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Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

Optimization and Control · Mathematics 2019-12-30 Julien Claisse , Zhenjie Ren , Xiaolu Tan

In this paper, we consider a mean field game model inspired by crowd motion where agents aim to reach a closed set, called target set, in minimal time. Congestion phenomena are modeled through a constraint on the velocity of an agent that…

Optimization and Control · Mathematics 2022-12-23 Saeed Sadeghi Arjmand , Guilherme Mazanti

Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…

Optimization and Control · Mathematics 2014-12-24 Pierre Degond , Michael Herty , Jian-Guo Liu

We present results of existence, regularity and uniqueness of solutions of the master equation associated with the mean field planning problem in the finite state space case, in the presence of a common noise. The results hold under…

Analysis of PDEs · Mathematics 2021-07-21 Charles Bertucci , Jean-Michel Lasry , Pierre-Louis Lions

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

Analysis of PDEs · Mathematics 2021-07-12 Simone Cacace , Fabio Camilli , Alessandro Goffi

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

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 introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable…

Optimization and Control · Mathematics 2017-08-07 Marcel Nutz , Yuchong Zhang

Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…

Computer Science and Game Theory · Computer Science 2013-08-19 Kevin Waugh , Brian D. Ziebart , J. Andrew Bagnell

In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…

Optimization and Control · Mathematics 2018-05-16 Saeed Hadikhanloo , Francisco José Silva

In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…

Optimization and Control · Mathematics 2026-02-04 P. Jameson Graber , Brady Zimmerman

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

Optimization and Control · Mathematics 2020-07-09 Géraldine Bouveret , Roxana Dumitrescu , Peter Tankov

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

Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…

Computer Science and Game Theory · Computer Science 2015-03-19 Kevin Waugh , Brian D. Ziebart , J. Andrew Bagnell

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…

Optimization and Control · Mathematics 2014-01-09 Pierre Cardaliaguet , Philip Jameson Graber

We study stochastic static teams with countably infinite number of decision makers, with the goal of obtaining (globally) optimal policies under a decentralized information structure. We present sufficient conditions to connect the concepts…

Optimization and Control · Mathematics 2020-05-14 Sina Sanjari , Serdar Yüksel

An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility…

Machine Learning · Computer Science 2025-06-17 Liad Erez , Tal Lancewicki , Uri Sherman , Tomer Koren , Yishay Mansour

In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…

Optimization and Control · Mathematics 2019-08-26 Naci Saldi

We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point…

Optimization and Control · Mathematics 2022-10-27 Alberto Bressan , Khai T. Nguyen

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…

Systems and Control · Computer Science 2017-01-17 Naci Saldi , Tamer Başar , Maxim Raginsky