相关论文: The planning problem in Mean Field Games as regula…

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…

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…

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…

This paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify conditions under which a paradoxical non-monotone behavior…

We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of…

This paper deals with the existence of solutions of a class of contact mean field games systems of first order. Cardaliaguet \cite{CAR} found a link between the weak KAM theory for Hamiltonian systems and mean field games systems. We prove…

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…

This paper presents a general existence and uniqueness result for mean field games equations on graphs ($\mathcal{G}$-MFG). In particular, our setting allows to take into account congestion effects of almost any form. These general…

We consider the problem of routing for logistics purposes, in a contested environment where an adversary attempts to disrupt the vehicle along the chosen route. We construct a game-theoretic model that captures the problem of optimal…

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…

Mean-field Games systems (MFGs) serve as paradigms to describe the games among a huge number of players. In this paper, we consider the ergodic Mean-field Games systems in the bounded domain with Neumann boundary conditions and the…

In many robotics applications, multiple robots are working in a shared workspace to complete a set of tasks as fast as possible. Such settings can be treated as multi-modal multi-robot multi-goal path planning problems, where each robot has…

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot…

We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…

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…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…