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We consider a stationary Mean Field Games system defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal control interpretation of the…

Analysis of PDEs · Mathematics 2015-05-20 Fabio Camilli , Claudio Marchi

In this paper, we explore Bertrand and Cournot Mean Field Games models for market competition with reflection boundary conditions. We prove existence, uniqueness and regularity of solutions to the system of equations, and show that this…

Analysis of PDEs · Mathematics 2017-09-13 P. Jameson Graber , Charafeddine Mouzouni

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…

Analysis of PDEs · Mathematics 2018-01-23 Fabio Camilli , Raul De Maio

The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…

Probability · Mathematics 2012-10-23 Rene Carmona , Francois Delarue

We discuss a class of explicitly solvable mean field type control problems/mean field games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional…

Optimization and Control · Mathematics 2021-04-28 Sören Christensen , Berenice Anne Neumann , Tobias Sohr

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…

Optimization and Control · Mathematics 2021-01-05 Minyi Huang , Yan Ma

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…

Probability · Mathematics 2015-04-09 Daniel Lacker

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

Optimization and Control · Mathematics 2019-05-28 Nevroz Sen , Peter E. Caines

Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary…

Computer Science and Game Theory · Computer Science 2023-12-14 Semih Kara , Nuno C. Martins

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

In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…

Optimization and Control · Mathematics 2024-11-05 Ziyu Huang , Shanjian Tang

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

In this paper, we examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…

Optimization and Control · Mathematics 2025-06-04 Asaf Cohen , Chuhao Sun

Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash…

Optimization and Control · Mathematics 2023-04-26 Jiajia Yu , Rongjie Lai , Wuchen Li , Stanley Osher

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…

Optimization and Control · Mathematics 2025-09-23 Haoyang Cao , Jodi Dianetti , Giorgio Ferrari

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

Optimization and Control · Mathematics 2020-07-23 Lisang Ding , Wuchen Li , Stanley Osher , Wotao Yin

We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation, to set-up a principal / agent contract theory model where the principal faces a large population of agents…

Probability · Mathematics 2018-08-27 Rene Carmona , Peiqi Wang

In this paper, we study the infinite-time mean field games with discounting, establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution. To solve this problem, we partition all agents…

Optimization and Control · Mathematics 2026-03-17 Yongsheng Song , Zeyu Yang

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…

Optimization and Control · Mathematics 2025-05-14 Giorgio Ferrari , Ioannis Tzouanas

We study in this paper three aspects of Mean Field Games. The first one is the case when the dynamics of each player depend on the strategies of the other players. The second one concerns the modeling of '' noise '' in discrete space models…

Analysis of PDEs · Mathematics 2018-08-02 Charles Bertucci , Jean Michel Lasry , Pierre Louis Lions