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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

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    1. 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.
    2. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
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    Cited by:

    1. Masaaki Fujii & Masashi Sekine, 2024. "Mean field equilibrium asset pricing model with habit formation," Papers 2406.02155, arXiv.org.
    2. Mansoor Saburov, 2022. "On Discrete-Time Replicator Equations with Nonlinear Payoff Functions," Dynamic Games and Applications, Springer, vol. 12(2), pages 643-661, June.
    3. Pierre Lavigne & Peter Tankov, 2023. "Decarbonization of financial markets: a mean-field game approach," Papers 2301.09163, arXiv.org.

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