Related papers: Mean Field Games with a Dominating Player
We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…
This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…
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 examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…
In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…
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…
We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…
We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
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 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…
Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…
In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…
Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…
Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…
We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…
We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand,…