相关论文: Global well-posedness of Master equations for dete…
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 include both deterministic models and dynamics driven solely by…
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 master equations. A rate of dissipation of a bilinear form is…
This paper is concerned with extending the notion of monotone solution to the mean field game (MFG) master equation to situations in which the coefficients are displacement monotone, instead of the previously introduced notion in the flat…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
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 games. The considered Hamiltonians are non-separable and $local$…
It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and…
We establish the first unconditional well-posedness result for the master equation associated with a general class of mean field games of controls. Our analysis covers games with displacement monotone or Lasry--Lions monotone data, as well…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
The aim of this paper is to study the long time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed on the torus ${\mathbb T}^n$ in [P. Cardaliaguet, {\it Long time average of first…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
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 time horizons and for general non-separable Hamiltonians that…
The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…
We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that…
In this manuscript, we establish the global well-posedness for master equations of mean field games of controls, where the interaction is through the joint law of the state and control. Our results are proved under two different conditions:…
We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows…
Here, we consider the planning problem for first-order mean-field games (MFG). When there is no coupling between players, MFG degenerate into optimal transport problems. Displacement convexity is a fundamental tool in optimal transport that…
We study the wellposedness of the master equation for a second-order mean field games with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by investigating a degenerate mean field games system for…
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs…
In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…