Corpus ID: 237396291

Set Values for Mean Field Games

  title={Set Values for Mean Field Games},
  author={Melih Iseri and Jianfeng Zhang},
In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the mean field game. When the mean field equilibrium is unique, typically under certain monotonicity conditions, our set value reduces to the singleton of the standard value function which solves the master equation. The set value is by nature unique, and we shall… Expand


Selection of equilibria in a linear quadratic mean-field game
Abstract In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study theExpand
Selection by vanishing common noise for potential finite state mean field games
The goal of this paper is to provide a selection principle for potential mean field games on a finite state space and, in this respect, to show that equilibria that do not minimize the correspondingExpand
Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications and includes original material and applications with explicit examples throughout, including numerical solutions. Expand
Convergence to the mean field game limit: A case study
We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it asExpand
On the connection between symmetric $N$-player games and mean field games
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 meanExpand
From the master equation to mean field game limit theory: Large deviations and concentration of measure
We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empiricalExpand
Probabilistic Analysis of Mean-Field Games
It is proved that a solution of the Mean-Field Game problem as formulated by Lasry and Lions, does indeed provide a solution and existence and regularity of the corresponding value function are proved. Expand
On the convergence of closed-loop Nash equilibria to the mean field game limit
This paper continues the study of the mean field game (MFG) convergence problem: In what sense do the Nash equilibria of $n$-player stochastic differential games converge to the mean field game asExpand
A general characterization of the mean field limit for stochastic differential games
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions areExpand
Closed-loop convergence for mean field games with common noise
This paper studies the convergence problem for mean field games with common noise. We define a suitable notion of weak mean field equilibria, which we prove captures all subsequential limit points,Expand