[图书][B] Probabilistic theory of mean field games with applications I-II
The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …
games with a common noise. We develop a general two-step strategy for the search of weak …
[图书][B] Regularity theory for mean-field game systems
This book brings together several recent developments on the regularity theory for mean-
field game systems. We detail several classes of methods and present a concise overview of …
field game systems. We detail several classes of methods and present a concise overview of …
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 …
Normalized solutions of mass supercritical Schrödinger equations with potential
This paper is concerned with the existence of normalized solutions of the nonlinear
Schrödinger equation− Δ u+ V (x) u+ λ u=| u| p− 2 u in RN in the mass supercritical and …
Schrödinger equation− Δ u+ V (x) u+ λ u=| u| p− 2 u in RN in the mass supercritical and …
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 …
Normalized solutions to mass supercritical Schrödinger equations with negative potential
We study the existence of positive solutions with prescribed L 2-norm for the mass
supercritical Schrödinger equation− Δ u+ λ u− V (x) u=| u| p− 2 uu∈ H 1 (RN), λ∈ R, where …
supercritical Schrödinger equation− Δ u+ λ u− V (x) u=| u| p− 2 uu∈ H 1 (RN), λ∈ R, where …
Normalized solutions for nonlinear Schrödinger systems on bounded domains
We analyze-normalized solutions of nonlinear Schrödinger systems of Gross–Pitaevskii
type, on bounded domains, with homogeneous Dirichlet boundary conditions. We provide …
type, on bounded domains, with homogeneous Dirichlet boundary conditions. We provide …
Normalized concentrating solutions to nonlinear elliptic problems
We prove the existence of solutions (λ, v)∈ R× H 1 (Ω) of the elliptic problem {− Δ v+(V (x)+
λ) v= vp in Ω, v> 0,∫ Ω v 2 dx= ρ. Any v solving such problem (for some λ) is called a …
λ) v= vp in Ω, v> 0,∫ Ω v 2 dx= ρ. Any v solving such problem (for some λ) is called a …
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 games models of segregation
This paper introduces and analyzes some models in the framework of mean field games
(MFGs) describing interactions between two populations motivated by the studies on urban …
(MFGs) describing interactions between two populations motivated by the studies on urban …