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This paper is devoted to the study of Mean-field Games (MFG) systems in the mass critical exponent case. We firstly establish the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some…

Analysis of PDEs · Mathematics 2024-08-05 Marco Cirant , Fanze Kong , Juncheng Wei , Xiaoyu Zeng

We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability…

Optimization and Control · Mathematics 2022-09-20 Erhan Bayraktar , Alekos Cecchin , Prakash Chakraborty

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…

Optimization and Control · Mathematics 2025-01-23 Alain Bensoussan , Ho Man Tai , Tak Kwong Wong , Sheung Chi Phillip Yam

Mean-field Games systems (MFGs) serve as paradigms to describe the games among a huge number of players. In this paper, we consider the ergodic Mean-field Games systems in the bounded domain with Neumann boundary conditions and the…

Functional Analysis · Mathematics 2025-01-28 Fanze Kong , Yonghui Tong , Xiaoyu Zeng

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…

Computer Science and Game Theory · Computer Science 2022-07-26 Yue Guan , Mi Zhou , Ali Pakniyat , Panagiotis Tsiotras

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…

Optimization and Control · Mathematics 2020-08-18 Weichen Wang , Jiequn Han , Zhuoran Yang , Zhaoran Wang

In this paper, we consider a finite horizon, non-stationary, mean field games (MFG) with a large population of homogeneous players, sequentially making strategic decisions, where each player is affected by other players through an aggregate…

Systems and Control · Electrical Eng. & Systems 2020-04-07 Rajesh K Mishra , Deepanshu Vasal , Sriram Vishwanath

This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions,…

Optimization and Control · Mathematics 2017-08-04 Guanxing Fu , Ulrich Horst

Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A…

Optimization and Control · Mathematics 2020-05-04 Kristoffer Lindensjö

We present a graphon mean-field logit dynamic, a stationary mean-field game based on logit interactions. This dynamic emerges from a stochastic control problem involving a continuum of nonexchangeable and interacting agents and reduces to…

Optimization and Control · Mathematics 2026-02-10 H. Yoshioka

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

We study an ergodic mean field game problem with state constraints. In our model the agents are affected by idiosyncratic noise and use a (singular) feedback control to prevent the Brownian motion from exiting the domain. We characterize…

Analysis of PDEs · Mathematics 2023-10-05 Alessio Porretta , Michele Ricciardi

This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.

Probability · Mathematics 2026-03-09 Imane Jarni , Ayoub Laayoun , Badr Missaoui

This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of whom interacts under a mean field game (MFG) framework. Unlike the conventional…

Optimization and Control · Mathematics 2024-07-02 Dantong Chu , Kenneth Tsz Hin Ng , Sheung Chi Phillip Yam , Harry Zheng

In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We allow the drift coefficient $b$ and the diffusion coefficient…

Probability · Mathematics 2025-10-01 Alain Bensoussan , Ziyu Huang , Shanjian Tang , Sheung Chi Phillip Yam

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Optimization and Control · Mathematics 2020-03-11 Yves Achdou , Mathieu Laurière

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

Probability · Mathematics 2014-08-13 Daniel Lacker

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

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