June 2022 On first order mean field game systems with a common noise
Pierre Cardaliaguet, Panagiotis E. Souganidis
Author Affiliations +
Ann. Appl. Probab. 32(3): 2289-2326 (June 2022). DOI: 10.1214/21-AAP1734

Abstract

We consider mean field games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution exists and is unique for monotone coupling functions. We also use the solution to find approximate optimal strategies (Nash equilibria) for N-player differential games with common but no idiosyncratic noise. An important step in the analysis is the study of the well-posedness of a stochastic backward Hamilton–Jacobi equation.

Funding Statement

P.Cardaliaguet was partially supported by AFOSR Grant FA9550-18-1-0494. P. E. Souganidis was partially supported by NSF Grants DMS-1600129 and DMS-1900599, ONR Grant N000141712095 and AFOSR Grant FA9550-18-1-0494.

Citation

Download Citation

Pierre Cardaliaguet. Panagiotis E. Souganidis. "On first order mean field game systems with a common noise." Ann. Appl. Probab. 32 (3) 2289 - 2326, June 2022. https://doi.org/10.1214/21-AAP1734

Information

Received: 1 September 2020; Revised: 1 June 2021; Published: June 2022
First available in Project Euclid: 29 May 2022

MathSciNet: MR4430014
zbMATH: 1498.91040
Digital Object Identifier: 10.1214/21-AAP1734

Subjects:
Primary: 49L25 , 49N80 , 60H15

Keywords: Backward stochastic partial differential equations , common noise , maximum principle , Mean field games

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.32 • No. 3 • June 2022
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