Mean Field Games

Mean Field Games Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Mean Field Games book. This book definitely worth reading, it is an incredibly well-written.

Mean Field Games

Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio
Mean Field Games Book PDF

Author : Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio
Publisher : Springer Nature
Page : 316 pages
File Size : 50,9 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : 9783030598372

Get Book

Mean Field Games by Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio Pdf

This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.

Probabilistic Theory of Mean Field Games with Applications I

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications I Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 714 pages
File Size : 54,6 Mb
Release : 2018-03-01
Category : Mathematics
ISBN : 9783319589206

Get Book

Probabilistic Theory of Mean Field Games with Applications I by René Carmona,François Delarue Pdf

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Mean Field Games and Mean Field Type Control Theory

Alain Bensoussan,Jens Frehse,Phillip Yam
Mean Field Games and Mean Field Type Control Theory Book PDF

Author : Alain Bensoussan,Jens Frehse,Phillip Yam
Publisher : Springer Science & Business Media
Page : 128 pages
File Size : 46,9 Mb
Release : 2013-10-16
Category : Science
ISBN : 9781461485087

Get Book

Mean Field Games and Mean Field Type Control Theory by Alain Bensoussan,Jens Frehse,Phillip Yam Pdf

​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. ​

Regularity Theory for Mean-Field Game Systems

Diogo A. Gomes,Edgard A. Pimentel,Vardan Voskanyan
Regularity Theory for Mean Field Game Systems Book PDF

Author : Diogo A. Gomes,Edgard A. Pimentel,Vardan Voskanyan
Publisher : Springer
Page : 156 pages
File Size : 53,7 Mb
Release : 2016-09-14
Category : Mathematics
ISBN : 9783319389349

Get Book

Regularity Theory for Mean-Field Game Systems by Diogo A. Gomes,Edgard A. Pimentel,Vardan Voskanyan Pdf

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Mean-Field-Type Games for Engineers

Julian Barreiro-Gomez,Hamidou Tembine
Mean Field Type Games for Engineers Book PDF

Author : Julian Barreiro-Gomez,Hamidou Tembine
Publisher : CRC Press
Page : 526 pages
File Size : 42,8 Mb
Release : 2021-11-18
Category : Technology & Engineering
ISBN : 9781000473537

Get Book

Mean-Field-Type Games for Engineers by Julian Barreiro-Gomez,Hamidou Tembine Pdf

The contents of this book comprise an appropriate background to start working and doing research on mean-field-type control and game theory. To make the exposition and explanation even easier, we first study the deterministic optimal control and differential linear-quadratic games. Then, we progressively add complexity step-by-step and little-by-little to the problem settings until we finally study and analyze mean-field-type control and game problems incorporating several stochastic processes, e.g., Brownian motions, Poisson jumps, and random coefficients. We go beyond the Nash equilibrium, which provides a solution for non- cooperative games, by analyzing other game-theoretical concepts such as the Berge, Stackelberg, adversarial/robust, and co-opetitive equilibria. For the mean-field-type game analysis, we provide several numerical examples using a Matlab-based user-friendly toolbox that is available for the free use to the readers of this book. We present several engineering applications in both continuous and discrete time. Among these applications we find the following: water distribution systems, micro-grid energy storage, stirred tank reactor, mechanism design for evolutionary dynamics, multi-level building evacuation problem, and the COVID-19 propagation control. Julian Barreiro-Gomez Hamidou Tembine With such a demand from engineering audiences, this book is very timely and provides a thorough study of mean-field-type game theory. The strenuous protagonist of this book is to bridge between the theoretical findings and engineering solutions. The book introduces the basics first, and then mathematical frameworks are elaborately explained. The engineering application examples are shown in detail, and the popular learning approaches are also investigated. Those advantageous characteristics will make this book a comprehensive handbook of many engineering fields for many years, and I will buy one when it gets published. Zhu Han

