Related papers: Mean Field Game and Control for Switching Hybrid S…
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…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a…
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…
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…
This paper discusses the control of coherent structures in turbulent flows, which has broad applications among complex systems in science and technology. Mean field games have been proved a powerful tool and are proposed here to control the…
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…
Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…
A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…
In this paper we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field of control setting, that is in which the dynamics of each agent is affected not only by the average position of the…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
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…
A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…
Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled agents in interaction. Here we consider such systems when the interactions between agents result in a negative coordination and analyze…