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Related papers: Obstacle Mean-Field Game Problem

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We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…

Analysis of PDEs · Mathematics 2020-09-28 Pierre Cardaliaguet , Panagiotis Souganidis

In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument through its Hessian matrix. We work under fairly natural…

Analysis of PDEs · Mathematics 2020-10-30 Pêdra D. S. Andrade , Edgard A. Pimentel

First, we study the existence of solutions for a class of first order mean field games systems \begin{equation*} \left\{\begin{aligned} &H(x,u,Du)=F(x,m(t)),\quad &&x\in M,\ \forall\ t\in[0,T],\\ &\partial_t…

Analysis of PDEs · Mathematics 2025-07-15 Xiaotian Hu

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

Optimization and Control · Mathematics 2023-08-29 Xin Guo , Anran Hu , Junzi Zhang

We discuss a class of explicitly solvable mean field type control problems/mean field games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional…

Optimization and Control · Mathematics 2021-04-28 Sören Christensen , Berenice Anne Neumann , Tobias Sohr

This article focuses two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (u,m) of the…

Analysis of PDEs · Mathematics 2025-09-19 Renato Iturriaga , Cristian Mendico , Kaizhi Wang , Yuchen Xu

This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this…

Analysis of PDEs · Mathematics 2021-07-27 Mariya Sardarli

We study the regularity and well-posedness of the local, first-order forward-backward mean field games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data that…

Analysis of PDEs · Mathematics 2022-02-25 Sebastian Munoz

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 a class of extended mean field games with common noises, where there exists a strictly terminal constraint. We solve the problem by reducing it to an unconstrained control problem by adding a penalized term in the cost…

Optimization and Control · Mathematics 2025-06-10 Tianjiao Hua , Peng Luo

We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…

Probability · Mathematics 2022-05-25 Matteo Burzoni , Luciano Campi

Here, we consider a regularized mean-field game model that features a low-order regularization. We prove the existence of solutions with positive density. To do so, we combine a priori estimates with the continuation method. In contrast…

We study a class of local, first-order, stationary mean-field games (MFGs) on bounded domains with nonstandard mixed boundary conditions: prescribed inflow on $\Gamma_N$ and a relaxed Signorini-type exit condition on $\Gamma_D$…

Analysis of PDEs · Mathematics 2026-03-03 AbdulRahman M. Alharbi , Diogo Gomes

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure…

Analysis of PDEs · Mathematics 2025-05-14 Hongyu Liu , Catharine W. K. Lo

We investigate time dependent, first order Mean Field Games on the torus comparing, in a broad and general framework, the classical differential formulation , given by a Hamilton Jacobi equation coupled with a continuity equation, with a…

Analysis of PDEs · Mathematics 2025-12-02 Antonio Siconolfi

In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…

Optimization and Control · Mathematics 2021-05-26 Ziyu Huang , Shanjian Tang

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

Optimization and Control · Mathematics 2011-03-18 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…

Optimization and Control · Mathematics 2024-11-13 Jiajia Yu , Quan Xiao , Tianyi Chen , Rongjie Lai

The long-run average payoff per transition (mean payoff) is the main tool for specifying the performance and dependability properties of discrete systems. The problem of constructing a controller (strategy) simultaneously optimizing several…

Artificial Intelligence · Computer Science 2024-12-19 David Klaška , Antonín Kučera , Vojtěch Kůr , Vít Musil , Vojtěch Řehák