Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises.
The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory.
Preface
Chapter 1. Introduction to Decision Theory
Preliminaries Ordinal Utility Linear Utility
Chapter 2. Strategic Games
Introduction to Strategic Games Nash Equilibrium in Strategic Games Two-Player Zero-Sum Games Mixed Strategies in Finite Games Bimatrix Games Matrix Games Algorithms for Matrix Games Matrix Games and Linear Programming Refinements of Nash Equilibrium in Finite Games A Basic Model of Knowledge Correlated Equilibrium On the Epistemic Foundations of the Different Solution Concepts for Strategic Games Fixed-Point Theorems On Extreme Points and Convex Sets: Krein-Milman Theorem Exercises of Chapter
Chapter 3. Extensive Games
Introduction to Extensive Games Strategies in Extensive Games: Mixed Strategies vs. Behavior Strategies Nash Equilibrium in Extensive Games Subgame Perfect Equilibrium Sequential Equilibrium Further Refinements Repeated Games Exercises of Chapter 3
Chapter 4. Games with Incomplete Information
Incomplete Information: Introduction and Modeling Bayesian Games and Bayesian Nash Equilibrium The Chain Store Paradox in Perspective A First Application of Bayesian Games: Auctions A Second Application of Bayesian Games: Mechanism Design and the Revelation Principle Extensive Games with Incomplete Information: Multistage Games and Perfect Bayesian Equilibrium An Outline of Harsanyi’s Approach Exercises of Chapter 4
Chapter 5. Cooperative Games
Introduction to Cooperative Games Nontransferable Utility Games Bargaining Transferable Utility Games The Core and Related Concepts The Shapley Value The Nucleolus Convex Games Noncooperative Models in Cooperative Game Theory: Implementation Theory Airport Problems and Airport Games Bankruptcy Problems and Bankruptcy Games Voting Problems and Voting Games: Power Indices Cooperation in Operations Research Models Exercises of Chapter Bibliography Notations Index of Authors Index of Solution Concepts Subject Index