English
Related papers

Related papers: On Classical Solutions to the Mean Field Game Syst…

200 papers

This paper investigates a novel class of mean field games involving a major agent and numerous minor agents, where the agents' functionals are recursive with nonlinear backward stochastic differential equation (BSDE) representations. We…

Optimization and Control · Mathematics 2024-12-17 Jianhui Huang , Wenqiang Li , Harry Zheng

This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…

Optimization and Control · Mathematics 2024-12-02 Yu Si , Jingtao Shi

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

Optimization and Control · Mathematics 2019-10-31 Martin Frank , Michael Herty , Torsten Trimborn

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

Numerical Analysis · Mathematics 2015-11-23 Simone Cacace , Fabio Camilli , Claudio Marchi

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an…

Optimization and Control · Mathematics 2018-02-15 Sen Li , Wei Zhang , Lin Zhao

H\"older stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic Hamiltonian. The main tool is the apparatus of Carleman…

Analysis of PDEs · Mathematics 2023-11-02 Michael V. Klibanov , Mikhail Y. Kokurin , Jingzhi Li

We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…

Optimization and Control · Mathematics 2022-04-05 Mao Fabrice Djete , Nizar Touzi

Independent learners are agents that employ single-agent algorithms in multi-agent systems, intentionally ignoring the effect of other strategic agents. This paper studies mean-field games from a decentralized learning perspective, with two…

Computer Science and Game Theory · Computer Science 2025-02-04 Bora Yongacoglu , Gürdal Arslan , Serdar Yüksel

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

We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As…

Optimization and Control · Mathematics 2019-05-14 Nacira Agram , Salah Eddine Choutri

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and…

Optimization and Control · Mathematics 2024-06-07 Fuzhong Zhou , Chenyu Zhang , Xu Chen , Xuan Di

This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur…

Optimization and Control · Mathematics 2020-01-31 Samer Dweik , Guilherme Mazanti

Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…

Probability · Mathematics 2016-08-23 Giulia Di Nunno , Hannes Haferkorn

We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such…

Mathematical Finance · Quantitative Finance 2018-09-13 Guanxing Fu , Ulrich Horst

The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…

Probability · Mathematics 2013-03-26 René Carmona , Francois Delarue

We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function.…

Optimization and Control · Mathematics 2024-10-30 Fabio Camilli , Mathieu Laurière , Qing Tang

In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a…

Analysis of PDEs · Mathematics 2024-08-16 Kui Ren , Nathan Soedjak , Kewei Wang , Hongyu Zhai

This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…

Optimization and Control · Mathematics 2022-02-21 Guilherme Mazanti , Filippo Santambrogio

In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing…

Optimization and Control · Mathematics 2026-03-17 Charles Meynard