English
Related papers

Related papers: Entropy Regularization in Mean-Field Games of Opti…

200 papers

This paper studies the mean-field Markov decision process (MDP) with the centralized stopping under the non-exponential discount. The problem differs fundamentally from most existing studies on mean-field optimal control/stopping due to its…

Optimization and Control · Mathematics 2025-01-22 Xiang Yu , Fengyi Yuan

We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…

Optimization and Control · Mathematics 2023-01-25 Roxana Dumitrescu , Marcos Leutscher , Peter Tankov

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…

Optimization and Control · Mathematics 2022-06-08 Jianhui Huang , Tinghan Xie

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…

Optimization and Control · Mathematics 2023-05-24 Han Huang , Jiajia Yu , Jie Chen , Rongjie Lai

We consider discrete-time stationary mean field games (MFG) with unknown dynamics and design algorithms for finding the equilibrium with finite-time complexity guarantees. Prior solutions to the problem assume either the contraction of a…

Optimization and Control · Mathematics 2025-02-13 Sihan Zeng , Sujay Bhatt , Alec Koppel , Sumitra Ganesh

This paper develops a unified framework for proving the existence of solutions to stationary first-order mean-field games (MFGs) based on the theory of monotone operators in Banach spaces. We cast the coupled MFG system as a variational…

Analysis of PDEs · Mathematics 2026-03-17 Rita Ferreira , Diogo Gomes , Melih Ucer

In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…

Optimization and Control · Mathematics 2026-03-27 François Delarue , Pierre Lavigne

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard…

Numerical Analysis · Mathematics 2017-05-02 Diogo Gomes , Joao Saude

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

Optimization and Control · Mathematics 2023-08-29 Xin Guo , Anran Hu , Junzi Zhang

Mean field games (MFGs) have emerged as a powerful framework for modeling interactions in large-scale multi-agent systems. Despite recent advancements in reinforcement learning (RL) for MFGs, existing methods are typically limited to finite…

Machine Learning · Computer Science 2025-10-28 Lorenzo Magnino , Kai Shao , Zida Wu , Jiacheng Shen , Mathieu Laurière

Reinforcement learning for multi-agent games has attracted lots of attention recently. However, given the challenge of solving Nash equilibria for large population games, existing works with guaranteed polynomial complexities either focus…

Optimization and Control · Mathematics 2025-09-04 Anran Hu , Junzi Zhang

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…

Computer Science and Game Theory · Computer Science 2010-12-13 Sachin Adlakha , Ramesh Johari

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

We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by…

Optimization and Control · Mathematics 2025-07-28 Giorgio Ferrari , Anna Pajola

Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…

Optimization and Control · Mathematics 2026-02-16 William Hofgard , Asaf Cohen , Mathieu Laurière

This paper investigates stationary mean-field games (MFGs) on the torus with Lipschitz non-homogeneous diffusion and logarithmic-like couplings. The primary objective is to understand the existence of $C^{1,\alpha}$ solutions to address the…

Analysis of PDEs · Mathematics 2023-10-27 Tigran Bakaryan , Giuseppe Di Fazio , Diogo A. Gomes

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

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

Optimization and Control · Mathematics 2020-07-09 Géraldine Bouveret , Roxana Dumitrescu , Peter Tankov

We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…

Analysis of PDEs · Mathematics 2016-02-16 Marco Cirant

In this paper, we study the long-time behavior of mean field game (MFG) systems influenced by a common noise. While classical results establish the convergence of deterministic MFG towards stationary solutions under suitable monotonicity…

Analysis of PDEs · Mathematics 2025-09-23 Pierre Cardaliaguet , Raphaël Maillet , Wenbin Yan