相关论文: Minimal-time mean field games

The theory of mean field games studies the limiting behaviors of large systems where the agents interact with each other in a certain symmetric way. The running and terminal costs are critical for the agents to decide the strategies.…

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

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…

We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite time horizons. We prove the existence of…

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential…

Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…

We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…

We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic…

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…

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with…

In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects.…

Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are "forbidden" to the generic player at some points. We establish the existence of a weak…

This paper is concerned with a class of linear-quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each…

This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most…

We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…

We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in Mean Field Games with a variational structure. We prove L infinity regularity…

We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a…