Description
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
Table of Contents
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
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