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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

We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by…

Optimization and Control · Mathematics 2025-07-28 Giorgio Ferrari , Anna Pajola

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…

Optimization and Control · Mathematics 2021-01-05 Minyi Huang , Yan Ma

In this paper we obtain Sobolev estimates for weak solutions of first oder variational Mean Field Game systems with coupling terms that are local function of the density variable. Under some coercivity condition on the coupling, we obtain…

Analysis of PDEs · Mathematics 2018-01-25 P. Jameson Graber , Alpár R. Mészáros

In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain $\Omega \subset \mathbb{R}^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of…

Analysis of PDEs · Mathematics 2016-03-04 Alpár Richárd Mészáros , Francisco J. Silva

Here, we examine the Wardrop equilibrium model on networks with flow-dependent costs and its connection with stationary mean-field games (MFG). In the first part of this paper, we present the Wardrop and the first-order MFG models on…

Analysis of PDEs · Mathematics 2022-07-05 Fatimah Al Saleh , Tigran Bakaryan , Diogo A. Gomes , Ricardo Ribeiro

We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics game governed by a coupled…

Numerical Analysis · Mathematics 2026-03-31 Alessio Basti , Fabio Camilli , Adriano Festa

We investigate the existence and stability of small perturbations of constant states of the generalized Hughes model for pedestrian flow in an infinitely large corridor. We show that constant flows are stable under a condition on the…

Analysis of PDEs · Mathematics 2023-10-24 Mohamed Ghattassi , Nader Masmoudi , Eliot Pacherie

In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distribution and control variables, and the diffusion term…

Optimization and Control · Mathematics 2025-03-24 Alain Bensoussan , Ziyu Huang , Shanjian Tang , Sheung Chi Phillip Yam

We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…

Optimization and Control · Mathematics 2023-10-10 Yuan Gao , Wuchen Li , Jian-Guo Liu

This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…

Optimization and Control · Mathematics 2022-02-21 Guilherme Mazanti , Filippo Santambrogio

We introduce a class of fully nonlinear mean field games posed in $[0,T]\times\mathbb{R}^d$. We justify that they are related to controlled local or nonlocal diffusions, and more generally in our setting, to a new control interpretation…

Analysis of PDEs · Mathematics 2024-08-30 Indranil Chowdhury , Espen R. Jakobsen , Miłosz Krupski

In this paper we study evolutive first order Mean Field Games in the Heisenberg group; each agent can move in the whole space but it has to follow "horizontal" trajectories which are given in terms of the vector fields generating the group…

Analysis of PDEs · Mathematics 2022-01-03 Paola Mannucci , Claudio Marchi , Nicoletta Tchou

The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations (the Nash system) when the coupling between the players becomes increasingly singular. The limit equation is a mean field game…

Optimization and Control · Mathematics 2017-10-12 P Cardaliaguet

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear…

Analysis of PDEs · Mathematics 2017-04-25 Diogo Gomes , Levon Nurbekyan , Marc Sedjro

In this paper we construct global in time classical solutions to mean field games master equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include both deterministic models and dynamics driven solely by…

Analysis of PDEs · Mathematics 2024-12-03 Mohit Bansil , Alpár R. Mészáros , Chenchen Mou

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…

Optimization and Control · Mathematics 2017-01-25 Minyi Huang , Yan Ma

In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the…

Computer Science and Game Theory · Computer Science 2024-08-13 Alexey Miroshnikov , Konstandinos Kotsiopoulos , Khashayar Filom , Arjun Ravi Kannan

In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…

Analysis of PDEs · Mathematics 2023-03-28 E Carlini , Francisco José Silva , Ahmad Zorkot

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