Games and Decisions

Introduction and Critical Survey

R. Duncan Luce, Howard Raiffa, Howard Raiffa

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486659435
• eBook ISBN: 9780486134833
• Topic: Mathematics
• Subtopic: Game Theory
• Index: Mathematics

"The best book available for non-mathematicians." — Contemporary Psychology.
This book represents the earliest clear, detailed, precise exposition of the central ideas and results of game theory and related decision-making models — unencumbered by technical mathematical details. It offers a comprehensive, time-tested conceptual introduction, with a social science orientation, to a complex of ideas related to game theory including decision theory, modern utility theory, the theory of statistical decisions, and the theory of social welfare functions.
The first three chapters provide a general introduction to the theory of games including utility theory. Chapter 4 treats two-person, zero-sum games. Chapters 5 and 6 treat two-person, nonzero-sum games and concepts developed in an attempt to meet some of the deficiencies in the von Neumann-Morgenstern theory. Chapters 7–12 treat n-person games beginning with the von Neumann-Morgenstern theory and reaching into many newer developments. The last two chapters, 13 and 14, discuss individual and group decision making. Eight helpful appendixes present proofs of the famous minimax theorem, several geometric interpretations of two-person zero-sum games, solution procedures, infinite games, sequential compounding of games, and linear programming.
Thought-provoking and clearly expressed, Games and Decisions: Introduction and Critical Survey is designed for the non-mathematician and requires no advanced mathematical training. It will be welcomed by economists concerned with economic theory, political scientists and sociologists dealing with conflict of interest, experimental psychologists studying decision making, management scientists, philosophers, statisticians, and a wide range of other decision-makers. It will likewise be indispensable for students in courses in the mathematical theory of games and linear programming.

Table of contents

• Cover
• Title Page
• Copyright Page
• Dedication
• Preface
• Contents
• 1 General Introduction to the Theory of Games
• 2 Utility Theory
• 3 Extensive and Normal Forms
• 4 Two-Person Zero-Sum Games
• 5 Two-Person Non-Zero-Sum Non-Cooperative Games
• 6 Two-Person Cooperative Games
• 7 Theories of n-Person Games in Normal Form
• 8 Characteristic Functions
• 9 Solutions
• 10 ψ-Stability
• 11 Reasonable Outcomes and Value
• 12 Applications of n-Person Theory
• 13 Individual Decision Making under Uncertainty
• 14 Group Decision Making
• 1 A Probabilistic Theory of Utility
• 2 The Minimax Theorem
• 3 First Geometrical Interpretation of a Two-Person Zero-Sum Game
• 4 Second Geometrical Interpretation of a Two-Person Zero-Sum Game
• 5 Linear Programing and Two-Person Zero-Sum Games
• 6 Solving Two-Person Zero-Sum Games
• 7 Games with Infinite Pure Strategy Sets
• 8 Sequential Compounding of Two-Person Games
• Bibliography
• Index