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Mean-field Games systems (MFGs) serve as paradigms to describe the games among a huge number of players. In this paper, we consider the ergodic Mean-field Games systems in the bounded domain with Neumann boundary conditions and the…

Functional Analysis · Mathematics 2025-01-28 Fanze Kong , Yonghui Tong , Xiaoyu Zeng

The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been…

Theoretical Economics · Economics 2020-06-05 Bar Light , Gabriel Weintraub

This paper studies two fundamental problems in regularized Graphon Mean-Field Games (GMFGs). First, we establish the existence of a Nash Equilibrium (NE) of any $\lambda$-regularized GMFG (for $\lambda\geq 0$). This result relies on weaker…

Computer Science and Game Theory · Computer Science 2023-10-13 Fengzhuo Zhang , Vincent Y. F. Tan , Zhaoran Wang , Zhuoran Yang

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

Optimization and Control · Mathematics 2023-08-22 Pierre Lavigne , Laurent Pfeiffer

Here, we introduce a price-formation model where a large number of small players can store and trade electricity. Our model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply vs. demand balance…

Analysis of PDEs · Mathematics 2018-07-20 Diogo Gomes , João Saúde

We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…

Probability · Mathematics 2026-05-19 Erhan Bayraktar , Xihao He , Xiang Yu , Fengyi Yuan

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

Optimization and Control · Mathematics 2017-12-01 Marcel Nutz

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…

Numerical Analysis · Mathematics 2023-06-30 Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

The goal of this paper is to study the long time behavior of solutions of the first-order mean field game (MFG) systems with a control on the acceleration. The main issue for this is the lack of small time controllability of the problem,…

Optimization and Control · Mathematics 2020-07-07 Pierre Cardaliaguet , Cristian Mendico

We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on…

Probability · Mathematics 2021-01-12 Erhan Bayraktar , Alekos Cecchin , Asaf Cohen , Francois Delarue

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

Probability · Mathematics 2018-08-24 Rene Carmona , Peiqi Wang

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

Numerical Analysis · Mathematics 2026-02-13 Haruka Nakamura , Norikazu Saito

In this paper we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or the consumer choice behaviour in the free market. The corresponding…

Analysis of PDEs · Mathematics 2015-06-19 Diogo A. Gomes , Roberto M. Velho , Marie-Therese Wolfram

This paper studies linear quadratic graphon mean field games (LQ-GMFGs) with common noise, in which a large number of agents are coupled via a weighted undirected graph. One special feature, compared with the well-studied graphon mean field…

Optimization and Control · Mathematics 2025-07-03 De-xuan Xu , Zhun Gou , Nan-jing Huang , Shuang Gao

In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…

Analysis of PDEs · Mathematics 2020-07-29 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

This paper establishes that $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More…

Optimization and Control · Mathematics 2020-04-28 Haoyang Cao , Xin Guo , Joon Seok Lee

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

The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…

Optimization and Control · Mathematics 2020-11-24 Yurii Averboukh

In this letter, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-field-type equilibrium can be characterized by the existence of a multiplier process…

Optimization and Control · Mathematics 2025-10-06 Partha Sarathi Mohapatra , Puduru Viswanadha Reddy

Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios…

Computer Science and Game Theory · Computer Science 2024-08-28 Batuhan Yardim , Niao He