English
Related papers

Related papers: Mean Field Games with Reflected Dynamics

200 papers

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

Optimization and Control · Mathematics 2026-02-20 Guilherme Mazanti , Laurent Pfeiffer , Saeed Sadeghi Arjmand

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with…

Optimization and Control · Mathematics 2022-01-21 Jodi Dianetti , Giorgio Ferrari , Markus Fischer , Max Nendel

We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general $\sigma$-compact Polish space. Under certain conditions, we show…

Probability · Mathematics 2015-11-02 Anup Biswas

This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is…

Optimization and Control · Mathematics 2025-10-13 Xiang Yu , Jiacheng Zhang , Keyu Zhang , Zhou Zhou

In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic…

Probability · Mathematics 2014-01-20 Qian Lin

We introduce a new class of reflected backward stochastic differential equations with two c\`adl\`ag barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove…

Probability · Mathematics 2021-03-16 Tomasz Klimsiak

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

Probability · Mathematics 2018-12-05 Alekos Cecchin , Guglielmo Pelino

In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Uğur Aydın , Naci Saldi

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 provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unbounded and there are also presence of cross terms in the…

Optimization and Control · Mathematics 2023-11-10 Alain Bensoussan , Bohan Li , Sheung Chi Phillip Yam

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

Optimization and Control · Mathematics 2011-10-19 Olivier Guéant

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

Probability · Mathematics 2014-08-13 Daniel Lacker

We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…

Analysis of PDEs · Mathematics 2019-03-18 Alessio Porretta , Michele Ricciardi

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of…

Optimization and Control · Mathematics 2016-07-08 P. Jameson Graber

In this paper, we study the well-posedness (existence and uniqueness) of the Master Equation of Mean Field Games under invariance-type conditions, otherwise known as viability conditions for the controlled dynamics. The interior regularity…

Analysis of PDEs · Mathematics 2022-11-15 Antonios Zitridis

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…

Optimization and Control · Mathematics 2024-09-26 Ziteng Cheng , Sebastian Jaimungal

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

Computer Science and Game Theory · Computer Science 2026-02-27 Yannick Eich , Christian Fabian , Kai Cui , Heinz Koeppl

We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…

Probability · Mathematics 2018-12-04 Enzo Miller , Huyen Pham

We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…

Probability · Mathematics 2012-10-23 Rene Carmona , Francois Delarue , Aime Lachapelle