A Random-Supply Mean Field Game Price Model*

Diogo Gomes, Julian Gutierrez, Ricardo Ribeiro

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading costs, the market clears, and supply meets demand. This problem arises in market economies, including electricity generation from renewable sources in smart grids. Our model includes noise on the supply side, which is counterbalanced on the consumption side by storing energy or reducing the demand according to a dynamic price process. By solving a constrained minimization problem, we prove that the Lagrange multiplier corresponding to the market-clearing condition defines the solution of the price formation problem. For the linear-quadratic structure, we characterize the price process of a continuum population using optimal control techniques. We include numerical schemes for the price computation in the finite and infinite games, and we illustrate the model using real data.

Original languageEnglish (US)
Pages (from-to)188-222
Number of pages35
JournalSIAM Journal on Financial Mathematics
Issue number1
StatePublished - Feb 2023

Bibliographical note

Funding Information:
*Received by the editors September 2, 2021; accepted for publication (in revised form) September 5, 2022; published electronically February 7, 2023. https://doi.org/10.1137/21M1443923 Funding: The authors were partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452. \dagger CEMSE Division, King Abdullah University of Science and Technology KAUST, Thuwal 23955-6900, Saudi Arabia (diogo.gomes@kaust.edu.sa, julian.gutierrezpineda@kaust.edu.sa, ricardo.ribeiro@kaust.edu.sa). 188

Publisher Copyright:
© 2023 Society for Industrial and Applied Mathematics.


  • common noise
  • Lagrange mulitplier
  • mean field games
  • price formation

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics


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