Synopses & Reviews
When J. D. Williams wrote this entertaining, witty introduction for the nonscientist, game theory was still a somewhat mysterious subject familiar to very few scientists beyond those researchers, like himself, working for the military. Now, over thirty years after its original publication as a Rand Corporation research study, his light-hearted though thoroughly effective primer is the recognized classic introduction to an increasingly applicable discipline. Used by amateurs, professionals, and students throughout the world in the classroom, on the job, and for personal amusement, the book has been through ten printings, and has been translated into at least five languages (including Russian and Japanese).
Revised, updated, and available for the first time in an inexpensive paperback edition, The Compleat Strategyst is a highly entertaining text essential for anyone interested in this provocative and engaging area of modern mathematics. In fully illustrated chapters complete with everyday examples and word problems, Williams offers readers a working understanding of the possible methods for selecting strategies in a variety of situations, simple to complex. With just a basic understanding of arithmetic, anyone can grasp all necessary aspects of two-, three-, four-, and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.
As research and study continues not only in this new discipline but in the related areas of statistics, probability and behavioral science, understanding of games, decision making, and the development of strategies will be increasingly important. In the areas of economics, sociology, politics, and the military, game theory is sure to have an even wider impact. For students and amateurs fascinated by game theory's implications there is no better, immediately applicable, or more entertaining introduction to the subject than this engaging text by the late J. D. Williams, Professor of Mathematics at Princeton University and a member of the Research Council of The Rand Corporation.
Synopsis
This entertaining text is essential for anyone interested in game theory. Only a basic understanding of arithmetic is needed to grasp the necessary aspects of strategy games for two, three, four, and more players that feature two or more sets of inimical interests and a limitless array of zero-sum payoffs.
Synopsis
Highly entertaining classic describes, with many illustrated examples, how to select best strategies in conflict situations. Prefaces. Appendices.
Synopsis
Only a basic understanding of arithmetic is needed to grasp these strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.
Table of Contents
PREFACE TO THE REVISED EDITION
PREFACE TO THE FIRST EDITION
CHAPTER 1. INTRODUCTION
Nature of the Subject
An Historical Theory
Lessons and Parallels
Sectarian Remarks on Method
Players and Persons
The Payoff
Strategies
The Game Matrix
Implicit Assumptions
The Criterion
Example 1. The Campers
CHAPTER 2. TWO - STRATEGY GAMES
PART 1: 2 X 2 Games
The Approach
Fluctuations
Saddle-points
Mixed Strategies
The Oddment
Rules for Finding Odds
Value of the Game
Scale Effects
Good Play vs. Poor
Example 2. The Hidden Object
Example 3. The Daiquiris
Example 4. The River Table
Example 5. The Attack-Defense Game
Example 6. The Music Hall Problem
Example 7. The Darkroom
Example 8. The Birthday
Example 9. The Huckster
Example 10. The Squad Car
Summary of 2 X 2 Methods
Exercises 1
PART 2: 2 X m Games
Saddle-points
Dominance
Mixed Strategies
Graphical Solutions
Example 11. The Spellers
Example 12. The Sports Kit
Example 13. The Hi-Fi
Chance Devices
Summary of 2 X m Methods
Exercises 2
CHAPTER 3. THREE - STRATEGY GAMES
PART 1: 3 X 3 Games
Morale-building Discourse
Saddle-points
Dominance
Value of the Game
Three Active Strategies
Games We Wish You'd Never Met
Example 14. Scissors-Paper-Stone
Example 15. The Coal Problem
Example 16. The Heir
Example 17. The Cattle Breeders' Separation
Example 18. The Date
Summary of 3 X 3 Methods
Exercises 3
PART 2: 3 X m Games
Method of Solving
Example 19. The Bass and the Professor
Example 20. The Bedside Manner
Example 21. The Chessers
Summary of 3 X m Methods
Exercises 4
CHAPTER 4. FOUR - STRATEGY GAMES AND LARGER ONES
Solution via Revelation
Saddle-points
Dominance
All-strategies-active
Example 22. The Secondhand Car
Example 23. The Silviculturists
Example 24. Color Poker
Example 25. For Older Children
Example 26. The Process Server
Example 27. The Palm Game
Example 28. The Administrator's Dilemma
Example 29. The Colonel Blotto Problem
Example 30. Morra
Example 31. The Maze
Example 32. Merlin
Summary of 4 X m Methods
Exercises 5
CHAPTER 5. MISCELLANY
Approximations
More on Dominance
Simple Solutions
Multiple Solutions
Exercise 6
On Measurement
Qualitative Payoffs
Example 33. Portia
Example 34. The Lady or the Tiger
Games Played Only Once
Symmetric Games
Linear Programming
Example 35. The Diet
Non-zero-sum Games
Conclusion
CHAPTER 6. GENERAL METHOD OF SOLVING GAMES
First Example
Basic Solutions
Second Example
Summary of Pivot Method
How to Check the Work
Control Sums
APPENDIX
Table of Random Digits
Solutions to Exercises
INDEX