Open Access
June 2015 A probabilistic weak formulation of mean field games and applications
René Carmona, Daniel Lacker
Ann. Appl. Probab. 25(3): 1189-1231 (June 2015). DOI: 10.1214/14-AAP1020


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.


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René Carmona. Daniel Lacker. "A probabilistic weak formulation of mean field games and applications." Ann. Appl. Probab. 25 (3) 1189 - 1231, June 2015.


Published: June 2015
First available in Project Euclid: 23 March 2015

zbMATH: 1332.60100
MathSciNet: MR3325272
Digital Object Identifier: 10.1214/14-AAP1020

Primary: 60H30
Secondary: 91A13 , 93E20

Keywords: flocking models , Mean field games , price impact , weak formulation

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.25 • No. 3 • June 2015
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