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The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy (Dover Books on Mathematics) Kindle Edition
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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.
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
Thats not at all to say I didn't enjoy this book. I thought it was great. The art has a fun vintage feel, and the author's Ivy-league snark really tickled me. Everyone interested in math should have some fun here, but would-be mathematicians should consider this a gateway to the subject, and not a "compleat" text by any stretch.
Most recent customer reviews
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