The Book
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.
The Author(s)
Julio González-Díaz, Universidade de Santiago de Compostela, Spain, Ignacio García-Jurado, Universidad de Coruña, Spain, and M. Gloria Fiestras-Janeiro, Universidade de Vigo, Spain
Table of Contents
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