相关论文: Obstacle Mean-Field Game Problem
A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton-Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption…
We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a…
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 introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning…
In this expository article, we give an overview of the concept of potential mean field games of first order. We give a new proof that minimizers of the potential are equilibria by using a Lagrangian formulation. We also provide criteria to…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
In this paper, we consider a class of linear quadratic extended mean field games (MFGs) with common noises where the state coefficients and the cost functional vary with the mean field term in a nonlinear way. Based on stochastic maximum…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
We consider a class of optimal control problems that arise in connection with optimal advertising under uncertainty. Two main features appear in the model: a delay in the control variable driving the state dynamics; a mean-field term both…
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…
We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…
The paper is concerned with two-person zero-sum mean-field linear-quadratic stochastic differential games over finite horizons. By a Hilbert space method, a necessary condition and a sufficient condition are derived for the existence of an…
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…
The paper considers a forward-backward system of parabolic PDEs arising in a Mean Field Game (MFG) model where every agent controls the drift of a trajectory subject to Brownian diffusion, trying to escape a given bounded domain $\Omega$ in…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…
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 of a same population, and the interaction between the two…
Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely…