Open Access
November 2016 Mean field games with common noise
René Carmona, François Delarue, Daniel Lacker
Ann. Probab. 44(6): 3740-3803 (November 2016). DOI: 10.1214/15-AOP1060


A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions.


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René Carmona. François Delarue. Daniel Lacker. "Mean field games with common noise." Ann. Probab. 44 (6) 3740 - 3803, November 2016.


Received: 1 July 2014; Revised: 1 July 2015; Published: November 2016
First available in Project Euclid: 14 November 2016

zbMATH: 06674837
MathSciNet: MR3572323
Digital Object Identifier: 10.1214/15-AOP1060

Primary: 93E20
Secondary: 60H10 , 91A13

Keywords: McKean–Vlasov equations , Mean field games , relaxed controls , stochastic optimal control , weak solutions

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 6 • November 2016
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