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A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…

Machine Learning · Statistics 2023-07-13 George Stamatescu

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…

Optimization and Control · Mathematics 2014-07-28 Alain Bensoussan , Michael Chau , Phillip Yam

In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…

Optimization and Control · Mathematics 2019-07-24 Dena Firoozi , Peter E. Caines , Sebastian Jaimungal

We investigate mean field games for players, who are weakly coupled via their empirical measure. To this end we investigate time-dependent pure jump type propagators over a finite space in the framework of non-linear Markov processes. We…

Optimization and Control · Mathematics 2015-03-25 Rani Basna , Astrid Hilbert , Vassili N. Kolokoltsov

Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of…

Optimization and Control · Mathematics 2020-10-20 Berenice Anne Neumann

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 propose a reinforcement learning algorithm for stationary mean-field games, where the goal is to learn a pair of mean-field state and stationary policy that constitutes the Nash equilibrium. When viewing the mean-field state and the…

Machine Learning · Computer Science 2020-10-12 Qiaomin Xie , Zhuoran Yang , Zhaoran Wang , Andreea Minca

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

We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our primary method employs a version of the double oracle, iteratively adding strategies…

Multiagent Systems · Computer Science 2023-02-14 Yongzhao Wang , Michael P. Wellman

This paper proposes and analyzes two neural network methods to solve the master equation for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash equilibria for stochastic, differential games with finite but large…

Optimization and Control · Mathematics 2024-12-24 Asaf Cohen , Mathieu Laurière , Ethan Zell

In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…

Optimization and Control · Mathematics 2009-03-10 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium…

Probability · Mathematics 2018-04-24 Francois Delarue , Daniel Lacker , Kavita Ramanan

We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…

Optimization and Control · Mathematics 2018-02-05 Charafeddine Mouzouni

We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that…

Analysis of PDEs · Mathematics 2025-01-14 Pierre Cardaliaguet , Benjamin Seeger , Panagiotis Souganidis

This paper studies singular mean field control problems and singular mean field stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some…

Optimization and Control · Mathematics 2014-06-10 Yaozhong Hu , Bernt Øksendal , Agnès Sulem

In this book, we present a curated collection of existing results on inverse problems for Mean Field Games (MFGs), a cutting-edge and rapidly evolving field of research. Our aim is to provide fresh insights, novel perspectives, and a…

Analysis of PDEs · Mathematics 2025-03-20 Hongyu Liu , Catharine W. K. Lo , Shen Zhang

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

Optimization and Control · Mathematics 2019-10-17 Zuyue Fu , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a…

Computer Science and Game Theory · Computer Science 2025-07-29 Kai Shao , Jiacheng Shen , Mathieu Laurière

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 toy model of linear-quadratic mean field game with delay. We "lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward…

Probability · Mathematics 2018-08-21 Jean-Pierre Fouque , Zhaoyu Zhang