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Related papers: Finite State Mean Field Games with Common Shocks

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We consider the mean field game of cross--holding introduced in \citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity value dynamics are affected by a common noise. In contrast with \cite{DjeteTouzi}, the problem…

Probability · Mathematics 2024-03-26 Leila Bassou , Mao Fabrice Djete , Nizar Touzi

In this paper, we consider the social optimal problem of discrete time finite state space mean field games (referred to as finite mean field games [1]). Unlike the individual optimization of their own cost function in competitive models, in…

Optimization and Control · Mathematics 2024-08-09 Zijia Niu , Sanjin Huang , Lu Ren , Wang Yao , Xiao Zhang

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…

Optimization and Control · Mathematics 2026-01-01 Grégoire Lambrecht , Mathieu Laurière

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Optimization and Control · Mathematics 2025-12-05 P. Jameson Graber , Kyle Rosengartner

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

In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…

Optimization and Control · Mathematics 2024-09-26 Ziteng Cheng , Sebastian Jaimungal

The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…

Optimization and Control · Mathematics 2024-01-23 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on…

Probability · Mathematics 2021-01-12 Erhan Bayraktar , Alekos Cecchin , Asaf Cohen , Francois Delarue

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

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Optimization and Control · Mathematics 2020-03-11 Yves Achdou , Mathieu Laurière

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…

Probability · Mathematics 2023-08-29 Mao Fabrice Djete

In this paper, we consider a mean field game model inspired by crowd motion where agents aim to reach a closed set, called target set, in minimal time. Congestion phenomena are modeled through a constraint on the velocity of an agent that…

Optimization and Control · Mathematics 2022-12-23 Saeed Sadeghi Arjmand , Guilherme Mazanti

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

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Probability · Mathematics 2022-04-21 Vassili Kolokoltsov , Marianna Troeva

We study an ergodic mean field game problem with state constraints. In our model the agents are affected by idiosyncratic noise and use a (singular) feedback control to prevent the Brownian motion from exiting the domain. We characterize…

Analysis of PDEs · Mathematics 2023-10-05 Alessio Porretta , Michele Ricciardi

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Optimization and Control · Mathematics 2022-12-21 Justina Gianatti , Francisco J. Silva

Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs. This leads to a nested-loop structure with millions of simulations of common…

Optimization and Control · Mathematics 2021-06-08 Ming Min , Ruimeng Hu

This paper investigates a class of general linear-quadratic mean field games with common noise, where the diffusion terms of the system contain the state variables, control variables, and the average state terms. We solve the problem using…

Optimization and Control · Mathematics 2025-08-29 Yu Si , Jingtao Shi

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

Optimization and Control · Mathematics 2017-11-07 Piermarco Cannarsa , Rossana Capuani

We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…

Analysis of PDEs · Mathematics 2016-02-16 Marco Cirant