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Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

Probability · Mathematics 2015-04-09 Rene Carmona , Daniel Lacker

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

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

Optimization and Control · Mathematics 2018-10-30 Alain Bensoussan , Tao Huang , Mathieu Laurière

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 tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Optimization and Control · Mathematics 2024-06-18 Gokce Dayanikli , Mathieu Lauriere

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

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

Systems and Control · Electrical Eng. & Systems 2023-01-18 Naci Saldi

Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a mean field games (MFG)-like scenario where a large number of agents…

Systems and Control · Computer Science 2016-01-26 Rabih Salhab , Roland P. Malhamé , Jerome Le Ny

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…

Optimization and Control · Mathematics 2020-08-12 Haoyang Cao , Xin Guo

We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…

Systems and Control · Computer Science 2017-08-21 Rabih Salhab , Roland P. Malhamé , Jerome Le Ny

In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…

Computer Science and Game Theory · Computer Science 2026-01-30 Mao Fabrice Djete , Nizar Touzi

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 analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…

Analysis of PDEs · Mathematics 2020-10-27 Jameson Graber , Alan Mullenix , Laurent Pfeiffer

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

A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the…

Systems and Control · Computer Science 2022-01-11 Dena Firoozi , Ali Pakniyat , Peter E. Caines

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an…

Optimization and Control · Mathematics 2018-02-15 Sen Li , Wei Zhang , Lin Zhao

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…

Mathematical Finance · Quantitative Finance 2019-04-02 Philippe Casgrain , Sebastian Jaimungal

Existing multi-agent reinforcement learning methods are limited typically to a small number of agents. When the agent number increases largely, the learning becomes intractable due to the curse of the dimensionality and the exponential…

Multiagent Systems · Computer Science 2020-12-16 Yaodong Yang , Rui Luo , Minne Li , Ming Zhou , Weinan Zhang , Jun Wang

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…

Mathematical Finance · Quantitative Finance 2019-12-13 Philippe Casgrain , Sebastian Jaimungal