A probabilistic weak formulation of mean field games and applications

René Carmona, Daniel Lacker

Research output: Contribution to journalArticle

54 Scopus citations

Abstract

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed strategies which provide approximate Nash equlibria for finite-player games. Our results are applied to a new class of multi-agent price impact models and a class of flocking models for which we prove existence of equilibria.

Original languageEnglish (US)
Pages (from-to)1189-1231
Number of pages43
JournalAnnals of Applied Probability
Volume25
Issue number3
DOIs
StatePublished - Jun 1 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Flocking models
  • Mean field games
  • Price impact
  • Weak formulation

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