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We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite time horizons. We prove the existence of…

Optimization and Control · Mathematics 2019-09-04 Josu Doncel , Nicolas Gast , Bruno Gaujal

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

Computer Science and Game Theory · Computer Science 2022-08-23 Paul Muller , Romuald Elie , Mark Rowland , Mathieu Lauriere , Julien Perolat , Sarah Perrin , Matthieu Geist , Georgios Piliouras , Olivier Pietquin , Karl Tuyls

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

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Optimization and Control · Mathematics 2021-10-12 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

Optimization and Control · Mathematics 2017-11-07 Piermarco Cannarsa , Rossana Capuani

We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative…

Probability · Mathematics 2022-01-19 Luciano Campi , Tiziano De Angelis , Maddalena Ghio , Giulia Livieri

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…

Optimization and Control · Mathematics 2026-01-01 Grégoire Lambrecht , Mathieu Laurière

In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our…

Optimization and Control · Mathematics 2026-04-14 Agustín Muñoz González , Juan I. Sequeira , Rafael Orive Illera

In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in…

Optimization and Control · Mathematics 2024-09-13 Gokce Dayanikli , Mathieu Lauriere

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

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

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

Probability · Mathematics 2018-08-24 Rene Carmona , Peiqi Wang

Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…

Computer Science and Game Theory · Computer Science 2018-09-28 Shaull Almagor , Rajeev Alur , Suguman Bansal

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

Analysis of PDEs · Mathematics 2017-10-05 David Evangelista , Rita Ferreira , Diogo A. Gomes , Levon Nurbekyan , Vardan Voskanyan

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…

Optimization and Control · Mathematics 2018-11-02 Erhan Bayraktar , Jakša Cvitanić , Yuchong Zhang

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic utility are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum…

Optimization and Control · Mathematics 2020-09-07 René Carmona , Kenza Hamidouche , Mathieu Laurière , Zongjun Tan

Mean field games (MFGs) have been introduced to study Nash equilibria in very large population of self-interested agents. However, when applied to common pool resource (CPR) games, MFG equilibria lead to the so-called tragedy of the commons…

Optimization and Control · Mathematics 2025-04-15 Gokce Dayanikli , Mathieu Lauriere

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

We study a general class of entropy-regularized multi-variate LQG mean field games (MFGs) in continuous time with $K$ distinct sub-population of agents. We extend the notion of actions to action distributions (exploratory actions), and…

Optimization and Control · Mathematics 2021-12-01 Dena Firoozi , Sebastian Jaimungal

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