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Related papers: Mean-field games with unbounded controls: a weak f…

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In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…

Optimization and Control · Mathematics 2016-10-20 Ying Hu , Huang Jianhui , Xun Li

This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions,…

Optimization and Control · Mathematics 2017-08-04 Guanxing Fu , Ulrich Horst

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…

Systems and Control · Computer Science 2017-01-17 Naci Saldi , Tamer Başar , Maxim Raginsky

This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual…

Optimization and Control · Mathematics 2025-08-05 Tian Chen , Tianyang Nie , Zhen Wu

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost…

Optimization and Control · Mathematics 2012-10-11 Hamidou Tembine , Quanyan Zhu , Tamer Basar

The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $\mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability…

Optimization and Control · Mathematics 2019-12-11 Piermarco Cannarsa , Cristian Mendico

We consider a class of $N$-player games and mean-field games of singular controls with ergodic performance criterion, providing a benchmark case for irreversible investment games featuring mean-field interaction and strategic…

Optimization and Control · Mathematics 2025-04-30 Federico Cannerozzi , Giorgio Ferrari

This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The…

Optimization and Control · Mathematics 2014-08-06 Said Hamadène , Rui Mu

Conditional McKean-Vlasov control problems involve controlling McKean-Vlasov diffusions where the interaction occurs through the law of the state process conditionally on it staying in a domain. Introduced by Lions in his 2016 lectures at…

Probability · Mathematics 2025-10-09 René Carmona , Ludovic Tangpi , Kaiwen Zhang

Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…

Optimization and Control · Mathematics 2020-01-09 Berenice Anne Neumann

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

Following Kolokoltsov's work [1], we present an extension of mean-field control theory in quantum framework. In particular such an extension is done naturally by considering the Belavkin quantum filtering and control theory in a mean-field…

Optimization and Control · Mathematics 2023-06-27 Sofiane Chalal , Nina H. Amini , Gaoyue Guo

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

Probability · Mathematics 2025-09-03 Dylan Possamaï , Mehdi Talbi

We consider stochastic differential games with $N$ nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the…

Analysis of PDEs · Mathematics 2014-03-18 Fabio S. Priuli

We consider a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…

Optimization and Control · Mathematics 2025-06-10 Tianjiao Hua , Peng Luo

This paper studies infinite horizon linear quadratic (LQ) mean field problems with common noise and regime switching, covering both control and game formulations. To establish a theoretical foundation for the LQ framework, we first analyze…

Optimization and Control · Mathematics 2025-11-24 Qingmeng Wei , Yaqi Xu

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

Optimization and Control · Mathematics 2023-08-29 Xin Guo , Anran Hu , Junzi Zhang

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

We address the problem of existence and (non-)uniqueness of solutions $\big(c,u(\cdot),\mu\big)$ to ergodic mean-field games in the whole space $\mathbb{R}^{m}$ with unbounded and merely measurable data, and for non-separable Hamiltonian.…

Analysis of PDEs · Mathematics 2023-11-09 Hicham Kouhkouh

This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a…

Mathematical Finance · Quantitative Finance 2026-05-26 Weilun Cheng , Zongxia Liang , Sheng Wang , Xiang Yu