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We provide an approximation scheme for first-order stationary mean field games with a separable Hamiltonian. First, we discretize Hamilton-Jacobi equations by discretizing in time, and then prove the existence of minimizing holonomic…

Analysis of PDEs · Mathematics 2021-11-24 Renato Iturriaga , Kaizhi Wang

We consider continuous-time heterogeneous agent models with recursive utility (Epstein-Zin utility) cast as mean field games, in which agents prefer late resolution of uncertainty. The model leads to a system coupling a pair of…

Optimization and Control · Mathematics 2026-05-27 Yves Achdou , Qing Tang

While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…

Analysis of PDEs · Mathematics 2024-02-01 Adriano Festa , Simone Gottlich , Michele Ricciardi

We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot…

Analysis of PDEs · Mathematics 2022-08-25 P. Jameson Graber , Ronnie Sircar

In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument through its Hessian matrix. We work under fairly natural…

Analysis of PDEs · Mathematics 2020-10-30 Pêdra D. S. Andrade , Edgard A. Pimentel

Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…

Optimization and Control · Mathematics 2026-02-16 William Hofgard , Asaf Cohen , Mathieu Laurière

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…

Mathematical Finance · Quantitative Finance 2019-04-02 Philippe Casgrain , Sebastian Jaimungal

The paper is devoted to the first-order mean field game system in the case when the distribution of players can contain atoms. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi…

Analysis of PDEs · Mathematics 2014-04-21 Yurii Averboukh

We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The…

Analysis of PDEs · Mathematics 2019-03-08 Yves Achdou , Manh-Khang Dao , Olivier Ley , Nicoletta Tchou

We consider a mean-field model for large banking systems, which takes into account default and recovery of the institutions. Building on models used for groups of interacting neurons, we first study a McKean-Vlasov dynamics and its…

Optimization and Control · Mathematics 2020-01-29 Romuald Élie , Tomoyuki Ichiba , Mathieu Laurière

In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our…

Economics · Quantitative Finance 2015-06-17 Shuhua Chang , Xinyu Wang , Alexander Shananin

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

Optimization and Control · Mathematics 2025-05-09 Julian Barreiro-Gomez , Tyrone E. Duncan , Bozenna Pasik-Duncan , Hamidou Tembine

A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton-Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption…

Analysis of PDEs · Mathematics 2016-11-29 Diogo A. Gomes , Levon Nurbekyan , Mariana Prazeres

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…

Optimization and Control · Mathematics 2026-03-09 Ulrich Horst , Takashi Sato

We study a degenerate second order mean field game (MFG) system in a Hilbert space $H$ which couples a Fokker--Planck equation describing the evolution of probability measures on $H$ with a Hamilton--Jacobi--Bellman (HJB) equation for the…

Analysis of PDEs · Mathematics 2026-05-14 Andrzej Święch , Lukas Wessels

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…

Probability · Mathematics 2017-05-29 Markus Fischer

We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant…

Analysis of PDEs · Mathematics 2018-05-30 Yves Achdou , Manh-Khang Dao , Olivier Ley , Nicoletta Tchou

We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…

Optimization and Control · Mathematics 2023-05-03 Justina Gianatti , Francisco J. Silva , Ahmad Zorkot

This work is devoted to finding the closed-loop equilibria for a class of mean-field games (MFGs) with infinitely many symmetric players in a common switching environment when the cost functional is under general discount in time. There are…

Optimization and Control · Mathematics 2024-03-04 Hongwei Mei , Son Luu Nguyen , George Yin

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva