Mean-Field-Type Games for Engineers

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

Biography

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.