Geodesic
On monotone solutions of mean field games master equations
Bertucci, Charles1
1 CMAP, Ecole Polytechnique, UMR 7641, 91120 Palaiseau, France
Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 14, 13 p.

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This note presents the concept of monotone solutions of mean field games master equations, in several cases. The first case that I treat is the one in which the underlying game has only a finite state space. The other are the case of a continuous state space and the so-called Hilbertian approach. Most of the results presented here come from the two papers [1, 2], except for results concerning the Hilbert space case and the case of general monotone operators which are new.

Publié le :
DOI : 10.5802/slsedp.153

Bertucci, Charles 1

1 CMAP, Ecole Polytechnique, UMR 7641, 91120 Palaiseau, France 
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Bertucci, Charles. On monotone solutions of mean field games master equations. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 14, 13 p. doi : 10.5802/slsedp.153. http://geodesic.mathdoc.fr/articles/10.5802/slsedp.153/

[1] Charles Bertucci. Monotone solutions for mean field games master equations: finite state space and optimal stopping. Journal de l’École polytechnique — Mathématiques, 8:1099–1132, 2021. | Zbl

[2] Charles Bertucci. Monotone solutions for mean field games master equations: continuous state space and common noise, 2021. | arXiv

[3] Charles Bertucci and Alekos Cecchin. Mean field games master equations: from discrete to continuous state space, 2022. Available at charles-bertucci@github.io.

[4] Charles Bertucci, Jean-Michel Lasry, and Pierre-Louis Lions. On Lipschitz solutions of mean field games master equations, 2022. Forthcoming.

[5] Pierre Cardaliaguet and Panagiotis Souganidis. Monotone solutions of the master equation for mean field games with idiosyncratic noise. SIAM Journal on Mathematical Analysis, 54(4):4198–4237, 2022. | Zbl | MR | DOI

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