduce a price formation model where a large number of small players can store and trade a commodity such as electricity. Our model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply versus demand balance condition. We establish the existence of a unique solution using a fixed-point argument. In particular, we show that the price is well defined, and it is a Lipschitz function of time. Then, we study linear-quadratic models that can be solved explicitly and compare our model with real data.

Suggested Citation

  • Diogo A. Gomes & João Saúde, 2021. "A Mean-Field Game Approach to Price Formation," Dynamic Games and Applications, Springer, vol. 11(1), pages 29-53, March.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:1:d:10.1007_s13235-020-00348-x
    DOI: 10.1007/s13235-020-00348-x
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    References listed on IDEAS

    as
    1. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    2. Noha Almulla & Rita Ferreira & Diogo Gomes, 2017. "Two Numerical Approaches to Stationary Mean-Field Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 657-682, December.
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    Cited by:

    1. Mansoor Saburov, 2022. "On Discrete-Time Replicator Equations with Nonlinear Payoff Functions," Dynamic Games and Applications, Springer, vol. 12(2), pages 643-661, June.
    2. Yves Achdou & Guillaume Carlier & Quentin Petit & Daniela Tonon, 2024. "A mean field model for the interactions between firms on the markets of their inputs," Mathematics and Financial Economics, Springer, volume 18, number 2, December.
    3. Pierre Lavigne & Peter Tankov, 2023. "Decarbonization of financial markets: a mean-field game approach," Papers 2301.09163, arXiv.org.
    4. Masaaki Fujii & Masashi Sekine, 2024. "Mean field equilibrium asset pricing model with habit formation," Papers 2406.02155, arXiv.org, revised Nov 2024.

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