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We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Berkay Anahtarcı , Can Deha Karıksız , Naci Saldi

Here, we study radial solutions for first- and second-order stationary Mean-Field Games (MFG) with congestion on $\mathbb{R}^d$. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial…

Analysis of PDEs · Mathematics 2017-03-23 David Evangelista , Diogo A. Gomes , Levon Nurbekyan

Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free…

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of…

Optimization and Control · Mathematics 2014-03-25 Jianhui Huang , Shujun Wang

In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…

Optimization and Control · Mathematics 2022-08-16 Saeed Sadeghi Arjmand , Guilherme Mazanti

The mean field games (MFG) paradigm was introduced to provide tractable approximations of games involving very large populations. The theory typically rests on two key assumptions: homogeneity, meaning that all players share the same…

Optimization and Control · Mathematics 2025-11-10 Mathieu Laurière

We propose a MFG model with quadratic Hamiltonian involving $N$ populations. This results in a system of $N$ Hamilton-Jacobi-Bellman and $N$ Fokker-Planck equations with non-local interactions. As in the classical case we introduce an…

Analysis of PDEs · Mathematics 2025-11-03 Luigi De Pascale , Luca Nenna

In the paper we present a model of discrete-time mean-field game with several populations of players. Mean-field games with multiple populations of the players have only been studied in the literature in the continuous-time setting. The…

Optimization and Control · Mathematics 2023-04-07 Piotr Więcek

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

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…

Statistical Mechanics · Physics 2007-05-23 Arne Traulsen , Jens Christian Claussen , Christoph Hauert

The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…

Optimization and Control · Mathematics 2024-01-23 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

The goal of this paper is to study a Mean Field Game (MFG) system stemming from the harvesting of resources. Modelling the latter through a reaction-diffusion equation and the harvesters as competing rational agents, we are led to a…

Analysis of PDEs · Mathematics 2024-06-11 Ziad Kobeissi , Idriss Mazari-Fouquer , Domènec Ruiz-Balet

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Probability · Mathematics 2025-11-03 Nicolai Jurek Gerber , Franca Hoffmann , Urbain Vaes

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

Optimization and Control · Mathematics 2022-03-29 Hui Ouyang

We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…

Optimization and Control · Mathematics 2025-11-11 Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

This paper addresses a linear-quadratic Stackelberg mean field (MF) games and teams problem with arbitrary population sizes, where the game among the followers is further categorized into two types: non-cooperative and cooperative, and the…

Optimization and Control · Mathematics 2024-12-24 Wenyu Cong , Jingtao Shi , Bingchang Wang

This paper is devoted to the study of the long time behavior of Nash equilibria in Mean Field Games within the framework of displacement monotonicity. We first show that any two equilibria defined on the time horizon $[0,T]$ must be close…

Optimization and Control · Mathematics 2025-11-07 Marco Cirant , Alpár R. Mészáros

This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…

Optimization and Control · Mathematics 2014-07-16 Dario Bauso , Thomas W L Norman

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows…

Optimization and Control · Mathematics 2023-03-07 J. Frédéric Bonnans , Pierre Lavigne , Laurent Pfeiffer

Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the…

Populations and Evolution · Quantitative Biology 2010-06-16 Tobias Galla