相关论文: The Mean Field Games System: Carleman Estimates, L…
A retrospective analysis process for the mean field games system (MFGS) is considered. For the first time, Carleman estimates are applied to the analysis of the MFGS. Two new Carleman estimates are derived. They allow to obtain the…
The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the solution the MFGS are given. Two H\"older stability estimates…
We are concerned with the mathematical study of the Mean Field Games system (MFGS). In the conventional setup, the MFGS is a system of two coupled nonlinear parabolic PDEs of the second order in a backward-forward manner, namely one…
In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish…
The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a system of two nonlinear parabolic partial differential…
A Coefficient Inverse Problem (CIP) of the determination of a coefficient of the Mean Field Games System (MFGS) of the second order is considered. The input data are generated by a single measurement event. Lateral Cauchy data, i.e.…
We investigate inverse backward-in-time problems for a class of second-order degenerate Mean-Field Game (MFG) systems. More precisely, given the final datum $(u(\cdot, T),m(\cdot, T))$ of a solution to the one-dimensional mean-field game…
H\"older stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic Hamiltonian. The main tool is the apparatus of Carleman…
We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…
For an inverse coefficient problem of determining a state-varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an…
In this paper we study second order master equations arising from mean field games with common noise over arbitrary time duration. A classical solution typically requires the monotonicity condition (or small time duration) and sufficiently…
In this article, from the viewpoint of control theory, we discuss the relationships among the commonly used monotonicity conditions that ensure the well-posedness of the solutions arising from problems of mean field games (MFGs) and mean…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…
The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…
In a bounded domain $\Omega \subset \mathbb{R}^d$ over time interval $(0,T)$, we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian. We attach the non-zero Robin…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…