Game theory and strategy / by Philip D. Straffin.

Format:

Book

Author/Creator:

Straffin, Philip D.

Series:

Anneli Lax New Mathematical Library ; 36

Language:

English

Subjects (All):

Game theory.

Algebra.

Physical Description:

x, 244 p.

Edition:

1st ed.

Place of Publication:

Washington, DC : Mathematical Association of America, 1993.

Language Note:

English

Summary:

This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals--or companies, or political parties, or nations--confront situations where the outcome for each depends on the behavior of all. What are the best strategies in such situations? If there are chances of cooperation, with whom should you cooperate, and how should you share the proceeds of cooperation? Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology.In this book, its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Ideas like "fairness" are presented via axioms that fair allocations should satisfy; thus the reader is introduced to axiomatic thinking as well as to mathematical modeling of actual situations.

Contents:

Front Cover

Game Theory and Strategy

Copyright Page

Note to the Reader

New Mathematical Library

Contents

Preface

Part I: Two-Person Zero-Sum Games

Chapter 1. The Nature of Games

Chapter 2. Matrix Games: Dominance and Saddle Points

Chapter 3. Matrix Games: Mixed Strategies

Chapter 4. Application to Anthropology: Jamaican Fishing

Chapter 5. Application to Warfare: Guerrillas, Police, and Missiles

Chapter 6. Application to Philosophy: Newcomb's Problem and Free Will

Chapter 7. Game Trees

Chapter 8. Application to Business: Competitive Decision Making

Chapter 9. Utility Theory

Chapter 10. Games Against Nature

Part II: Two-Person Non-Zero-Sum Games

Chapter 11. Nash Equilibria and Non-Cooperative Solutions

Chapter 12. The Prisoner's Dilemma

Chapter 13. Application to Social Psychology: Trust, Suspicion, and the F-Scale

Chapter 14. Strategic Moves

Chapter 15. Application to Biology: Evolutionarily Stable Strategies

Chapter 16. The Nash Arbitration Scheme and Cooperative Solutions

Chapter 17. Application to Business: Management-Labor Arbitration

Chapter 18. Application to Economics: The Duopoly Problem

Part III: N-Person Games

Chapter 19. An Introduction to N-Person Games

Chapter 20. Application to Politics: Strategic Voting

Chapter 21. N-Person Prisoner's Dilemma

Chapter 22. Application to Athletics: Prisoner's Dilemma and the Football Draft

Chapter 23. Imputations, Domination, and Stable Sets

Chapter 24. Application to Anthropology: Pathan Organization

Chapter 25. The Core

Chapter 26. The Shapley Value

Chapter 27. Application to Politics: The Shapley-Shubik Power Index

Chapter 28. Application to Politics: The Banzhaf Index and the Canadian Constitution

Chapter 29. Bargaining Sets.

Chapter 30. Application to Politics: Parliamentary Coalitions

Chapter 31. The Nucleolus and the Gately Point

Chapter 32. Application to Economics: Cost Allocation in India

Chapter 33. The Value of Game Theory

Bibliography

Answers to Exercises

Index

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-88385-950-5

OCLC:

929120483