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The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy
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.
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.
268 pages, Paperback
First published January 1, 1965
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February 7, 2021
The Compleat Strategyst
Being a Primer on the Theory of Games of Strategy
by John D. Williams
Free download pdf:
https://www.rand.org/pubs/commercial_...
pdf is 286 pages. 18 + book page = pdf page.
1954, Chapter 6 added 1966, RAND Corporation.
Library-of-Congress QA270
Dewey 519.3
ISBN 0486251012
RAND Corporation and the many collaborating universities were contracted by the US Air Force, intending to use game theory to win wars. Games are stated in terms of maximizing Blue bombers' chances of evading Red fighters, with various strategies on each side. pp. 48, 51-52.
The games are all, "Suppose Blue has a mission-critical bomber and an identical-looking support plane. Suppose, if the bomber leads, and is attacked, it has an 80% chance of surviving a Red fighter pass, with cover from the support plane's guns. Suppose the following plane, if attacked, has a 60% chance of surviving, thanks to the less-effective cover the leading plane can provide. The game is to get the mission-critical bomber past the Red fighter. If Blue /always/ leads with the bomber, and Red knows it, Blue wins 80%. But if Blue mixes it up, so Red doesn't know which to attack, and Blue leads with the bomber 2/3 of the time and follows with it 1/3 of the time, and Red attacks the leader 2/3 of the time and attacks the follower 1/3 of the time, then Blue wins (.8*4 + .6*1 + 1*4)/9 = 7.8/9 = .8667"
And similar.
The book is all about how to determine the optimal mix of strategies given the stated presumptions.
The stated presumptions have all been so immensely oversimplified as to have zero relation to the real world.
So it's a pure intellectual exercise.
One interesting idea is: since Blue doesn't want Red to know what Blue will do, it's important that Blue not decide until the last minute what to do, and then make that decision based on the random-number tables in the back of the book.
Cites /Theory of Games and Economic Behavior/, John von Neuman, 1944.
PROBABILITY
In ten Prussian army corps, in the 20 years 1875-1894, 122 soldiers were kicked to death by horses. The number of these deaths in a given corps, in a single year, year was
The expected number of the 200 corps-years in which k of the 122 deaths occurred is
(122!/(k!*(122 - k)!))*200*(1 - 1/200)^(122 - k)*(1/200)^k
But the author doesn't tell us this. We can ask Wolfram Alpha to remind us how to compute binomial coefficients: (click "more details" for the formula)
https://www.wolframalpha.com/input/?i...
Here's the table:
Table[(122!/(k!*(122 - k)!))*200.*(1 - 1/200.)^(122. - k)*(1/200.)^k, {k, 0, 8}]
https://www.wolframalpha.com/input/?i...
Because the author has a sense of humor, he also tells us that in these years no horses were kicked to death by Prussian soldiers.
Being a Primer on the Theory of Games of Strategy
by John D. Williams
Free download pdf:
https://www.rand.org/pubs/commercial_...
pdf is 286 pages. 18 + book page = pdf page.
1954, Chapter 6 added 1966, RAND Corporation.
Library-of-Congress QA270
Dewey 519.3
ISBN 0486251012
RAND Corporation and the many collaborating universities were contracted by the US Air Force, intending to use game theory to win wars. Games are stated in terms of maximizing Blue bombers' chances of evading Red fighters, with various strategies on each side. pp. 48, 51-52.
The games are all, "Suppose Blue has a mission-critical bomber and an identical-looking support plane. Suppose, if the bomber leads, and is attacked, it has an 80% chance of surviving a Red fighter pass, with cover from the support plane's guns. Suppose the following plane, if attacked, has a 60% chance of surviving, thanks to the less-effective cover the leading plane can provide. The game is to get the mission-critical bomber past the Red fighter. If Blue /always/ leads with the bomber, and Red knows it, Blue wins 80%. But if Blue mixes it up, so Red doesn't know which to attack, and Blue leads with the bomber 2/3 of the time and follows with it 1/3 of the time, and Red attacks the leader 2/3 of the time and attacks the follower 1/3 of the time, then Blue wins (.8*4 + .6*1 + 1*4)/9 = 7.8/9 = .8667"
And similar.
