Probability, finance and signal: conference in honour of René Carmona / Probabilités, finance et signal: conférence en l'honneur de René Carmona

Collection Probability, finance and signal: conference in honour of René Carmona / Probabilités, finance et signal: conférence en l'honneur de René Carmona

Organizer(s) Acciaio, Beatrice ; Crepey, Stephane ; Delarue, Franзois ; Lacker, Daniel ; Oudjane, Nadia

Date(s) 19/05/2025 - 23/05/2025

linked URL https://conferences.cirm-math.fr/3238.html

00:00:00 / 00:00:00

2 6

Continuous-time mean field games: a primal-dual characterization

In this talk, we will establish a primal-dual formulation for continuous-time mean field games (MFGs) and provide a complete analytical characterization of the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the representative player's control problem with measurable coefficients is equivalent to a linear program over the space of occupation measures. We then establish the dual formulation of this linear program as a maximization problem over smooth subsolutions of the associated Hamilton-Jacobi-Bellman (HJB) equation, which plays a fundamental role in characterizing NEs of MFGs. Finally, a complete characterization of all NEs for MFGs is established by the strong duality between the linear program and its dual problem. This strong duality is obtained by studying the solvability of the dual problem, and in particular through analyzing the regularity of the associated HJB equation. its NE characterization do not require the convexity of the associated Hamiltonianor the uniqueness of its optimizer, and remain applicable when the HJB equation lacks classical or even continuous solutions.

Information about the video

Date of recording 20/05/2025
Date of publication 04/06/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20347903
Cite this video Guo, Xin (20/05/2025). Continuous-time mean field games: a primal-dual characterization. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20347903
URL https://dx.doi.org/10.24350/CIRM.V.20347903

Domain(s)

Bibliography

GUO, Xin, HU, Anran, ZHANG, Jiacheng, et al. Continuous-time mean field games: a primal-dual characterization. arXiv preprint arXiv:2503.01042, 2025 - https://doi.org/10.48550/arXiv.2503.01042

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