Mean-Field-Type Games for Engineers

Julian Barreiro-Gomez, Hamidou Tembine

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000473551
• Edition: 1
• Topic: Computer Science
• Subtopic: Computer Networking
• Index: Computer Science

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.

"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

Part IIIOne-Dimensional Mean-Field-Type Games

4Continuous-Time Mean-Field-Type Games

DOI: 10.1201/9781003098607-4

The previous chapters mainly helped to make the reader familiar with different deterministic and stochastic game problems that do not belong to the mean-field-type class. Indeed, these previous chapters also served as introduction to the direct method, which we will continue using along the book. Here in this chapter, we start working with the main topic and objective of this book, we start studying mean-field-type control and game theory from the simplest setting, and progressively, we will introduce new concepts and terms later on.

Mean-field-type games are a class of stochastic games where the distribution of either the system states or the control inputs/strategies (or both) are taken into consideration for the cost functional and for the evolution of the system states i...

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• List of Figures
• List of Tables
• Foreword
• Preface
• Acknowledgments
• Author Biographies
• Symbols
• I Preliminaries
• II Mean-Field-Free and Mean-Field Games
• III One-Dimensional Mean-Field-Type Games
• IV Matrix-Valued Mean-Field-Type Games
• V  Discrete-Time Mean-Field-Type Games
• VI Learning Approaches and Applications
• Bibliography
• Index