Probabilistic Theory of Mean Field Games with Applications II

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications II Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 700 pages
File Size : 40,8 Mb
Release : 2018-03-08
Category : Mathematics
ISBN : 9783319564364

Get Book

Probabilistic Theory of Mean Field Games with Applications II by René Carmona,François Delarue Pdf

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

The Master Equation and the Convergence Problem in Mean Field Games

Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
The Master Equation and the Convergence Problem in Mean Field Games Book PDF

Author : Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
Publisher : Princeton University Press
Page : 224 pages
File Size : 41,7 Mb
Release : 2019-08-13
Category : Mathematics
ISBN : 9780691190716

Get Book

The Master Equation and the Convergence Problem in Mean Field Games by Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions Pdf

This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Paris-Princeton Lectures on Mathematical Finance 2010

Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov
Paris Princeton Lectures on Mathematical Finance 2010 Book PDF

Author : Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 48,5 Mb
Release : 2011-06-29
Category : Mathematics
ISBN : 9783642146596

Get Book

Paris-Princeton Lectures on Mathematical Finance 2010 by Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov Pdf

The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.

Mean Field Game and its Applications in Wireless Networks

Reginald A. Banez,Lixin Li,Chungang Yang,Zhu Han
Mean Field Game and its Applications in Wireless Networks Book PDF

Author : Reginald A. Banez,Lixin Li,Chungang Yang,Zhu Han
Publisher : Springer Nature
Page : 184 pages
File Size : 48,5 Mb
Release : 2021-10-30
Category : Computers
ISBN : 9783030869052

Get Book

Mean Field Game and its Applications in Wireless Networks by Reginald A. Banez,Lixin Li,Chungang Yang,Zhu Han Pdf

This book covers the basic theory of mean field game (MFG) and its applications in wireless networks. It starts with an overview of the current and future state-of-the-art in 5G and 6G wireless networks. Then, a tutorial is presented for MFG, mean-field-type game (MFTG), and prerequisite fields of study such as optimal control theory and differential games. This book also includes a literature survey of MFG-based research in wireless network technologies such as ultra-dense networks (UDNs), device-to-device (D2D) communications, internet-of-things (IoT), unmanned aerial vehicles (UAVs), and mobile edge networks (MENs). Several applications of MFG and MFTG in UDNs, social networks, and multi-access edge computing networks (MECNs) are introduced as well. Applications of MFG covered in this book are divided in three parts. The first part covers three single-population MFG research works or case studies in UDNs including ultra-dense D2D networks, ultra-dense UAV networks, and dense-user MECNs. The second part centers on a multiple-population MFG (MPMFG) modeling of belief and opinion evolution in social networks. It focuses on a recently developed MPMFG framework and its application in analyzing the behavior of users in a multiple-population social network. Finally, the last part concentrates on an MFTG approach to computation offloading in MECN. The computation offloading algorithms are designed for energy- and time-efficient offloading of computation-intensive tasks in an MECN. This book targets advanced-level students, professors, researchers, scientists, and engineers in the fields of communications and networks. Industry managers and government employees working in these same fields will also find this book useful.

Mean Field Games

François Delarue
Mean Field Games Book PDF

Author : François Delarue
Publisher : American Mathematical Society
Page : 284 pages
File Size : 52,8 Mb
Release : 2021-12-14
Category : Mathematics
ISBN : 9781470455866

Get Book

Mean Field Games by François Delarue Pdf

This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.

Active Particles, Volume 1

Nicola Bellomo,Pierre Degond,Eitan Tadmor
Active Particles Volume 1 Book PDF

Author : Nicola Bellomo,Pierre Degond,Eitan Tadmor
Publisher : Birkhäuser
Page : 402 pages
File Size : 42,8 Mb
Release : 2017-04-06
Category : Mathematics
ISBN : 9783319499963

Get Book

Active Particles, Volume 1 by Nicola Bellomo,Pierre Degond,Eitan Tadmor Pdf

This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

Handbook of Dynamic Game Theory

Tamer Basar,Georges Zaccour
Handbook of Dynamic Game Theory Book PDF

Author : Tamer Basar,Georges Zaccour
Publisher : Unknown
Page : 128 pages
File Size : 46,9 Mb
Release : 19??
Category : Differential games
ISBN : 3319273353

