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Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria, yet ensuring mathematically consistent density-coupled evolution remains a major challenge. This paper proposes the…

Machine Learning · Computer Science 2025-03-11 Jinwei Liu , Lu Ren , Wang Yao , Xiao Zhang

Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

Analysis of PDEs · Mathematics 2017-03-30 Diogo Gomes , Marc Sedjro

We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…

Optimization and Control · Mathematics 2026-04-17 Eyal Neuman , Sturmius Tuschmann

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

Analysis of PDEs · Mathematics 2017-10-05 David Evangelista , Rita Ferreira , Diogo A. Gomes , Levon Nurbekyan , Vardan Voskanyan

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

Systems and Control · Electrical Eng. & Systems 2023-01-18 Naci Saldi

Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games which involve a large number of agents that are weakly coupled via a weighted undirected graph on which each node represents an agent. The links of the graph…

Systems and Control · Electrical Eng. & Systems 2021-06-24 Shuang Gao , Rinel Foguen Tchuendom , Peter E. Caines

The goal of the paper is to develop the theory of finite state mean field games with major and minor players when the state space of the game is finite. We introduce the finite player games and derive a mean field game formulation in the…

Probability · Mathematics 2016-10-19 Rene Carmona , Peiqi Wang

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses…

Numerical Analysis · Mathematics 2015-11-23 Noha Almulla , Rita Ferreira , Diogo Gomes

We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is…

Analysis of PDEs · Mathematics 2014-07-10 Martino Bardi , Fabio S. Priuli

We propose and study several inverse problems for the mean field games (MFG) system in a bounded domain. Our focus is on simultaneously recovering the running cost and the Hamiltonian within the MFG system by the associated boundary…

Optimization and Control · Mathematics 2024-03-05 Hongyu Liu , Shen Zhang

We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition…

Optimization and Control · Mathematics 2021-06-16 Alexander Aurell , Rene Carmona , Gokce Dayanikli , Mathieu Lauriere

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

We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as network connection a large number of nodes, where each node is characterized by a local electricity consumption,…

Probability · Mathematics 2019-06-21 Clemence Alasseur , Imen Ben Tahar , Anis Matoussi

Here, we examine the Wardrop equilibrium model on networks with flow-dependent costs and its connection with stationary mean-field games (MFG). In the first part of this paper, we present the Wardrop and the first-order MFG models on…

Analysis of PDEs · Mathematics 2022-07-05 Fatimah Al Saleh , Tigran Bakaryan , Diogo A. Gomes , Ricardo Ribeiro

A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the…

Systems and Control · Computer Science 2022-01-11 Dena Firoozi , Ali Pakniyat , Peter E. Caines

In this work, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population based on a limited set of noisy partial observations of the…

Numerical Analysis · Mathematics 2022-04-12 Yat Tin Chow , Samy Wu Fung , Siting Liu , Levon Nurbekyan , Stanley Osher

This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…

Optimization and Control · Mathematics 2024-01-18 Charles Bertucci , Alekos Cecchin

This paper studies the dynamic pricing mechanism for data products in demand-driven markets through a game-theoretic framework. We develop a three-tier Stackelberg game model to capture the hierarchical strategic interactions among key…

Optimization and Control · Mathematics 2025-12-29 Lijun Bo , Dongfang Yang , Shihua Wang

In this article, we propose two numerical methods, the Gaussian Process (GP) method and the Fourier Features (FF) algorithm, to solve mean field games (MFGs). The GP algorithm approximates the solution of a MFG with maximum a posteriori…

Numerical Analysis · Mathematics 2022-05-10 Chenchen Mou , Xianjin Yang , Chao Zhou

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

Analysis of PDEs · Mathematics 2016-10-04 Diogo A. Gomes , Stefania Patrizi