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We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…

Optimization and Control · Mathematics 2019-05-30 Marcel Nutz , Jaime San Martin , Xiaowei Tan

In this paper, we investigate a class of mean field games where the mean field interactions are achieved through the joint (conditional) distribution of the controlled state and the control process. The strategies are of $open\;loop$ type,…

Probability · Mathematics 2021-08-05 Mao Fabrice Djete

This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…

Optimization and Control · Mathematics 2016-09-27 Sen Li , Wei Zhang , Lin Zhao

In this article we study the convergence of the Nash Equilibria in a N-player differential game towards the optimal strategies in the Mean Field Games, when the dynamic of the generic player includes a reflection process which guarantees…

Analysis of PDEs · Mathematics 2022-03-16 Michele Ricciardi

This work studies the behaviors of two large-population teams competing in a discrete environment. The team-level interactions are modeled as a zero-sum game while the agent dynamics within each team is formulated as a collaborative…

Systems and Control · Electrical Eng. & Systems 2024-02-26 Yue Guan , Mohammad Afshari , Panagiotis Tsiotras

We introduce a general representation of large-population games in which each player s influence ON the others IS centralized AND limited, but may otherwise be arbitrary.This representation significantly generalizes the class known AS…

Computer Science and Game Theory · Computer Science 2013-01-07 Michael Kearns , Yishay Mansour

This paper studies the limits of empirical means of open-loop Nash equilibria of linear-quadratic stochastic differential games as the number of players goes to infinity, when the corresponding mean field game is of potential type and may…

Probability · Mathematics 2026-02-27 Alekos Cecchin , Jodi Dianetti

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

Probability · Mathematics 2015-04-09 Rene Carmona , Daniel Lacker

Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…

Optimization and Control · Mathematics 2025-05-21 Hui Huang , Jethro Warnett

Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that…

Computer Science and Game Theory · Computer Science 2020-03-27 Paulin Jacquot , Cheng Wan , Olivier Beaude , Nadia Oudjane

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

Optimization and Control · Mathematics 2021-12-20 Franco Flandoli , Maddalena Ghio , Giulia Livieri

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 introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…

Probability · Mathematics 2017-09-28 Luciano Campi , Markus Fischer

This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…

Optimization and Control · Mathematics 2019-07-03 Athanasios Vasiliadis

We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…

Computer Science and Game Theory · Computer Science 2026-02-18 Rafael Frongillo , Melody Hsu , Mary Monroe , Anish Thilagar

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

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

This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…

Optimization and Control · Mathematics 2024-12-02 Yu Si , Jingtao Shi