Related papers: Microscopic Derivation of Mean Field Game Models
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…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
Learning in games provides a powerful framework to design control policies for self-interested agents that may be coupled through their dynamics, costs, or constraints. We consider the case where the dynamics of the coupled system can be…
Coordinating communication and control is a key component in the stability and performance of networked multi-agent systems. While single user networked control systems have gained a lot of attention within this domain, in this work, we…
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…
Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…
Traditional multi-agent reinforcement learning algorithms are not scalable to environments with more than a few agents, since these algorithms are exponential in the number of agents. Recent research has introduced successful methods to…
For noncooperative games the mean field (MF) methodology provides decentralized strategies which yield Nash equilibria for large population systems in the asymptotic limit of an infinite (mass) population. The MF control laws use only the…
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
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.…
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…
In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…
Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash…
This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility…
Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…
We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…
In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…