1st Edition

Mean-Field-Type Games for Engineers

    526 Pages 170 B/W Illustrations
    by CRC Press

    526 Pages 170 B/W Illustrations
    by CRC Press

    528 Pages 170 B/W Illustrations
    by CRC Press

    Also available as eBook on:

    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

    I. Preliminaries

    1. Introduction
    1.1 Linear-Quadratic Games
    1.2 Linear-Quadratic Gaussian Mean-Field-Type Game
    1.3 Game Theoretical Solution Concepts
    1.4 Partial Integro-Differential System for a Mean-Field-Type Control
    1.5 A Simple Method for Solving Mean-Field-Type Games and Control
    1.6 A Simple Derivation of the Itô's Formula
    1.7 Outline
    1.8 Exercises

    II. Mean-Field-Free and Mean-Field Games

    2. Mean-Field-Free Games
    2.1 A Basic Continuous-Time Optimal Control Problem
    2.2 Continuous-Time Di erential Game
    2.3 Stochastic Mean-Field-Free Di erential Game
    2.4 A Basic Discrete-Time Optimal Control Problem
    2.5 Deterministic Di erence Games
    2.6 Stochastic Mean-Field-Free Difference Game
    2.7 Exercises

    3. Mean-Field Games
    3.1 A Continuous-Time Deterministic Mean-Field Game
    3.2 A Continuous-Time Stochastic Mean-Field Game
    3.3 A Discrete-Time Deterministic Mean-Field Game
    3.4 A Discrete-Time Stochastic Mean-Field Game
    3.5 Exercises

    III. One-Dimensional Mean-Field-Type Games

    4. Continuous-Time Mean-Field-Type Games
    4.1 Mean-Field-Type Game Set-up
    4.2 Semi-explicit Solution of the Mean-Field-Type Game Problem
    4.3 Numerical Examples
    4.4 Exercises

    5. Co-opetitive Mean-Field-Type Games
    5.1 Co-opetitive Mean-Field-Type Game Set-up
    5.2 Semi-explicit Solution of the Co-opetitive Mean-Field-Type Game Problem
    5.3 Connections between the Co-opetitive Solution with the Non-Cooperative and Cooperative Solutions
    5.4 Numerical Examples
    5.5 Exercises

    6. Mean-Field-Type Games with Jump-Diffusion and Regime Switching
    6.1 Mean-Field-Type Game Set-up
    6.2 Semi-explicit Solution of the Mean-Field-Type Game with Jump-Diffusion Process and Regime Switching
    6.3 Numerical Example
    6.4 Exercises

    7. Mean-Field-Type Stackelberg Games
    7.1 Mean-Field-Type Stackelberg Game Set-up
    7.2 Semi-explicit Solution of the Stackelberg Mean-Field-Type Game with Jump-Diffusion Process and Regime Switching
    7.3 When Nash Solution Corresponds to Stackelberg Solution for Mean-field-type Games
    7.4 Numerical Example
    7.5 Exercises

    8. Berge Equilibrium in Mean-Field-Type Games
    8.1 On the Berge Solution Concept
    8.2 Berge Mean-Field-Type Game Problem
    8.3 Semi-explicit Mean-field-type Berge Solution
    8.4 When Berge Solution Corresponds to Co-opetitive Solution for Mean-field-type Games
    8.5 Numerical Example
    8.6 Exercises

    IV. Matrix-Valued Mean-Field-Type Games

    9. Matrix-Valued Mean-Field-Type Games
    9.1 Mean-Field-Type Game Set-up
    9.2 Semi-explicit Solution of the Mean-Field-Type Game Problems: Risk-Neutral Case
    9.3 Semi-explicit Solution of the Mean-Field-Type Game Problems: Risk-Sensitive Case
    9.4 Numerical Examples
    9.5 Exercises

    10. A Class of Constrained Matrix-Valued Mean-Field-Type Games
    10.1 Constrained Mean-Field-Type Game Set-up
    10.2 Semi-explicit Solution of the Constrained Mean-Field-Type Game Problem
    10.3 Exercise

    V. Discrete-Time Mean-Field-Type Games

    11. One-Dimensional Discrete-Time Mean-Field-Type Games
    11.1 Discrete-Time Mean-Field-Type Game Set-up
    11.2 Semi-explicit Solution of the Discrete-Time Non-Cooperative Mean-Field-Type Game Problem
    11.3 Semi-explicit Solution of the Discrete-Time Cooperative Mean-Field-Type Game Problem
    11.4 Exercises

    12. Matrix-Valued Discrete-Time Mean-Field-Type Games
    12.1 Discrete-Time Mean-Field-Type Game Set-up
    12.2 Semi-explicit Solution of the Discrete-Time Mean-Field-Type Game Problem
    12.3 Numerical Examples
    12.4 Exercises

    VI. Learning Approaches and Applications

    13. Constrained Mean-Field-Type Games: Stationary Case
    13.1 Constrained Games
    13.2 Model
    13.3 Learning Algorithms
    13.4 Equilibrium under migration constraints

    14. Mean-Field-Type Model Predictive Control
    14.1 Problem Statement
    14.2 Risk-Aware Model Predictive Control Approaches

    15. Data-Driven Mean-Field-Type Games
    15.1 Data-Driven Mean-Field-Type Game Problem
    15.2 Machine Learning Philosophy
    15.3 Machine-learning-based (Linear Regression) Data-driven Mean-field-type games
    15.4 Error and Performance Metrics
    15.5 Numerical Example

    16. Applications
    16.1 Water Distribution Systems
    16.2 Microgrid Energy Storage
    16.3 Continuous Stirred Tank Reactor
    16.4 Mechanism Design in Evolutionary Games
    16.5 Multi-level Building Evacuation with Smoke
    16.6 Coronavirus Propagation Control


    Julian Barreiro-Gomez is a Post-Doctoral Associate in the Learning & Game Theory Laboratory (L&G-Lab) at the New York University in Abu Dhabi (NYUAD), United Arab Emirates, and since 2019, he is also with the Research Center on Stability, Instability and Turbulence (SITE) at the New York University in Abu Dhabi (NYUAD).

    Hamidou Tembine is presently affiliated with New York University in Abu Dhabi (NYUAD), United Arab Emirates. He is a prolific Researcher and has been co-organizer of several scientific meetings on game theory in networking, wireless Communications, smart energy systems, and smart transportation systems.