Scaling up mean field games with online mirror descent
We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online
Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash …
Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash …
An introduction to mean field game theory
These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …
games involving infinitely many interacting players. We focus here on the Partial Differential …
On non-uniqueness and uniqueness of solutions in finite-horizon mean field games
M Bardi, M Fischer - ESAIM: Control, Optimisation and Calculus of …, 2019 - esaim-cocv.org
This paper presents a class of evolutive Mean Field Games with multiple solutions for all
time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T …
time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T …
Stable solutions in potential mean field game systems
A Briani, P Cardaliaguet - Nonlinear Differential Equations and …, 2018 - Springer
Stable solutions in potential mean field game systems Page 1 Nonlinear Differ. Equ. Appl. (2018)
25:1 c 2017 Springer International Publishing AG, part of Springer Nature 1021-9722/18/010001-26 …
25:1 c 2017 Springer International Publishing AG, part of Springer Nature 1021-9722/18/010001-26 …
Mean field control and mean field game models with several populations
A Bensoussan, T Huang, M Lauriere - arXiv preprint arXiv:1810.00783, 2018 - arxiv.org
In this paper, we investigate the interaction of two populations with a large number of
indistinguishable agents. The problem consists in two levels: the interaction between agents …
indistinguishable agents. The problem consists in two levels: the interaction between agents …
Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics
A Aurell, B Djehiche - SIAM Journal on Control and Optimization, 2018 - SIAM
We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram
[Transp. Res. B: Methodol., 45 (2011), pp. 1572--1589] to allow for nonlocal crowd aversion …
[Transp. Res. B: Methodol., 45 (2011), pp. 1572--1589] to allow for nonlocal crowd aversion …
On the existence and uniqueness of solutions to time-dependent fractional MFG
We establish existence and uniqueness of solutions to evolutive fractional mean field game
systems with regularizing coupling for any order of the fractional Laplacian s∈(0,1). The …
systems with regularizing coupling for any order of the fractional Laplacian s∈(0,1). The …
Time-dependent focusing mean-field games: the sub-critical case
M Cirant, D Tonon - Journal of Dynamics and Differential Equations, 2019 - Springer
We consider time-dependent viscous mean-field games systems in the case of local,
decreasing and unbounded couplings. These systems arise in mean-field game theory, and …
decreasing and unbounded couplings. These systems arise in mean-field game theory, and …
Short time solution to the master equation of a first order mean field game
S Mayorga - Journal of Differential Equations, 2020 - Elsevier
The goal of this paper is to show existence of short-time classical solutions to the so called
Master Equation of first order Mean Field Games, which can be thought of as the limit of the …
Master Equation of first order Mean Field Games, which can be thought of as the limit of the …
Unique determination of cost functions in a multipopulation mean field game model
K Ren, N Soedjak, K Wang - arXiv preprint arXiv:2312.01622, 2023 - arxiv.org
This paper studies an inverse problem for a multipopulation mean field game (MFG) system
where the objective is to reconstruct the running and terminal cost functions of the system …
where the objective is to reconstruct the running and terminal cost functions of the system …