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Mean Field Game is a rather new field initially developed in applied mathematics and engineering in order to deal with the dynamics of a large number of controlled agents or objects in interaction. For a large class of these models, there…

Physics and Society · Physics 2021-08-25 Thibault Bonnemain , Thierry Gobron , Denis Ullmo

This paper proposes a novel Mean-Field Game (MFG) framework for large-scale attacker-defender systems aimed at protecting one or multiple High-Value Units (HVUs). Motivated by classical agent-wise attrition models, we introduce a…

Analysis of PDEs · Mathematics 2026-04-03 Avetik Arakelyan , Tigran Bakaryan , Davit Alaverdyan , Naira Hovakimyan , Isaac Kaminer

This paper investigates a class of mixed stochastic linear-quadratic-Gaussian (LQG) social optimization and Nash game in the context of a large scale system. Two types of interactive agents are involved: a major agent and a large number of…

Optimization and Control · Mathematics 2021-12-14 Xinwei Feng , Jianhui Huang , Zhenghong Qiu

The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the solution the MFGS are given. Two H\"older stability estimates…

Analysis of PDEs · Mathematics 2023-11-27 Michael V. Klibanov , Jingzhi Li , Hongyu Liu

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the…

Optimization and Control · Mathematics 2019-08-09 Fabio Bagagiolo , Silvia Faggian , Rosario Maggistro , Raffaele Pesenti

We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large…

Mathematical Physics · Physics 2012-12-27 Pierre Degond , Jian-Guo Liu , Christian Ringhofer

In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our…

Optimization and Control · Mathematics 2026-04-14 Agustín Muñoz González , Juan I. Sequeira , Rafael Orive Illera

We explore the problem of imitation learning (IL) in the context of mean-field games (MFGs), where the goal is to imitate the behavior of a population of agents following a Nash equilibrium policy according to some unknown payoff function.…

Machine Learning · Computer Science 2023-06-27 Giorgia Ramponi , Pavel Kolev , Olivier Pietquin , Niao He , Mathieu Laurière , Matthieu Geist

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…

Optimization and Control · Mathematics 2026-01-01 Grégoire Lambrecht , Mathieu Laurière

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…

Optimization and Control · Mathematics 2024-05-06 Zongxia Liang , Keyu Zhang

This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a…

Numerical Analysis · Mathematics 2023-10-10 Chengfeng Shen , Yifan Luo , Zhennan Zhou

We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…

Analysis of PDEs · Mathematics 2024-03-18 Martino Bardi , Hicham Kouhkouh

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…

Optimization and Control · Mathematics 2018-11-08 Pierre Cardaliaguet , Marco Cirant , Alessio Porretta

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established…

Machine Learning · Statistics 2025-05-30 Antonio Ocello , Daniil Tiapkin , Lorenzo Mancini , Mathieu Laurière , Eric Moulines

We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field Game…

Optimization and Control · Mathematics 2023-11-28 Philippe Bergault , Pierre Cardaliaguet , Catherine Rainer

In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects…

Optimization and Control · Mathematics 2024-03-07 Xin Yue Ren , Dena Firoozi

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…

Optimization and Control · Mathematics 2021-07-12 René Carmona , Mathieu Laurière

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…

Optimization and Control · Mathematics 2024-12-17 Tejaswi K. C. , Taeyoung Lee

We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as network connection a large number of nodes, where each node is characterized by a local electricity consumption,…

Probability · Mathematics 2019-06-21 Clemence Alasseur , Imen Ben Tahar , Anis Matoussi