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In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…

Analysis of PDEs · Mathematics 2026-04-10 Jameson Graber , Kyle Rosengartner

Mean Field Control Games (MFCG), introduced in [Angiuli et al., 2022a], represent competitive games between a large number of large collaborative groups of agents in the infinite limit of number and size of groups. In this paper, we prove…

Optimization and Control · Mathematics 2024-06-05 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

We are concerned with the mathematical study of the Mean Field Games system (MFGS). In the conventional setup, the MFGS is a system of two coupled nonlinear parabolic PDEs of the second order in a backward-forward manner, namely one…

Analysis of PDEs · Mathematics 2023-04-04 Michael V. Klibanov , Jingzhi Li , Hongyu Liu

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

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

We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers…

Optimization and Control · Mathematics 2020-01-22 Takashi Tanaka , Ehsan Nekouei , Ali Reza Pedram , Karl Henrik Johansson

Mean field games (MFGs) have been introduced to study Nash equilibria in very large population of self-interested agents. However, when applied to common pool resource (CPR) games, MFG equilibria lead to the so-called tragedy of the commons…

Optimization and Control · Mathematics 2025-04-15 Gokce Dayanikli , Mathieu Lauriere

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…

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

In this paper we establish quantitative convergence results for both open and closed-loop Nash equilibria of N-player stochastic differential games in the setting of Mean Field Games of Controls (MFGC), a class of models where interactions…

Probability · Mathematics 2025-07-24 Joe Jackson , Alpár R. Mészáros

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

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

Adaptation and Self-Organizing Systems · Physics 2018-06-22 Piyush Grover , Kaivalya Bakshi , Evangelos A. Theodorou

In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a…

Trading and Market Microstructure · Quantitative Finance 2017-09-22 Pierre Cardaliaguet , Charles-Albert Lehalle

In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish…

Analysis of PDEs · Mathematics 2024-12-12 Qi Lü , Zhonghua Liao

In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…

Optimization and Control · Mathematics 2018-05-16 Saeed Hadikhanloo , Francisco José Silva

This paper explores the use of Maximum Causal Entropy Inverse Reinforcement Learning (IRL) within the context of discrete-time stationary Mean-Field Games (MFGs) characterized by finite state spaces and an infinite-horizon,…

Systems and Control · Electrical Eng. & Systems 2025-07-22 Berkay Anahtarci , Can Deha Kariksiz , Naci Saldi

We propose a reinforcement learning algorithm for stationary mean-field games, where the goal is to learn a pair of mean-field state and stationary policy that constitutes the Nash equilibrium. When viewing the mean-field state and the…

Machine Learning · Computer Science 2020-10-12 Qiaomin Xie , Zhuoran Yang , Zhaoran Wang , Andreea Minca

In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the…

Machine Learning · Computer Science 2012-10-18 Hamidou Tembine , Raul Tempone , Pedro Vilanova

Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Jun He , Andrew L. Liu , Yihsu Chen

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the…

Analysis of PDEs · Mathematics 2019-05-07 Rita Ferreira , Diogo Gomes , Xianjin Yang

The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…

Analysis of PDEs · Mathematics 2019-08-20 Sergio Mayorga