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Related papers: One-dimensional forward-forward mean-field games

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In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…

Analysis of PDEs · Mathematics 2020-07-29 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

Motivated by the recent interests in asymmetric mean field games, this paper provides a general framework of Heterogeneous Mean Field Game (HMFG) that subsumes different formulations of graphon mean field games. The key feature of the HMFG…

Optimization and Control · Mathematics 2025-11-26 Bixing Qiao

We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. In generative flows, a Lagrangian formulation is used where each particle (generated sample)…

Machine Learning · Statistics 2023-10-25 Benjamin J. Zhang , Markos A. Katsoulakis

The intersection of Mean Field Games (MFGs) and Reinforcement Learning (RL) has fostered a growing family of algorithms designed to solve large-scale multi-agent systems. However, the field currently lacks a standardized evaluation…

Machine Learning · Computer Science 2026-02-16 Lorenzo Magnino , Jiacheng Shen , Matthieu Geist , Olivier Pietquin , Mathieu Laurière

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…

Mathematical Finance · Quantitative Finance 2021-09-28 Masaaki Fujii , Akihiko Takahashi

This article presents the variant of the approach introduced in the recent work of Bensoussan, Wong, Yam and Yuan [13] to the generic first-order mean field game problem. A major contribution here is the provision of new crucial a priori…

Optimization and Control · Mathematics 2023-12-13 Alain Bensoussan , Tak Kwong Wong , Sheung Chi Phillip Yam , Hongwei Yuan

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

Optimization and Control · Mathematics 2025-06-03 Dirk Becherer , Christoph Reisinger , Jonathan Tam

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure…

Analysis of PDEs · Mathematics 2025-05-14 Hongyu Liu , Catharine W. K. Lo

Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…

Optimization and Control · Mathematics 2014-12-24 Pierre Degond , Michael Herty , Jian-Guo Liu

We consider the mean-field game price formation model introduced by Gomes and Sa\'ude. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and…

Numerical Analysis · Mathematics 2022-04-05 Yuri Ashrafyan , Tigran Bakaryan , Diogo Gomes , Julian Gutierrez

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

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

We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…

Optimization and Control · Mathematics 2026-02-23 Andreas Sojmark , Zeng Zhang

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a…

Computer Science and Game Theory · Computer Science 2025-07-29 Kai Shao , Jiacheng Shen , Mathieu Laurière

Mean field games equations are examined for conservation laws. The system of mean field games equations consists of two partial differential equations: the Hamilton-Jacobi-Bellman equation for the value function and the forward Kolmogorov…

Mathematical Physics · Physics 2023-05-12 Roman Kozlov

This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…

Optimization and Control · Mathematics 2025-11-10 Lijun Bo , Jingfei Wang , Xiang Yu

In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…

Analysis of PDEs · Mathematics 2015-06-23 Diogo A. Gomes , Vardan K. Voskanyan

In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…

Analysis of PDEs · Mathematics 2023-03-28 E Carlini , Francisco José Silva , Ahmad Zorkot

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 analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…

Analysis of PDEs · Mathematics 2020-10-27 Jameson Graber , Alan Mullenix , Laurent Pfeiffer