An Introductory Course on Mathematical Game Theory and Applications

Cover
Table of Contents
Preface
Chapter 1. Introduction to Decision Theory
	1.1. Preliminaries
	1.2. Ordinal Utility
	1.3. Linear Utility
Chapter 2. Strategic Games
	2.1. Introduction to Strategic Games
	2.2. Nash Equilibrium in Strategic Games
	2.3. Two-Player Zero-Sum Games
	2.4. Mixed Strategies in Finite Games
	2.5. Bimatrix Games
	2.6. Matrix Games
	2.7. Algorithms for Matrix Games
	2.8. Matrix Games and Linear Programming
	2.9. Refinements of Nash Equilibrium in Finite Games
	2.10. A Basic Model of Knowledge
	2.11. Correlated Equilibrium
	2.12. On the Epistemic Foundations of the Different Solution Concepts for Strategic Games
	2.13. Fixed-Point Theorems
	2.14. Extreme Points and Convex Sets: Krein–Milman Theorem
	Exercises of Chapter 2
Chapter 3. Extensive Games
	3.1. Introduction to Extensive Games
	3.2. Strategies in Extensive Games: Mixed Strategies vs. Behavior Strategies
	3.3. Nash Equilibrium in Extensive Games
	3.4. Subgame Perfect Equilibrium
	3.5. Sequential Equilibrium
	3.6. Further Refinements
	3.7. Repeated Games
	Exercises of Chapter 3
Chapter 4. Games with Incomplete Information
	4.1. Incomplete Information: Introduction and Modeling
	4.2. Bayesian Games and Bayesian Nash Equilibrium
	4.3. The Chain Store Paradox in Perspective
	4.4. A First Application of Bayesian Games: Auctions
	4.5. A Second Application of Bayesian Games: Mechanism Design and the Revelation Principle
	4.6. Extensive Games with Incomplete Information: Multistage Games and Perfect Bayesian Equilibrium
	4.7. An Outline of Harsanyi\'s Approach
	Exercises of Chapter 4
Chapter 5. Fundamentals of Cooperative Games
	5.1. Introduction to Cooperative Games
	5.2. Nontransferable Utility Games
	5.3. Bargaining
	5.4. Transferable Utility Games
	5.5. The Core and Related Concepts
	5.6. The Shapley Value
	5.7. Computation of the Shapley Value
	5.8. The Banzhaf Value
	5.9. Equal Division Values
	5.10. The Nucleolus
	5.11. The Core-Center
	5.12. Convex Games
	5.13. Games with Communication Graphs: The Myerson Value
	5.14. Games with A Priori Unions: The Owen Value
	5.15. Noncooperative Models in Cooperative Game Theory: Implementation Theory
	Exercises of Chapter 5
Chapter 6. Applications of Cooperative Games
	6.1. Preliminaries
	6.2. Airport Problems and Airport Games
	6.3. Bankruptcy Problems and Bankruptcy Games
	6.4. Voting Problems and Voting Games: Power Indices
	6.5. Apportionments and Data Science
	6.6. Linear Production Games
	6.7. Maximum Flow Games
	6.8. Inventory Games
	6.9. Project Planning
	6.10. Assignment Games
	6.11. Cooperation on Minimum Cost Spanning Tree Problems
	6.12. Cooperation on Queueing Problems
	6.13. Cooperation on Sequencing Problems
	Exercises of Chapter 6
Bibliography
Notations
Index of Authors
Index of Solution Concepts
Subject Index
Back Cover