Add to ORKGIn this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study mean field games and master equations. We consider both deterministic problems and problems in presence of idiosyncratic noise. The point of view via this transport equation has two important consequences. First, this equation reveals a new monotonicity condition that is sufficient both for the uniqueness of MFG Nash equilibria and for the global in time well-posedness of master equations. Interestingly, this condition is in general in dichotomy with both the Lasry--Lions and displacement monotonicity conditions, studied so far in the literature. Second, in the absence of monotonicity, the conservative form of th...
In this paper we construct short time classical solutions to a class of master equations in the pres...
We present the notion of monotone solution of mean field games master equations in the case of a con...
Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential gam...
We present the notion of monotone solution of mean field games master equations in the case of a con...
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games inv...
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games inv...
The purpose of this work is to introduce a notion of weak solution to the master equation of a poten...
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games inv...
We consider $N$-player and mean field games in continuous time over a finite horizon, where the posi...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sen...
openThe purpose of this paper is to develop the mean field game theory with several populations. In ...
In this paper we construct short time classical solutions to a class of master equations in the pres...
We present the notion of monotone solution of mean field games master equations in the case of a con...
Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential gam...
We present the notion of monotone solution of mean field games master equations in the case of a con...
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games inv...
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games inv...
The purpose of this work is to introduce a notion of weak solution to the master equation of a poten...
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games inv...
We consider $N$-player and mean field games in continuous time over a finite horizon, where the posi...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
For a mean field game model with a major and infinite minor players, we characterize a notion of Nas...
It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sen...
openThe purpose of this paper is to develop the mean field game theory with several populations. In ...
In this paper we construct short time classical solutions to a class of master equations in the pres...
We present the notion of monotone solution of mean field games master equations in the case of a con...
Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential gam...