Annals of Applied Probability

A probabilistic weak formulation of mean field games and applications

René Carmona and Daniel Lacker

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 3 (2015), 1189-1231.

Dates
First available in Project Euclid: 23 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1427124127

Digital Object Identifier
doi:10.1214/14-AAP1020

Mathematical Reviews number (MathSciNet)
MR3325272

Zentralblatt MATH identifier
1332.60100

Subjects
Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 93E20: Optimal stochastic control 91A13: Games with infinitely many players

Keywords
Mean field games weak formulation price impact flocking models

Citation

Carmona, René; Lacker, Daniel. A probabilistic weak formulation of mean field games and applications. Ann. Appl. Probab. 25 (2015), no. 3, 1189--1231. doi:10.1214/14-AAP1020. https://projecteuclid.org/euclid.aoap/1427124127


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