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A Mean-Field Game Approach to Price Formation


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.

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Correspondence to Diogo A. Gomes.

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Diogo A. Gomes was partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452. João Saúde was partially supported by FCT/Portugal through the CMU-Portugal Program.

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Gomes, D.A., Saúde, J. A Mean-Field Game Approach to Price Formation. Dyn Games Appl 11, 29–53 (2021).

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  • Mean-field games
  • Price formation
  • Monotonicity methods

Mathematics Subject Classification

  • 91A13
  • 91A10
  • 49M30