The book is all about how to determine the optimal mix of strategies given the stated presumptions.
The stated presumptions have all been so immensely oversimplified as to have zero relation to the real world.
So it's a pure intellectual exercise.
One interesting idea is: since Blue doesn't want Red to know what Blue will do, it's important that Blue not decide until the last minute what to do, and then make that decision based on the random-number tables in the back of the book.
Cites /Theory of Games and Economic Behavior/, John von Neuman, 1944.
PROBABILITY
In ten Prussian army corps, in the 20 years 1875-1894, 122 soldiers were kicked to death by horses. The number of these deaths in a given corps, in a single year, year was
. . . . . . . . . . Corps-years . Corps-years
. . . . Corps-years . expected: .. expected:
Deaths .. Actual . .. Wolfram . .. Book p. 10
0 . . . . . 109 . . . 108.504 . .. 109 [should say 108]
1 . . . . .. 65 . . .. 66.520 . . . 66 [should say 67]
2 . . . . .. 22 . . .. 20.223 . . . 20
3 . . . . . . 3 . . . . 4.065 . . .. 4
4 . . . . . . 1 . . . .. .608 . . .. 1
5 . . . . . . 0 . . . .. .072 . . .. 0
6 . . . . . . 0 . . . .. .007 . . .. 0
7 . . . . . . 0 . . . .. .001 . . .. 0
8 . . . . . . 0 . . . .. .000 . . .. 0
The expected number of the 200 corps-years in which k of the 122 deaths occurred is
(122!/(k!*(122 - k)!))*200*(1 - 1/200)^(122 - k)*(1/200)^k
But the author doesn't tell us this. We can ask Wolfram Alpha to remind us how to compute binomial coefficients: (click "more details" for the formula)
https://www.wolframalpha.com/input/?i...
Here's the table:
Table[(122!/(k!*(122 - k)!))*200.*(1 - 1/200.)^(122. - k)*(1/200.)^k, {k, 0, 8}]
https://www.wolframalpha.com/input/?i...
Because the author has a sense of humor, he also tells us that in these years no horses were kicked to death by Prussian soldiers.
May 16, 2018
A charming and dapper little book that is more remarkable for its tone than its content. Anyone hoping for an actual compleat guide to strategy will be disappointed to find a incompleat guide (lacking fundamental concepts like risk minimization or payoff maximization) to a single strand of game theory -- which is in any event a field of knowledge considerably less fun than it sounds. Key insight: sometimes you want to mix things up to keep your adversaries on their toes. It's the mathematical truth!
December 3, 2008
This book teaches you how, given a set of choices, how to make the least offensive one. For example, in a game of Paper-Rock (no Scissors), always choose Paper; at worst, you fail to lose.
By the end you're playing Paper-Rock-Scissors-And-Twelve-Other-Things and your head is swimming, but the writing is accessible, and the wit is positively Saharan. For example, "The following exercises offer opportunities for error."
Even if you don't follow the author down into the arithmetic too deeply, he does an excellent job of explaining the theory, making it accessible to everyone who has even a passing interest in mathematics.
By the end you're playing Paper-Rock-Scissors-And-Twelve-Other-Things and your head is swimming, but the writing is accessible, and the wit is positively Saharan. For example, "The following exercises offer opportunities for error."
Even if you don't follow the author down into the arithmetic too deeply, he does an excellent job of explaining the theory, making it accessible to everyone who has even a passing interest in mathematics.
February 27, 2011
This is a fun and engaging (although old and presumably outdated) introduction to game theory. The book is concerned with techniques, not proofs.
my favorite quote: "We have a smooth and mechanical process, which could be subcontracted to child labor, and no clue to its significance."
my favorite quote: "We have a smooth and mechanical process, which could be subcontracted to child labor, and no clue to its significance."
