Introduction to the Theory of Games

Concepts, Methods, Applications
1. Auflage. Softcover version of original hardcover Auflage 1999
ISBN: 978-1-4419-4811-3
Verlag: Springer US

Buch, Englisch, Band 32, 340 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 534 g

Reihe: Nonconvex Optimization and Its Applications

Game theory, defined in the broadest sense, is a collection of mathematical models designed for the analysis of strategic aspects of situations of conflict and cooperation in a broad spectrum of fields including economics, politics, biology, engineering, and operations research. This book, besides covering the classical results of game theory, places special emphasis on methods of determining `solutions' of various game models. Generalizations reaching beyond the `convexity paradigm' and leading to nonconvex optimization problems are enhanced and discussed in more detail than in standard texts on this subject. The development is theoretical-mathematical interspersed with elucidating interpretations and examples.
Audience: The material in the book is accessible to PhD and graduate students and will also be of interest to researchers. Solid knowledge of standard undergraduate mathematics is required to read the book.

Zielgruppe

Research

Autoren/Hrsg.

Forgó, Ferenc

Szidarovszky, Ferenc

Szép, Jeno

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik

Inhaltsverzeichnis

Preface. Introduction. I: Noncooperative games. 1. Noncooperative games forms. 2. Nash equilibria. 3. Existence of Nash equilibrium. 4. Uniqueness of Nash equilibrium. 5. Mixed extensions of finite games. 6. Computation of equilibria in mixed extensions of finite games. 7. The oligopoly game. 8. Two-person zero-sum games. 9. Matrix games. 10. Games played over the unit hypercube. 11. Bimatrix games. 12. Repeated games. 13. Games with incomplete information. II: Cooperative games. 14. Games in characteristic function form. 15. The core. 16. Stable sets. 17. The nucleolus. 18. The Shapley value. 19. The kernel and the bargaining set. 20. Game theory and cost allocation. 21. Games without transferable utility. 22. The Nash bargaining solution and its extensions. 23. Two-person bargaining processes. Problems and exercises. Appendix. References. Index.