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

• #19 in Best Game Theory Books

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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.

The Compleat Strategyst provides an entertaining introduction to the mathematics of everyday decisions, reduced to the form of a game. J.D. Williams, with illustrations by Charles Satterfield, opens up this arcane subject to anyone with the curiosity to read it. A PhD in math is not required!

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.

I majored in political science. Any course on International Relations would have one day were Game Theory was introduced, followed by a brief discription of two common political games (PD and Chicken). This was interesting mabey the first three times I heard it.

Obviously if I wanted to have a greater understanding of Game Theory I would have to look in to it on my own. This book provided a excellent background in how to solve for the best solution in a game. Which I had not encounterd before. It also introduced me to more complex games, PD and Chicken are both 2x2. What this book does fail to do is give it's reader an understanding of how game theory can be applied to real economic and political problems. But when push comes to shove this book is still an excellent intro.

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

Warning: This book only tells you how to solve game theory problems, NOT WHY the solutions work! So you actually aren't truly learning game theory at all. It's really more an answer key than a primer on game theory. If that's what you want, fine, but if you're looking for an initial step on the road to UNDERSTANDING game theory, look elsewhere.

It takes a lot of time to work thru the examples in this book. (I use Excel to speed things up). But it's a great book. First read it at around 1970. Still in love with it.

It's cheap, it's a classic, and it's got a sense of humor. These would
seem good reasons to choose this as your intro to game theory.
On the other hand, it's dated, the elaborate writing style can
get tiring, and most importantly the ideas are not communicated
very well. For example, there's quite a bit of focus at
the beginning on the formalism itself (the payoff matrix),
instead of tying to applications and intuition.

I highly recommend Philip Straffin's book on game theory as an
alternative. My son and I were reading The Compleat Strategyst
together and he found it a turn-off. We switched to Straffin's
book and are both enjoying it. The pedagogy is excellent, the
writing is clear, and there are many examples and exercises.
It not only gets the ideas across better -- it is also more
precise, with many explicit definitions, theorems, and proofs.
Game Theory and Strategy (New Mathematical Library)

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 could be very useful: the work here uses algorithms that can be reproduced easily on a computer. Then again, maybe it's more important to know the mechanics of game theory rather than relying on a computer.

Most of the math in this book is basic addition and multiplication, so if you're patient enough, you can learn this material even if you're not mathematically inclined. And even if you don't want to learn the more complex methods (or do the sample exercises), you can still get a lot of good insight from this book. The Compleat Strategyst may not help you win many games - at least directly - but it will give you an opportunity to think about them in a new manner.

I had the original 1954 edition. I thought that this new edition of the book may have been updated in the intervening 28 years. Nope. Not at all. Same exact book only with a different cover.

I first read this book when I was in high school, around 1957. I still remember it today, for a clear, coherent, and funny discussion of game theory, and the statistics controlling the optimum strategy. I hope I can raise a copy of it, since it is out of print!