相关论文: Non-coercive first order Mean Field Games

We study first order evolutive Mean Field Games whose operators are non-coercive. This situation occurs, for instance, when some directions are `forbidden' to the generic player at some points. Under some regularity assumptions, we…

In this paper we study evolutive first order Mean Field Games in the Heisenberg group; each agent can move in the whole space but it has to follow "horizontal" trajectories which are given in terms of the vector fields generating the group…

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…

In this paper we study evolutive first order Mean Field Games in the Heisenberg group~$\He^1$; each agent can move only along "horizontal" trajectories which are given in terms of the vector fields generating~$\He^1$ and the kinetic part of…

We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both…

We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove…

We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…

In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain $\Omega \subset \mathbb{R}^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of…

Motivated by parallels between mean field games and random matrix theory, we develop stochastic optimal control problems and viscosity solutions to Hamilton-Jacobi equations in the setting of non-commutative variables. Rather than real…

We study the regularity and long time behavior of the one-dimensional, local, first-order mean field games system and the planning problem, assuming a Hamiltonian of superlinear growth, with a non-separated, strictly monotone dependence on…

Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-order quasi-stationary Mean Field Games system, which involves…

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 study the regularity and well-posedness of the local, first-order forward-backward mean field games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data that…

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…

We investigate time dependent, first order Mean Field Games on the torus comparing, in a broad and general framework, the classical differential formulation , given by a Hamilton Jacobi equation coupled with a continuity equation, with a…

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…

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…