相关论文: Existence of Optimal Stationary Singular Controls …

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…

We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…

This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is…

This paper establishes the existence of equilibria result of a class of mean field games with singular controls. The interaction takes place through both states and controls. A relaxed solution approach is used. To circumvent the tightness…

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…

This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process,…

Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…

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 consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

We provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unbounded and there are also presence of cross terms in the…

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

The paper is concerned with the study of a control system consisting of one major agent and many identical minor agents in the limit case when the number of agents tends to infinity. To study the limiting system we use the mean field…

Motivated by continuous-time optimal inventory management, we study a class of stationary mean-field control problems with singular controls. The dynamics are modeled by a mean-reverting Ornstein-Uhlenbeck process, and the performance…

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…

We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…