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Related papers: Mean Field Games with a Dominating Player

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We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…

Optimization and Control · Mathematics 2021-03-09 Marcel Nutz , Yuchong Zhang

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…

Optimization and Control · Mathematics 2024-05-06 Zongxia Liang , Keyu Zhang

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 examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…

Optimization and Control · Mathematics 2025-06-04 Asaf Cohen , Chuhao Sun

In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…

Optimization and Control · Mathematics 2024-11-05 Ziyu Huang , Shanjian Tang

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…

Optimization and Control · Mathematics 2025-05-14 Giorgio Ferrari , Ioannis Tzouanas

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

Probability · Mathematics 2018-12-05 Alekos Cecchin , Guglielmo Pelino

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…

Optimization and Control · Mathematics 2017-10-10 Ying Hu , Jianhui Huang , Tianyang Nie

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Optimization and Control · Mathematics 2014-01-09 Pierre Cardaliaguet , Philip Jameson Graber

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…

Optimization and Control · Mathematics 2021-01-05 Minyi Huang , Yan Ma

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated It\^o-diffusion via a two-sided singular stochastic control…

Optimization and Control · Mathematics 2024-12-31 Jodi Dianetti , Giorgio Ferrari , Ioannis Tzouanas

This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a…

Information Theory · Computer Science 2013-01-30 François Mériaux , Vineeth Varma , Samson Lasaulce

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

Systems and Control · Computer Science 2018-06-06 Naci Saldi , Tamer Basar , Maxim Raginsky

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

Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…

Optimization and Control · Mathematics 2019-01-01 Piermarco Cannarsa , Rossana Capuani , Pierre Cardaliaguet

Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…

Optimization and Control · Mathematics 2024-12-17 Tejaswi K. C. , Taeyoung Lee

We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for…

Optimization and Control · Mathematics 2020-11-09 Michael Herty , Sonja Steffensen , Anna Thünen

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…

Analysis of PDEs · Mathematics 2018-07-13 Erhan Bayraktar , Asaf Cohen

In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…

Optimization and Control · Mathematics 2022-08-16 Saeed Sadeghi Arjmand , Guilherme Mazanti

We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand,…

Trading and Market Microstructure · Quantitative Finance 2024-01-11 Philippe Bergault , Leandro Sánchez-Betancourt