December 28, 2010
A cartoon-illustrated nonmathematical introduction to game theory, published by the RAND Corporation, Dr. Strangelove's employer, in 1954. When Russian roulette is mentioned, the author wonders why it is not the official sport of the Party; William Poundstone's Prisoner's Dilemma says that in the Russian translation it is called American roulette; in fact it is called Hussar roulette.
November 22, 2014
A 60's RAND Classic. I understood the theory that the author was trying to teach however, it was still a little abstract. A bit more correlation between the underlying theory and wargaming would have been nice.
December 21, 2020
Review:
This book was mostly about the nitty gritty details of the theory which I found terribly boring. I think I picked the wrong field of study, I didn't think that this would be a deep math thing.
The notes are mostly from the first chapter, because it was the general part of the book, after that it was about calculation and examples.
Main points:
This book was mostly about the nitty gritty details of the theory which I found terribly boring. I think I picked the wrong field of study, I didn't think that this would be a deep math thing.
The notes are mostly from the first chapter, because it was the general part of the book, after that it was about calculation and examples.
Main points:
April 11, 2016
This book is alright. It isn't great, but it isn't bad. With a witty down home style of prose, J. D. Williams relates some aspects of Game Theory as it was in the infancy of the discipline. Using simple mathematics and cartoon illustrations, this book is a good introduction to Game Theory, but I am not really sure how far it has come, since I am not a mathematician.
The book is quite short. It starts with a short history of Game Theory with John von Neumann. It goes on to describe different varieties of games, with the zero-sum games being the ones that are followed since the non-zero-sum games add in a number of other factors and might not end neatly. It gives some simple calculations to determine the value of the game and some other things. All of the problems are related with a breezy style and a droll sense of humor.
At the end of the book is a table of random numbers and a list of solutions to the problems.
The book is quite short. It starts with a short history of Game Theory with John von Neumann. It goes on to describe different varieties of games, with the zero-sum games being the ones that are followed since the non-zero-sum games add in a number of other factors and might not end neatly. It gives some simple calculations to determine the value of the game and some other things. All of the problems are related with a breezy style and a droll sense of humor.
At the end of the book is a table of random numbers and a list of solutions to the problems.
March 4, 2009
An excellent, charming, and well-written book on an incredibly boring and pointless topic.
January 9, 2021
Interesting book if you like math and game theory already. I think is a little bit outdated for someone who doesn’t know anything about game theory or its applications.
June 13, 2022
This is one of the earlier books on game theory. However, there really isn't a lot about game theory itself. Instead, if you can place a value on different outcomes, this book gives you a mathematical way of calculating the ideal choice or choices to minimize losses. It starts with two players with two choices and grows to many players with many choices, using a matrix to calculate the top choice. All of this assumes that your opponent is also operating/playing optimally. While pretty narrowly focused and outdated, the humor was completely refreshing and unexpected.
February 19, 2021
Теория игр, все таки не для жизни, сложновато, даже если ты математик
October 5, 2021
Interesting ideas but takes a lot of focus to get through
March 21, 2011
The best introduction to game theory book I have come across. It's illustrated, funny, and dare I say, the easiest thing to read of everything ever published by Rand. The edition I have is from 1954, not 1966 like the description says from Goodreads. Also, the PDF version is available for free on Rand's website.
June 24, 2010
Surprisingly, this seems to be a text book. Considering that, it was quite readable, and at times enjoyable. I just don't have much interest in the dull mechanics of solving game matrixes, which becomes more-and-more the focus of the text.
Want to read
March 20, 2021This is a nice book to get an idea of what game theory is about. There are lots of applications, but little formal theory.
Currently reading
July 11, 2012cool
June 26, 2014
Excellent primer on Game theory. very readable
Displaying 1 - 20 of 20 reviews