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In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a…

Trading and Market Microstructure · Quantitative Finance 2017-09-22 Pierre Cardaliaguet , Charles-Albert Lehalle

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global interaction term is recovered from the single measurement…

Numerical Analysis · Mathematics 2023-10-16 Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG)…

Numerical Analysis · Mathematics 2024-05-20 Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

Mean Field Games (MFGs) provide a powerful framework for modeling the collective behavior of large populations of interacting agents. In this paper, we address the problem of Imitation Learning (IL) in MFGs subject to common noise, where…

Machine Learning · Computer Science 2026-05-06 Grégoire Lambrecht , Mathieu Laurière

This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…

Optimization and Control · Mathematics 2025-10-15 Anran Hu , Zijiu Lyu

The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of…

Optimization and Control · Mathematics 2025-04-21 Hidekazu Yoshioka

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…

Optimization and Control · Mathematics 2025-06-09 Philipp Plank , Yufei Zhang

A Coefficient Inverse Problem (CIP) of the determination of a coefficient of the Mean Field Games System (MFGS) of the second order is considered. The input data are generated by a single measurement event. Lateral Cauchy data, i.e.…

Analysis of PDEs · Mathematics 2023-07-03 Michael V. Klibanov

We propose a MFG model with quadratic Hamiltonian involving $N$ populations. This results in a system of $N$ Hamilton-Jacobi-Bellman and $N$ Fokker-Planck equations with non-local interactions. As in the classical case we introduce an…

Analysis of PDEs · Mathematics 2025-11-03 Luigi De Pascale , Luca Nenna

We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…

Numerical Analysis · Mathematics 2026-05-12 Elisabetta Carlini , Valentina Coscetti

We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies…

Optimization and Control · Mathematics 2023-02-16 Andrea Angiuli , Nils Detering , Jean-Pierre Fouque , Mathieu Lauriere , Jimin Lin

Mean field games (MFGs) offer a versatile framework for modeling large-scale interactive systems across multiple domains. This paper builds upon a previous work, by developing a state-of-the-art unified approach to decode or design the…

Analysis of PDEs · Mathematics 2025-01-22 Hongyu Liu , Catharine W. K. Lo

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

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…

Machine Learning · Statistics 2025-12-02 Jiajia Yu , Junghwan Lee , Yao Xie , Xiuyuan Cheng

To model complex real-world systems, such as traders in stock markets, or the dissemination of contagious diseases, graphon mean-field games (GMFG) have been proposed to model many agents. Despite the empirical success, our understanding of…

Computer Science and Game Theory · Computer Science 2024-10-14 Jing Dong , Baoxiang Wang , Yaoliang Yu

Coordinating large populations of autonomous agents, such as UAV swarms or satellite constellations, poses significant computational challenges for traditional multi-agent control methods. This paper introduces a new optimization framework…

Optimization and Control · Mathematics 2026-03-18 Di Yu , Sixiong You , Chaoying Pei

Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

Analysis of PDEs · Mathematics 2017-10-05 David Evangelista , Rita Ferreira , Diogo A. Gomes , Levon Nurbekyan , Vardan Voskanyan

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a…

Systems and Control · Electrical Eng. & Systems 2020-10-02 Muhammad Aneeq uz Zaman , Kaiqing Zhang , Erik Miehling , Tamer Başar