Solving MFGs with a Common Noise

René Carmona, François Delarue

Research output: Chapter in Book/Report/Conference proceedingChapter


The lion’s share of this chapter is devoted to the construction of equilibria for mean field games with a common noise. We develop a general two-step strategy for the search of weak solutions. The first step is to apply Schauder’s theorem in order to prove the existence of strong solutions to mean field games driven by a discretized version of the common noise. The second step is to make use of a general stability property of weak equilibria in order to pass to the limit along these discretized equilibria. We also present several criteria for strong uniqueness, in which cases weak equilibria are known to be strong.

Original languageEnglish (US)
Title of host publicationProbability Theory and Stochastic Modelling
PublisherSpringer Nature
Number of pages81
StatePublished - 2018

Publication series

NameProbability Theory and Stochastic Modelling
ISSN (Print)2199-3130
ISSN (Electronic)2199-3149

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Modeling and Simulation
  • Statistics and Probability


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