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Related papers: Discrete mean field games

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The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. The framework is that of mean-field and of cooperative…

Systems and Control · Computer Science 2017-12-12 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

Optimization and Control · Mathematics 2019-05-28 Nevroz Sen , Peter E. Caines

The theory of mean field games studies the limiting behaviors of large systems where the agents interact with each other in a certain symmetric way. The running and terminal costs are critical for the agents to decide the strategies.…

Optimization and Control · Mathematics 2023-07-05 Hongyu Liu , Chenchen Mou , Shen Zhang

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Optimization and Control · Mathematics 2024-06-18 Gokce Dayanikli , Mathieu Lauriere

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

Optimization and Control · Mathematics 2026-02-20 Guilherme Mazanti , Laurent Pfeiffer , Saeed Sadeghi Arjmand

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

Optimization and Control · Mathematics 2019-10-31 Martin Frank , Michael Herty , Torsten Trimborn

We propose a new approach to proving the uniqueness of solutions to a certain class of mean field games of controls. In this class, the equilibrium is determined by an aggregate quantity $Q(t)$, e.g. the market price or production, which…

Optimization and Control · Mathematics 2024-10-21 Jameson Graber , Elizabeth Matter

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…

Optimization and Control · Mathematics 2014-07-28 Alain Bensoussan , Michael Chau , Phillip Yam

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

Optimization and Control · Mathematics 2020-07-09 Géraldine Bouveret , Roxana Dumitrescu , Peter Tankov

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

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

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer (2018) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting…

Probability · Mathematics 2021-11-05 Luciano Campi , Maddalena Ghio , Giulia Livieri

We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…

Systems and Control · Electrical Eng. & Systems 2025-11-04 Leonardo Pedroso , Andrea Agazzi , W. P. M. H. Heemels , Mauro Salazar

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 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

In this paper, we consider a first-order mean field game model motivated by crowd motion in which agents evolve in a (not necessarily compact) metric space and wish to reach a given target set. Each agent aims to minimize the sum of their…

Optimization and Control · Mathematics 2024-12-20 Guilherme Mazanti

In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…

Probability · Mathematics 2016-07-05 Saran Ahuja

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

The planning problem for the mean field game implies the one tries to transfer the system of infinitely many identical rational agents from the given distribution to the final one using the choice of the terminal payoff. It can be…

Optimization and Control · Mathematics 2022-11-21 Yurii Averboukh , Aleksei Volkov