Mean-Field-Type Games for Engineers

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Foreword
Preface
Acknowledgments
Author Biographies
Symbols
I. Preliminaries
	1. Introduction
		1.1. Linear-Quadratic Games
			1.1.1. Structure of the Optimal Strategies and Optimal Costs
			1.1.2. Solvability of the Linear-Quadratic Gaussian Games
			1.1.3. Beyond Brownian Motion
		1.2. Linear-Quadratic Gaussian Mean-Field-Type Game
			1.2.1. Variance-Awareness and Higher Order Mean-Field Terms
			1.2.2. The Role of the Risk in Engineering Applications
			1.2.3. Uncertainties in Engineering Applications
			1.2.4. Network of Networks/System of Systems
			1.2.5. Optimality Systems
		1.3. Game Theoretical Solution Concepts
			1.3.1. Non-cooperative Game Problem
			1.3.2. Fully-Cooperative Game Problem
			1.3.3. Adversarial Game Problem
			1.3.4. Berge Game Problem
			1.3.5. Stackelberg Game Problem
			1.3.6. Co-opetitive Game Problem
			1.3.7. Partial-Altruism and Self-Abnegation Game Problem
		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
			1.5.1. Continuous-Time Direct Method
			1.5.2. Discrete-Time Direct Method
		1.6. A Simple Derivation of the It^o'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 Di erence 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 Noncooperative and Cooperative Solutions
			5.3.1. Non-cooperative Relationship
			5.3.2. Cooperative Relationship
		5.4. Numerical Examples
		5.5. Exercises
	6. Mean-Field-Type Games with Jump-Diusion 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- Mean-Field-Type Game with Jump-Di usion 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
			9.1.1. Matrix-Valued Applications
			9.1.2. Risk-Neutral
			9.1.3. Risk-Sensitive
		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
			10.1.1. Auxiliary Dynamics
			10.1.2. Augmented Formulation of the Constrained MFTG
		10.2. Semi-explicit Solution of the Constrained Mean-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
			13.1.1. A Constrained Deterministic Game
			13.1.2. A Constrained Mean-Field-Type Game
			13.1.3. Constrained Variational Equilibrium
			13.1.4. Potential Constrained Mean-Field-Type Game
			13.1.5. E ciency Analysis
				13.1.5.1. Variations of the Variance
				13.1.5.2. Variations of the "-parameters
				13.1.5.3. Variations of the Number of Players
				13.1.5.4. Variations of Connectivity under Graphs
			13.1.6. Learning Variational Equilibria
		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
			14.2.1. Chance-Constrained Model Predictive Control
			14.2.2. Mean-Field-Type Model Predictive Control
			14.2.3. Chance-Constrained vs Mean-Field Type Model Predictive Control
			14.2.4. Decomposition and Stability
	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
			15.3.1. Availability of Data
			15.3.2. Preparation of Data
			15.3.3. Machine-Learning Core
		15.4. Error and Performance Metrics
		15.5. Numerical Example
	16. Applications
		16.1. Water Distribution Systems
			16.1.1. Five-Tank Water System
			16.1.2. Barcelona Drinking Water Distribution Network
		16.2. Micro-grid Energy Storage
			16.2.1. Model
			16.2.2. Numerical Results
		16.3. Continuous Stirred Tank Reactor
			16.3.1. Linearization-Based Scheduling and Risk-Aware Con-
			16.3.2. Gain-Scheduled Mean-Field-Type Control
				16.3.2.1. Design
				16.3.2.2. Local Stability of the Operating Points
			16.3.3. Risk-Aware Numerical Illustrative Example
		16.4. Mechanism Design in Evolutionary Games
			16.4.1. A Risk-Aware Approach to the Equilibrium Selection
				16.4.1.1. Known Desired Nash Equilibrium
				16.4.1.2. Unknown Desired Nash Equilibrium
			16.4.2. Risk-Aware Control Design
			16.4.3. Illustrative Example
		16.5. Multi-level Building Evacuation with Smoke
			16.5.1. Markov-Chain-Based Motion Model for Evacuation
				16.5.1.1. Reaching Evacuation Areas
				16.5.1.2. Evacuation of the Whole Area
				16.5.1.3. Jump Intensities for Evacuation
			16.5.2. Markov-Chain-Based Modeling for Smoke Motion
			16.5.3. Mean-Field-Type Control for the Evacuation
			16.5.4. Single-Level Numerical Results
		16.6. Coronavirus Propagation Control
			16.6.1. Single-Player Problem
				16.6.1.1. Control Problem of Mean-Field Type
			16.6.2. Multiple-Decision-Maker Problem
				16.6.2.1. Non-cooperative Games
Bibliography
Index