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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

We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…

Analysis of PDEs · Mathematics 2023-01-12 Sebastian Munoz

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…

Probability · Mathematics 2020-03-03 Yinggu Chen , Boualem Djehiche , Said Hamadene

We consider a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…

Optimization and Control · Mathematics 2025-06-10 Tianjiao Hua , Peng Luo

In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We allow the drift coefficient $b$ and the diffusion coefficient…

Probability · Mathematics 2025-10-01 Alain Bensoussan , Ziyu Huang , Shanjian Tang , Sheung Chi Phillip Yam

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…

Probability · Mathematics 2022-05-26 Jian Song , Meng Wang

We consider a couple of integrodifferential PDEs arising from a stochastic Markovian control problem subjected to initial-terminal conditions. These equations correspond to the MFG system for a controlled jump-diffusion process. We prove…

Mathematical Physics · Physics 2022-10-12 Olga Rozanova , Ilnar Manapov

We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…

Analysis of PDEs · Mathematics 2021-05-04 Indranil Chowdhury , Olav Ersland , Espen R. Jakobsen

In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…

Optimization and Control · Mathematics 2018-05-16 Saeed Hadikhanloo , Francisco José Silva

We propose a mean field game (MFG) framework to model the evolution of renewable energy production in competitive electricity markets. Producers interact through the spot price while optimising their profits under production, installation,…

Optimization and Control · Mathematics 2026-03-25 Luciano Campi , Zhuoshu Wu

This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process,…

Optimization and Control · Mathematics 2017-02-03 Khaled Bahlali , Meriem Mezerdi , Brahim Mezerdi

The collective behaviour of stochastic multi-agents swarms driven by Gaussian and non-Gaussian environments is analytically discussed in a mean-field approach. We first exogenously implement long range mutual interactions rules with…

Statistical Mechanics · Physics 2018-11-21 Max-Olivier Hongler

We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…

Optimization and Control · Mathematics 2020-10-06 Matteo Basei , Haoyang Cao , Xin Guo

Here, we consider the planning problem for first-order mean-field games (MFG). When there is no coupling between players, MFG degenerate into optimal transport problems. Displacement convexity is a fundamental tool in optimal transport that…

Analysis of PDEs · Mathematics 2018-07-20 Diogo Gomes , Tommaso Seneci

This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized…

Optimization and Control · Mathematics 2021-04-09 Liangquan Zhang , Xun Li

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

Machine Learning · Computer Science 2026-04-16 Anna C. M. Thöni , Yoram Bachrach , Tal Kachman

In this paper, we focus on stationary (ergodic) mean-field games (MFGs). These games arise in the study of the long-time behavior of finite-horizon MFGs. Motivated by a prior scheme for Hamilton-Jacobi equations introduced in Aubry-Mather's…

Analysis of PDEs · Mathematics 2021-09-28 Tigran Bakaryan , Diogo Gomes , Héctor Sánchez Morgado

In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…

Analysis of PDEs · Mathematics 2022-12-21 Hongyu Liu , Shen Zhang

We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…

Optimization and Control · Mathematics 2026-05-28 Hanchao Liu , Dena Firoozi

In this paper, we study a class of degenerate mean field game systems arising from the mean field games with H\"ormander diffusion, where the generic player may have a ``forbidden'' direction at some point. Here we prove the existence and…

Analysis of PDEs · Mathematics 2023-08-22 Yiming Jiang , Jingchuang Ren , Yawei Wei , Jie Xue