相关论文: Discrete mean field games

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company…

Multiagent reinforcement learning algorithms have not been widely adopted in large scale environments with many agents as they often scale poorly with the number of agents. Using mean field theory to aggregate agents has been proposed as a…

In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion, by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem similar…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +$\infty$, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a…

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated It\^o-diffusion via a two-sided singular stochastic control…

This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…

In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN)…

A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the…

We study a class of deterministic mean field games on finite and infinite time horizons arising in models of optimal exploitation of exhaustible resources. The main characteristic of our game is an absorption constraint on the players'…

This paper studies a multi-agent system starting from a single agent dynamics which is a nonlinear affine control system. It analyze what happens when the number of agents goes to infinity using two different approaches, a granular…

In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…

This article focuses two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (u,m) of the…

We investigate mean field games for players, who are weakly coupled via their empirical measure. To this end we investigate time-dependent pure jump type propagators over a finite space in the framework of non-linear Markov processes. We…

We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…

In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process…

We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…

We consider team optimal control of decentralized systems with linear dynamics, quadratic costs, and arbitrary disturbance that consist of multiple sub-populations with exchangeable agents (i.e., exchanging two agents within the same…

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…