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We analyze a fractional mean field game of controls system, showing existence of solutions when the order of the fractional Laplacian is $s\in(\frac{1}{2},1)$. Here the running cost depends on the distribution $\mu$ of not only the states…

Analysis of PDEs · Mathematics 2025-09-08 P. Jameson Graber , Elizabeth Matter , Jesus Ruiz Bolanos

In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…

Analysis of PDEs · Mathematics 2023-02-01 Fabio Camilli , Claudio Marchi

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

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

Optimization and Control · Mathematics 2015-09-23 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Analysis of PDEs · Mathematics 2020-06-24 Z Kobeissi

In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…

Optimization and Control · Mathematics 2025-05-30 Facundo Oliú

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

We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonlinear function of all its possible realizations, encompassing…

Optimization and Control · Mathematics 2026-04-24 François Delarue , Pierre Lavigne

Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs…

Analysis of PDEs · Mathematics 2016-11-28 David Evangelista , Diogo A. Gomes

This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process,…

Optimization and Control · Mathematics 2017-02-03 Khaled Bahlali , Meriem Mezerdi , Brahim Mezerdi

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

A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…

Optimization and Control · Mathematics 2019-08-21 Ari Arapostathis , Anup Biswas , Johnson Carroll

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

Optimization and Control · Mathematics 2025-06-03 Dirk Becherer , Christoph Reisinger , Jonathan Tam

Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with…

Robotics · Computer Science 2021-06-01 Simon Le Cleac'h , Mac Schwager , Zachary Manchester

We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…

Optimization and Control · Mathematics 2022-04-05 Mao Fabrice Djete , Nizar Touzi

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

The paper is concerned with the feedback approach to the deterministic mean field type differential games. Previously, it was shown that suboptimal strategies in the mean field type differential game can constructed based on functions of…

Optimization and Control · Mathematics 2019-03-28 Yurii Averboukh

This paper studies a type of rank-based mean field game in which competing agents strategically switch among multiple effort regimes. We propose an entropy regularized auxiliary problem where the switching decisions are randomized to the…

Optimization and Control · Mathematics 2026-05-29 Zongxia Liang , Shu Wang , Xiang Yu

We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite time horizons. We prove the existence of…

Optimization and Control · Mathematics 2019-09-04 Josu Doncel , Nicolas Gast , Bruno Gaujal