16 citations · 36 across the 13 of their papers we have counts for
15 papers
Numerical analysis of first-order mean field games under displacement monotonicity
Alpár R. Mészáros, Yohance A. P. Osborne
We introduce a particle method for the numerical approximation of time-dependent first-order Mean Field Games (MFGs) systems with non-separable, displacement monotone Hamiltonians…
On monotonicity conditions for Mean Field Games
P. Jameson Graber, Alpár R. Mészáros
In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $…
On Some Mean Field Games and Master Equations through the lens of conservation laws
P. Jameson Graber, Alpár R. Mészáros
In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and mast…
A variational approach to first order kinetic Mean Field Games with local couplings
Megan Griffin-Pickering, Alpár R. Mészáros
First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit…
Mean Field Games systems under displacement monotonicity
Alpár R. Mészáros, Chenchen Mou
In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long t…
Well-posedness of mean field games master equations involving non-separable local Hamiltonians
David M. Ambrose, Alpár R. Mészáros
In this paper we construct short time classical solutions to a class of master equations in the presence of non-degenerate individual noise arising in the theory of mean field game…
Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity
Wilfrid Gangbo, Alpár R. Mészáros, Chenchen Mou +1
In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games maste…
On nonexpansiveness of metric projection operators on Wasserstein spaces
Anshul Adve, Alpár Mészáros
In this paper we investigate properties of metric projections onto specific closed and geodesically convex proper subsets of Wasserstein spaces …
Global well-posedness of Master equations for deterministic displacement convex potential mean field games
Wilfrid Gangbo, Alpár R. Mészáros
This manuscript constructs global in time solutions to the for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions,…
Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients
Dohyun Kwon, Alpár Richárd Mészáros
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models.…
Weak solutions to the Muskat problem with surface tension via optimal transport
Matt Jacobs, Inwon Kim, Alpár R. Mészáros
Inspired by recent works on the threshold dynamics scheme for multi-phase mean curvature flow (by Esedoglu-Otto and Laux-Otto), we introduce a novel framework to approximate soluti…
Sobolev regularity for first order Mean Field Games
P. Jameson Graber, Alpár R. Mészáros
In this paper we obtain Sobolev estimates for weak solutions of first oder variational Mean Field Game systems with coupling terms that are local function of the density variable.…
Uniqueness issues for evolution equations with density constraints
Simone Di Marino, Alpár Richárd Mészáros
In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialis…
Advection-diffusion equations with density constraints
Alpár Richárd Mészáros, Filippo Santambrogio
In the spirit of the macroscopic crowd motion models with hard congestion (i.e. a strong density constraint ) introduced by Maury {\it et al.} some years ago, we analyze a…
A variational approach to second order mean field games with density constraints: the stationary case
Alpár Richárd Mészáros, Francisco J. Silva
In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain . We show the existence of weak solution…