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We show the existence of "mild solutions" for a first-order mean field game of controls under the state constraint that trajectories be confined in a closed and bounded set in euclidean space. This extends the results of Cannarsa and…

Optimization and Control · Mathematics 2023-01-24 Jameson Graber , Sergio Mayorga

We consider continuous-time mean-field stochastic games with strategic complementarities. The interaction between the representative productive firm and the population of rivals comes through the price at which the produced good is sold and…

Optimization and Control · Mathematics 2024-02-13 Jodi Dianetti , Salvatore Federico , Giorgio Ferrari , Giuseppe Floccari

Mean field control provides a robust framework for coordinating large-scale populations with complex interactions and has wide applications across diverse fields. However, the inherent nonlinearity and the presence of unknown system…

Optimization and Control · Mathematics 2024-11-12 Yuhan Zhao , Juntao Chen , Yingdong Lu , Quanyan Zhu

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

This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…

Optimization and Control · Mathematics 2026-02-16 Alessandra Cutrì , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…

Mathematical Finance · Quantitative Finance 2019-12-13 Philippe Casgrain , Sebastian Jaimungal

We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift,…

Probability · Mathematics 2020-07-14 Chiara Benazzoli , Luciano Campi , Luca Di Persio

We investigate the existence of an optimal policy to monitor a mean field systems of agents managing a risky project under moral hazard with accidents modeled by L\'evy processes magnified by the law of the project. We provide a general…

Optimization and Control · Mathematics 2022-07-25 Thibaut Mastrolia , Jiacheng Zhang

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential…

Analysis of PDEs · Mathematics 2016-11-08 Yves Achdou , Mathieu Lauriere

We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…

Optimization and Control · Mathematics 2020-10-06 Matteo Basei , Haoyang Cao , Xin Guo

This paper discusses the control of coherent structures in turbulent flows, which has broad applications among complex systems in science and technology. Mean field games have been proved a powerful tool and are proposed here to control the…

Optimization and Control · Mathematics 2024-01-22 Yuan Gao , Di Qi

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…

Optimization and Control · Mathematics 2022-06-08 Jianhui Huang , Tinghan Xie

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

In this paper, we consider a class of mean field games in which the optimal strategy of a representative agent depends on the statistical distribution of the states and controls. We prove some existence results for the forward-backward…

Analysis of PDEs · Mathematics 2020-07-13 Z Kobeissi

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…

Probability · Mathematics 2022-05-26 Jian Song , Meng Wang

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…

Optimization and Control · Mathematics 2019-07-26 Jodi Dianetti , Giorgio Ferrari , Markus Fischer , Max Nendel

An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a…

Optimization and Control · Mathematics 2019-06-24 J. Frédéric Bonnans , Saeed Hadikhanloo , Laurent Pfeiffer

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…

Optimization and Control · Mathematics 2019-09-09 Fabio Bagagiolo , Rosario Maggistro , Raffaele Pesenti