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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

We study a mean field optimal control problem with general non-Markovian dynamics, including both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are…

Optimization and Control · Mathematics 2025-05-12 Felix Höfer , H. Mete Soner

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this context, we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global…

Optimization and Control · Mathematics 2018-02-20 Pierre Cardaliaguet , Catherine Rainer

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

This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major…

Optimization and Control · Mathematics 2013-06-07 Mojtaba Nourian , Peter E. Caines

This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…

Optimization and Control · Mathematics 2025-11-10 Lijun Bo , Jingfei Wang , Xiang Yu

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

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

Optimization and Control · Mathematics 2018-10-30 Alain Bensoussan , Tao Huang , Mathieu Laurière

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

This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the $n$-player model, each agent aims to…

Optimization and Control · Mathematics 2026-04-16 Lijun Bo , Yijie Huang , Xiang Yu

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

Analysis of PDEs · Mathematics 2016-10-04 Diogo A. Gomes , Stefania Patrizi

In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…

Analysis of PDEs · Mathematics 2026-04-10 Jameson Graber , Kyle Rosengartner

We study the short-time existence and uniqueness of solutions to a coupled system of partial differential equations arising in mean field game theory. It has the generic form $$ \left\{ \begin{array}{c} -\partial_t u - \Delta u +…

Analysis of PDEs · Mathematics 2015-03-27 Philip Jameson Graber

This paper builds on the work of Degond, Herty and Liu by considering N-player stochastic differential games. The control corresponding to a Nash equilibrium of such a game is approximated through model predictive control (MPC) techniques.…

Optimization and Control · Mathematics 2019-11-12 Matt Barker

In this study, we investigate $N$-player stochastic differential games with regime switching, where the player dynamics are modulated by a finite-state Markov chain. We analyze the associated Nash system, which consists of a system of…

Probability · Mathematics 2025-02-26 Mingrui Wang , Prakash Chakraborty

Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…

Optimization and Control · Mathematics 2021-03-08 Aathira Prasad , Puduru Viswanadha Reddy

We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a…

Optimization and Control · Mathematics 2014-07-28 Pierre Cardaliaguet , J. Graber , Alessio Porretta , Daniela Tonon

We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual…

Optimization and Control · Mathematics 2024-04-24 Gokce Dayanikli , Mathieu Lauriere

In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN)…

Systems and Control · Electrical Eng. & Systems 2022-08-26 Shubham Aggarwal , Muhammad Aneeq uz Zaman , Tamer Başar

We study mean field portfolio games with random market parameters, where each player is concerned with not only her own wealth but also relative performance to her competitors. We use the martingale optimality principle approach to…

Mathematical Finance · Quantitative Finance 2022-04-26 Guanxing Fu , Chao Zhou