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Related papers: Probabilistic Approach to Mean Field Games and Mea…

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In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…

Optimization and Control · Mathematics 2022-06-13 Min Li , Chenchen Mou , Zhen Wu , Chao Zhou

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated It\^o-diffusion via a two-sided singular stochastic control…

Optimization and Control · Mathematics 2024-12-31 Jodi Dianetti , Giorgio Ferrari , Ioannis Tzouanas

We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…

Probability · Mathematics 2018-12-04 Enzo Miller , Huyen Pham

Collaborative multi-agent robotic systems where agents coordinate by modifying a shared environment often result in undesired dynamical couplings that complicate the analysis and experiments when solving a specific problem or task.…

Robotics · Computer Science 2022-03-10 Daniel Jarne Ornia , Pedro J Zufiria , Manuel Mazo

This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual…

Optimization and Control · Mathematics 2014-03-18 Jianhui Huang , Shujun Wang , Hua Xiao

We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…

Optimization and Control · Mathematics 2019-02-20 Massimo Fornasier , Francesco Solombrino

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

Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…

Numerical Analysis · Mathematics 2012-07-13 Yves Achdou , Fabio Camilli , Italo Capuzzo Dolcetta

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the…

Optimization and Control · Mathematics 2019-08-09 Fabio Bagagiolo , Silvia Faggian , Rosario Maggistro , Raffaele Pesenti

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

Systems and Control · Computer Science 2015-03-19 H. Tembine

We investigate mean-field games from the point of view of a large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The dynamics of the states of the…

Optimization and Control · Mathematics 2017-02-21 Rani Basna , Astrid Hilbert , Vassili N. Kolokoltsov

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…

Probability · Mathematics 2016-10-19 Rene Carmona , Peiqi Wang

We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…

Optimization and Control · Mathematics 2025-10-16 Nicole Bäuerle

In this paper, we consider a first-order deterministic mean field game model inspired by crowd motion in which agents moving in a given domain aim to reach a given target set in minimal time. To model interaction between agents, we assume…

Optimization and Control · Mathematics 2022-02-21 Saeed Sadeghi Arjmand , Guilherme Mazanti

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…

Analysis of PDEs · Mathematics 2019-06-05 Antonin Della Noce , Amélie Mathieu , Paul-Henry Cournède

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 consider network aggregative games to model and study multi-agent populations in which each rational agent is influenced by the aggregate behavior of its neighbors, as specified by an underlying network. Specifically, we examine systems…

Systems and Control · Computer Science 2015-06-26 Francesca Parise , Sergio Grammatico , Basilio Gentile , John Lygeros

Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…

Optimization and Control · Mathematics 2020-01-09 Berenice Anne Neumann

Motivated by recent interest in graphon mean field games and their applications, this paper provides a comprehensive probabilistic analysis of graphon mean field control (GMFC) problems, where the controlled dynamics are governed by a…

Optimization and Control · Mathematics 2025-12-19 Zhongyuan Cao , Mathieu Laurière

In this paper, we propose and study a mean field game model with multiple populations of minor players and multiple major players, motivated by applications to the regulation of carbon emissions. Each population of minor players represent a…

Optimization and Control · Mathematics 2023-09-29 Gokce Dayanikli , Mathieu Lauriere