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The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…

Machine Learning · Computer Science 2012-12-12 Eric P. Xing , Michael I. Jordan , Stuart Russell

In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects…

Optimization and Control · Mathematics 2024-03-07 Xin Yue Ren , Dena Firoozi

We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the…

Optimization and Control · Mathematics 2024-09-13 Erhan Bayraktar , Zhenhua Wang

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…

Mathematical Finance · Quantitative Finance 2019-12-13 Philippe Casgrain , Sebastian Jaimungal

We study a mean-field version of Bank-El Karoui's representation theorem of stochastic processes. Under different technical conditions, we establish some existence and uniqueness results. As motivation and first applications, our mean-field…

Probability · Mathematics 2025-07-16 Xihao He , Xiaolu Tan , Jun Zou

Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…

Probability · Mathematics 2025-03-18 Anton Braverman , Ziv Scully

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…

Machine Learning · Statistics 2025-12-02 Jiajia Yu , Junghwan Lee , Yao Xie , Xiuyuan Cheng

We investigate a mean field game model for the production of exhaustible resources. In this model, firms produce comparable goods, strategically set their production rate in order to maximise profit, and leave the market as soon as they…

Optimization and Control · Mathematics 2019-02-27 P. Jameson Graber , Charafeddine Mouzouni

We propose a simple model of the banking system incorporating a game feature where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The Markov Nash equilibrium generated through minimizing the linear…

Mathematical Finance · Quantitative Finance 2026-05-22 Li-Hsien Sun

This paper proposes and analyzes two neural network methods to solve the master equation for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash equilibria for stochastic, differential games with finite but large…

Optimization and Control · Mathematics 2024-12-24 Asaf Cohen , Mathieu Laurière , Ethan Zell

We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…

Probability · Mathematics 2018-02-01 Alekos Cecchin , Markus Fischer

In this paper we study a fully discrete Semi-Lagrangian approximation of a second order Mean Field Game system, which can be degenerate. We prove that the resulting scheme is well posed and, if the state dimension is equals to one, we prove…

Numerical Analysis · Mathematics 2014-04-24 Elisabetta Carlini , Francisco José Silva Álvarez

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…

Performance · Computer Science 2021-11-03 Sebastian Allmeier , Nicolas Gast

Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free…

In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our…

Optimization and Control · Mathematics 2026-04-14 Agustín Muñoz González , Juan I. Sequeira , Rafael Orive Illera

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

Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that…

Numerical Analysis · Mathematics 2025-01-31 Yuri Ashrafyan , Diogo Gomes

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

Mean field game (MFG) is an expressive modeling framework for systems with a continuum of interacting agents. While many approaches exist for solving the forward MFG, few have studied its \textit{inverse} problem. In this work, we seek to…

Optimization and Control · Mathematics 2025-07-28 Han Huang , Jiajia Yu , Tianyi Chen , Rongjie Lai

We introduce and study a two-player zero-sum game between a probabilist and Nature defined by a convex function $f$, a finite collection $\mathcal{B}$ of Markov generators (or its convex hull), and a target distribution $\pi$. The…

Probability · Mathematics 2025-09-11 Michael C. H. Choi , Geoffrey Wolfer