English
Related papers

Related papers: Value Iteration Algorithm for Mean-field Games

200 papers

Recently, Sidford, Wang, Wu and Ye (2018) developed an algorithm combining variance reduction techniques with value iteration to solve discounted Markov decision processes. This algorithm has a sublinear complexity when the discount factor…

Optimization and Control · Mathematics 2019-09-16 Marianne Akian , Stéphane Gaubert , Zheng Qu , Omar Saadi

We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…

Computer Science and Game Theory · Computer Science 2008-09-25 Krishnendu Chatterjee , Luca de Alfaro , Thomas A. Henzinger

In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an…

Numerical Analysis · Mathematics 2019-12-24 Laura Aquilanti , Simone Cacace , Fabio Camilli , Raul De Maio

We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov Decision Process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as…

Optimization and Control · Mathematics 2019-01-31 Dileep Kalathil , Vivek S. Borkar , Rahul Jain

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…

Optimization and Control · Mathematics 2019-08-21 Ari Arapostathis , Anup Biswas , Johnson Carroll

This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual…

Optimization and Control · Mathematics 2025-08-05 Tian Chen , Tianyang Nie , Zhen Wu

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…

Optimization and Control · Mathematics 2024-05-06 Zongxia Liang , Keyu Zhang

We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…

Computer Science and Game Theory · Computer Science 2014-10-02 Krishnendu Chatterjee , Rasmus Ibsen-Jensen

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of…

Machine Learning · Computer Science 2022-03-21 Raghuram Bharadwaj Diddigi , Chandramouli Kamanchi , Shalabh Bhatnagar

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…

Optimization and Control · Mathematics 2026-03-09 Ulrich Horst , Takashi Sato

We consider the mean field game of cross--holding introduced in \citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity value dynamics are affected by a common noise. In contrast with \cite{DjeteTouzi}, the problem…

Probability · Mathematics 2024-03-26 Leila Bassou , Mao Fabrice Djete , Nizar Touzi

We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting…

Optimization and Control · Mathematics 2022-03-31 Giacomo Borghi , Michael Herty , Lorenzo Pareschi

Quantilized mean-field game models involve quantiles of the population's distribution. We study a class of such games with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative…

Optimization and Control · Mathematics 2025-07-02 Rinel Foguen Tchuendom , Dena Firoozi , Michèle Breton

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

Optimization and Control · Mathematics 2022-01-19 Joseph Frédéric Bonnans , Justina Gianatti , Laurent Pfeiffer

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

This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…

Optimization and Control · Mathematics 2019-07-03 Athanasios Vasiliadis

We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…

Optimization and Control · Mathematics 2021-03-09 Marcel Nutz , Yuchong Zhang

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…

Optimization and Control · Mathematics 2025-09-23 Haoyang Cao , Jodi Dianetti , Giorgio Ferrari

In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…

Optimization and Control · Mathematics 2021-07-12 Luciano Campi , Markus Fischer