The Compleat Strategyst: Being a Primer on the Theory of Games Strategy (Dover Books on Mathematics) Paperback – 26 May 1987

The Compleat Strategyst by J.D. Williams is a wonderful introduction to the ins and outs of game theory. The pace of the primer I found quite reasonable, and the organization is very natural. The Compleat Strategyst begins with the gist (as it should) regarding game matrices and how to interpret them. Williams's discussion then proceeds through 2 x 2 games, 2 x m games, 3 x 3 games, 3 x m games, and so on. Each section contains clever story problems chosen to both re-enforce basic principles and point to potential pitfalls. Also provided are numerous exercises to build the skills necessary to understand game theory.
One of the most enjoyable facets of The Compleat Strategyst is J.D. Williams's entertaining writing style. He seems to know the kind of people reading his book (non-mathematicians who think they might be able to apply game theory to their own work - in my case anyway), and the text is taylored to that audience. In addition, while making the subject matter of game theory accessible strictly through arithmatic, the author provides fair reminders that a great deal of actual mathmatics is being swept beneath the rug.

I share the feedback of the other reviewers in that this book is extremely fun to read, very well-written and comprehensively covers (thoroughly teaches the so inclined) a few aspects of game theory. The drawback is that it limits itself, consciously it seems, to zero-sum games played between two players. So after reading this book, you have no excuse for not being able to solve any such games. The narrative, the examples and the exercises take care of this. However, you will learn near nothing about non-zero-sum games, which are in actuality more life-like (hence a probable reason for the complaint of one reviewer who wants more real examples).

Nevertheless, this book is extremely well-written, and truly accomplishes what it aims: giving the reader an appreciation of the basis of game theory and teaching them to solve zero-sum games. And quite a many witty jokes come in extra!

I found this book to be an excellent introduction to game theory that doesn't require much mathamatical background beyond simple algebra. It comes complete with theoretical explainations of the game matrix, problems to help sharpen your skills, and strategic stories that fit with a game matrix, to help show how game theory can be applied to real problems. A definite must for anyone who wants to start learning about game theory.

This is a superlative introduction to a mathematical concept which, with a lesser writer, could be tedious to learn. Williams includes many entertaining and enjoyable story problems, replete with attractive illustrations. He takes an inherently interesting topic and makes it easy and fun to learn.

Game theory for the users not for mathematicians.

Write a book on jet engines for engineers and you'll have chapters on the choice of alloy for the turbine blades and casing, formulae for fuel nozzle diameters, air flow and compression ratios, etc. Write a book on jet engines for mechanics, and it might be just as long, but have very different content, with types of failures and their causes, proper tool selections, techniques for cleaning internal components, etc.

"The Compleat Strategyst" is for people who (figuratively) turn wrenches in problems of decision-making. Were it for mathematicians, it would have long, convuluted derivations of axioms, and use sigma notation on 2 out of three pages. As a liberal arts major, it was a relief to find out that calculus appears nowhere in this book, as greek letters mixed in math disturb my digestion, and cause anxiety attacks. You'll need some math, but only what would show up in junior high school pre-algebra. The worst you'll run into are ratios with five or more elements and some long division problems, nothing that requires a recovery period.

What it does have is a first rate explaination of decision matrices for economists, historians, and poli-sci majors, along with other essential topics in game theory. The focus is basic, two-player games with only passing mention to anything other than zero-sum games, but within its limits, it is very good. Use of matrices to support decisions, the value of randomness in situations where strategies are of similar risk-benefit, and multiple strategy games are covered very well. Although basic, enough detail and examples are given, that the concepts can be readily applied to real world decisions. Any student of political science would do well to read this book and do the problems.

The book was first publish in 1954, and the illustrations and prose can be a little 'camp' at times, but younger readers will be mildly amused at the corniness of their elders, and have a brief glimpse of life during the Cold War, and the early post-WW II era.

Within in its limits, Great! But it is limited.

E. M. Van Court