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An Introductory Course on Mathematical Game Theory
About this Title
Julio González-Díaz, Universidade de Santiago de Compostela, Santiago de Compostela, Spain, Ignacio García-Jurado, Universidad de Coruña, Coruña, Spain and M. Gloria Fiestras-Janeiro, Universidade de Vigo, Vigo, Spain
Publication: Graduate Studies in Mathematics
Publication Year 2010: Volume 115
ISBNs: 978-0-8218-5151-7 (print); 978-1-4704-1177-0 (online)
MathSciNet review: MR2654274
MSC: Primary 91-01; Secondary 91A10, 91A12, 91A18, 91A35, 91A80
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.
Advanced undergraduates and graduate students interested in game theory.
Table of Contents
- Chapter 1. Introduction to decision theory
- Chapter 2. Strategic games
- Chapter 3. Extensive games
- Chapter 4. Games with incomplete information
- Chapter 5. Cooperative games