On monotone solutions of mean field games master equations
Charles Bertucci1
1 CMAP, Ecole Polytechnique, UMR 7641, 91120 Palaiseau, France
Séminaire Laurent Schwartz — EDP et applications (2021-2022), Talk no. 14, 13 p.

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.

Published online:
DOI: 10.5802/slsedp.153
Charles Bertucci 1

1 CMAP, Ecole Polytechnique, UMR 7641, 91120 Palaiseau, France 
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Charles Bertucci. On monotone solutions of mean field games master equations. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Talk no. 14, 13 p. doi : 10.5802/slsedp.153. https://proceedings.centre-mersenne.org/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. | DOI | MR | Zbl

[6] Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, and Pierre-Louis Lions. The Master Equation and the Convergence Problem in Mean Field Games:(AMS-201), volume 201. Princeton University Press, 2019. | Zbl

[7] Jean-Michel Lasry and Pierre-Louis Lions. Mean field games. Japanese Journal of Mathematics, 2(1):229–260, 2007. | DOI | MR | Zbl

[8] Pierre-Louis Lions. Cours au College de France, 2011. www.college-de-france.fr.

[9] Charles Stegall. Optimization of functions on certain subsets of Banach spaces. Mathematische Annalen, 236(2):171–176, 1978. | DOI | MR | Zbl

[10] Charles Stegall. Optimization and differentiation in Banach spaces. Linear Algebra and Its Applications, 84:191–211, 1986. | DOI | MR | Zbl

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