10 papers
Quantitative convergence for displacement monotone Mean Field Games of control
Joe Jackson, Alpár R. Mészáros
In this paper we establish quantitative convergence results for both open and closed-loop Nash equilibria of N-player stochastic differential games in the setting of Mean Field Gam…
On the equivalence between static and dynamic optimal transport governed by linear control systems
Amit Einav, Yue Jiang, Alpár R. Mészáros
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\…
On a Cross-Diffusion System with Independent Drifts and no Self-Diffusion: The Existence of Totally Mixed Solutions
Alpár R. Mészáros, Guy Parker
We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governe…
Long Time Behavior and Stabilization for Displacement Monotone Mean Field Games
Marco Cirant, Alpár R. Mészáros
This paper is devoted to the study of the long time behavior of Nash equilibria in Mean Field Games within the framework of displacement monotonicity. We first show that any two eq…
Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials
Noemi David, Alpár R. Mészáros, Filippo Santambrogio
Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to…
Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size
Huafu Liao, Alpár R. Mészáros, Chenchen Mou +1
This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural S…
Kinetic-type Mean Field Games with Non-separable Local Hamiltonians
David M. Ambrose, Megan Griffin-Pickering, Alpár R. Mészáros
We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables repres…
Hidden monotonicity and canonical transformations for mean field games and master equations
Mohit Bansil, Alpár R. Mészáros
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional . Our findings contr…
On classical solutions and canonical transformations for Hamilton--Jacobi--Bellman equations
Mohit Bansil, Alpár R. Mészáros
In this note we show how canonical transformations reveal hidden convexity properties for deterministic optimal control problems, which in turn result in global existence of $C^{1,…
Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations
Mohit Bansil, Alpár R. Mészáros, Chenchen Mou
In this paper we construct global in time classical solutions to mean field games master equations in the lack of idiosyncratic noise in the individual agents' dynamics. These incl…