The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy

Funny thing about words: depending on context, they can evoke quite different moods. Take, for example, "matrix": when referring to a certain movie with Keanu Reeves and Carrie Anne Moss, most people react favorably. Used, however, when discussing mathematics, and the majority will feel something different, perhaps akin to fear and repulsion. On the one hand, this is understandable; working with matrices can be tedious grunt work with little of the theoretical beauty that much of math offers; on the other hand, it is the heart and soul of one particularly interesting branch, game theory. J.D. Williams's The Compleat Strategyst is an introduction to game theory and by the end of the volume you will see your fair share of matrices, but this should not be overly intimidating. Williams knows that they can be unwieldy and does his best to simplify matters. But first, he introduces us to game theory itself. Essentially, game theory is a mathematical method for calculating strategies. In most games, the theory will be too overly simple, but it does offer a lot of insights with practical implications in fields such as economics (for example, John Nash of "A Beautiful Mind" won his Nobel Prize for work in this field). The classic illustration, not really discussed in this book, involves the Prisoner's Dilemma: two men are held for a crime. If neither confesses, both go free; if only one confesses, he gets a light sentence and the other gets a heavy one; if both confess, they each get a medium sentence. What should the prisoner's strategy be? Silence can result in the best payout (freedom), but also the worst if the other prisoner confesses. Confession guarantees a sentence, but at worst, it will not be as bad as the one that can result from silence. So what is the best strategy? Generally, if both prisoners act rationally, they will take the choice that results with the least "bad" result: That would mean confession, which at worst, results in a medium sentence (which is better than the long sentence that silence could lead to). Of course, things can work out differently in the real world. In many games (though not the Prisoner's Dilemma), the player gets to play multiple times, in which case, the best strategy can actually be a mix of various strategies. The laying out of these various strategies and the various payouts is in the form of a matrix, a square or rectangular grid of numbers, with each row representing a strategy of player A and each column one for player B. Even if this seems a little bewildering, Williams does a good job at explaining it, lacing his examples with plenty of humor (which I actually found only mildly funny, but it does lighten the prose). But no matter how good the writing is, eventually, the complexity of matrices can get overwhelming. It is here that one of the weaknesses of the book shows: due to its age (this edition was written in 1966), the use of computers is virtually ignored, although they c

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!

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.

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 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.