Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games

Boualem Djehiche, Julian Barreiro-Gomez, Hamidou Tembine

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)798-818
Number of pages21
JournalDynamic Games and Applications
Issue number4
StatePublished - Dec 2020


  • Electricity price dynamics
  • Mean-field-type games
  • Smart grids

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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