- Series: Dover Books on Mathematics
- Paperback: 288 pages
- Publisher: Dover Publications; Subsequent edition (July 1, 1997)
- Language: English
- ISBN-10: 0486296725
- ISBN-13: 978-0486296722
- Product Dimensions: 5.5 x 0.5 x 8.8 inches
- Shipping Weight: 12.6 ounces (View shipping rates and policies)
- Average Customer Review: 33 customer reviews
- Amazon Best Sellers Rank: #350,012 in Books (See Top 100 in Books)
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Game Theory: A Nontechnical Introduction (Dover Books on Mathematics) Subsequent Edition
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From the Back Cover
"A lucid and penetrating development of game theory that will appeal to the intuition . . . a most valuable contribution."—Douglas R. Hofstadter, author of Gödel, Escher, Bach
The foundations of game theory were laid by John von Neumann, who in 1928 proved the basic minimax theorem, and with the 1944 publication of the Theory of Games and Economic Behavior, the field was established. Since then, game theory has become an enormously important discipline because of its novel mathematical properties and its many applications to social, economic, and political problems.
Game theory has been used to make investment decisions, pick jurors, commit tanks to battle, allocate business expenses equitably—even to measure a senator's power, among many other uses. In this revised edition of his highly regarded work, Morton Davis begins with an overview of game theory, then discusses the two-person zero-sum game with equilibrium points; the general, two-person zero-sum game; utility theory; the two-person, non-zero-sum game; and the n-person game.
A number of problems are posed at the start of each chapter and readers are given a chance to solve them before moving on. (Unlike most mathematical problems, many problems in game theory are easily understood by the lay reader.) At the end of the chapter, where solutions are discussed, readers can compare their "common sense" solutions with those of the author. Brimming with applications to an enormous variety of everyday situations, this book offers readers a fascinating, accessible introduction to one of the most fruitful and interesting intellectual systems of our time.
Top customer reviews
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Without calculus, Davis provides a complete introduction to an arcane but useful mathematical discipline. The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy by Williams was too soft. It used the simplest possible methods to address the concepts being discussed, and barely acknowledged some of the most interesting topics in game theory. Games and Decisions: Introduction and Critical Survey by Luce and Raiffa was good, up until you hit the calculus (pretty quickly in each chapter), after which I have no basis to form an opinion.
Davis hits all the important concepts of game theory without resorting to sigma notation or even more occult symbols (unlike Luce and Raiffa). He does, however, require a fairly solid understanding of algebra, (unlike Williams). With this fairly humble prerequisite knowledge, Davis takes the non-mathematician where he or she needs to go, and provides a fairly complete level of understanding.
I would recommend this one as a perfect sequel to Williams, should the reader not be challenged, or as a stand-alone for the marginally mathematically literate (such as myself) who need a practical understanding of mathematically grounded decision making.
E. M. Van Court
Part of the project to explain the gulf between the rational and the real has been the development of Game Theory in the last half century. The book here, a Dover edition of the nontechnical aspects of the theory, is a fantastic and economical find. Each chapter walks you through the basics of understanding how people react in "Games" with other people. It builds from simple thought exercises with clear answers between two actors to situations between near-infinite numbers of actors with ambiguous outcomes.
Although labeled "Nontechnical," I would assume a bit of background is needed to fully realize the usefulness of this text. I think it is non-technical because it lacks the mathematical justification behind the "answers" to the problems and instead relies on a narrative track to explain the consequences of the models built in the theory.
The biggest take-away here is this: be selfish. Humans act far from rationally, especially if there are no consequences from a chance encounter with a stranger.
If you are a mathematician, this book is probably excruciatingly easy for you, and probably has little academic value. But, if you are a layman, with an interest in systems and games, it really gives you a lot to think about, and a new way to think about it. It introduces a method of determining possible outcomes, as well as giving a nice overview of more sophisticated concepts, should you decide to explore the topic more fully.
Each chapter begins with some questions to consider while reading, and detailed answers to help at the back of each chapter. The only real issue I found with the book is that the questions are missing from chapter one, yet the answers are there. Odd.
The chapters on zero sum games hold together nicely and manage to leave the reader with an understanding of their nature as well as how to arrive at a Pareto-optimal solution. (Small rant: It drives me absolutely bonkers when I hear business school grads tossing around the word "Pareto" as if they had any idea of what they spoke!) When non-zero sum games are introduced, however, Davis simply cannot overcome the complexity of trying to explain multi-variable solutions with mere words. He resorts to quasi-mathematical explanations or makes assumptions that would not be at all obvious to the lay reader.
This book is an excellent refresher in game theory, or a good primer for those with some knowledge of the topic and some intuitive mathematics.