Get Book

Handbook of Dynamic Game Theory by Tamer Basar,Georges Zaccour Pdf

Résumé : "This will be a two-part handbook on Dynamic Game Theory and part of the Springer Reference program. Part I will be on the fundamentals and theory of dynamic games. It will serve as a quick reference and a source of detailed exposure to topics in dynamic games for a broad community of researchers, educators, practitioners, and students. Each topic will be covered in 2-3 chapters with one introducing basic theory and the other one or two covering recent advances and/or special topics. Part II will be on applications in fields such as economics, management science, engineering, biology, and the social sciences."

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications

Rene Carmona
Lectures on BSDEs Stochastic Control and Stochastic Differential Games with Financial Applications Book PDF

Author : Rene Carmona
Publisher : SIAM
Page : 265 pages
File Size : 41,9 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974249

Get Book

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by Rene Carmona Pdf

The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.

Ultra-Dense Networks for 5G and Beyond

Trung Q. Duong,Xiaoli Chu,Himal A. Suraweera
Ultra Dense Networks for 5G and Beyond Book PDF

Author : Trung Q. Duong,Xiaoli Chu,Himal A. Suraweera
Publisher : John Wiley & Sons
Page : 312 pages
File Size : 49,8 Mb
Release : 2019-04-15
Category : Technology & Engineering
ISBN : 9781119473695

Get Book

Ultra-Dense Networks for 5G and Beyond by Trung Q. Duong,Xiaoli Chu,Himal A. Suraweera Pdf

Offers comprehensive insight into the theory, models, and techniques of ultra-dense networks and applications in 5G and other emerging wireless networks The need for speed—and power—in wireless communications is growing exponentially. Data rates are projected to increase by a factor of ten every five years—and with the emerging Internet of Things (IoT) predicted to wirelessly connect trillions of devices across the globe, future mobile networks (5G) will grind to a halt unless more capacity is created. This book presents new research related to the theory and practice of all aspects of ultra-dense networks, covering recent advances in ultra-dense networks for 5G networks and beyond, including cognitive radio networks, massive multiple-input multiple-output (MIMO), device-to-device (D2D) communications, millimeter-wave communications, and energy harvesting communications. Clear and concise throughout, Ultra-Dense Networks for 5G and Beyond - Modelling, Analysis, and Applications offers a comprehensive coverage on such topics as network optimization; mobility, handoff control, and interference management; and load balancing schemes and energy saving techniques. It delves into the backhaul traffic aspects in ultra-dense networks and studies transceiver hardware impairments and power consumption models in ultra-dense networks. The book also examines new IoT, smart-grid, and smart-city applications, as well as novel modulation, coding, and waveform designs. One of the first books to focus solely on ultra-dense networks for 5G in a complete presentation Covers advanced architectures, self-organizing protocols, resource allocation, user-base station association, synchronization, and signaling Examines the current state of cell-free massive MIMO, distributed massive MIMO, and heterogeneous small cell architectures Offers network measurements, implementations, and demos Looks at wireless caching techniques, physical layer security, cognitive radio, energy harvesting, and D2D communications in ultra-dense networks Ultra-Dense Networks for 5G and Beyond - Modelling, Analysis, and Applications is an ideal reference for those who want to design high-speed, high-capacity communications in advanced networks, and will appeal to postgraduate students, researchers, and engineers in the field.

Advanced Mean Field Methods

Manfred Opper,David Saad
Advanced Mean Field Methods Book PDF

Author : Manfred Opper,David Saad
Publisher : MIT Press
Page : 300 pages
File Size : 55,5 Mb
Release : 2001
Category : Computers
ISBN : 0262150549

Get Book

Advanced Mean Field Methods by Manfred Opper,David Saad Pdf

This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.