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We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…

Analysis of PDEs · Mathematics 2016-02-16 Marco Cirant

This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major…

Optimization and Control · Mathematics 2013-06-07 Mojtaba Nourian , Peter E. Caines

We investigate the stability and robustness properties of a continuification-based strategy for the control of large-scale multiagent systems. Within continuation-based strategy, one transforms the microscopic, agent-level description of…

Systems and Control · Electrical Eng. & Systems 2023-10-04 Gian Carlo Maffettone , Maurizio Porfiri , Mario di Bernardo

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

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…

Probability · Mathematics 2015-04-09 Daniel Lacker

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…

Optimization and Control · Mathematics 2022-04-05 Mao Fabrice Djete , Nizar Touzi

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

Analysis of PDEs · Mathematics 2024-07-31 Vincenzo Ignazio , Michele Ricciardi

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

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

Adaptation and Self-Organizing Systems · Physics 2018-06-22 Piyush Grover , Kaivalya Bakshi , Evangelos A. Theodorou

In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE of continuity-type, governing the dynamics of the probability distribution of the…

Optimization and Control · Mathematics 2016-08-08 Giacomo Albi , Young-Pil Choi , Massimo Fornasier , Dante Kalise

In this paper we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field of control setting, that is in which the dynamics of each agent is affected not only by the average position of the…

Optimization and Control · Mathematics 2023-06-21 Mattia Bongini , Francesco Salvarani

The mean-field game system is treated as an Euler Lagrange system corresponding to an optimal control problem governed by Fokker-Planck equation.

Optimization and Control · Mathematics 2024-11-18 Viorel Barbu

Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safety sets. Recent work extended this paradigm to mean-field…

Systems and Control · Electrical Eng. & Systems 2026-03-20 Cinzia Tomaselli , Gian Carlo Maffettone , Samy Wu Fung , Levon Nurbekyan , Mario di Bernardo

A mean field type control system is a dynamical system in the Wasserstein space describing an evolution of a large population of agents with mean-field interaction under a control of a unique decision maker. We develop the viability theorem…

Optimization and Control · Mathematics 2018-02-01 Yurii Averboukh

In this paper, we are concerned with the stabilizatbility of Stackelberg game-based systems. In particular, two players are involved in the system where one is the follower to minimize the related cost function and the other is the leader…

Optimization and Control · Mathematics 2021-05-04 Yue Sun , Juanjuan Xu , Huanshui Zhang

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…

Probability · Mathematics 2022-08-11 Chenchen Mou , Jianfeng Zhang

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

Optimization and Control · Mathematics 2011-10-19 Olivier Guéant

Gradual advancement of control technology gives rise to the studies of the stability of linear systems. The stability of the linear multiagent system is motivated by increasing utilization of agent dynamics together with the number of…

Systems and Control · Electrical Eng. & Systems 2023-08-22 Gurmu Meseret Debele

Motivated by models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents evolving on a finite state space. The agents play a non-cooperative game in which…

Optimization and Control · Mathematics 2021-05-26 Alexander Aurell , Rene Carmona , Gokce Dayanikli , Mathieu Lauriere