Game Theory: A Nontechnical Introduction (Dover Books on Mathematics) Paperback – 28 Mar 2003
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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 Godel, 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.
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Top customer reviews
The bad: At times the examples juggle about excessively, it would perhaps be better if each chapter picked one type of scenario(military, business or political) and stuck with it instead of jumping about all the time. I personally found myself going back and fourth sometimes to remember a previous description.
This is my first book on game theory exclusively. I feel like this is a good book for those who will not pursue the matter further, its self-contained and discusses plenty of the approaches briefly enough to get the gist but without really setting up the mathematical basis to take it further.
The first games examined in this book are the standard ones of two-person zero-sum games, first with and then without equilibrium points. A two-person zero-sum game is one where the winnings of one player must match the losses of the other. In other words, the sum total of value held by the two players is a constant. This is followed by an examination of utility theory, which is a determination of the true value of the rewards and punishments. It is here where emotions and personal preference are the strongest. Something as simple as bragging rights can often have more value than large monetary payments. The next chapter deals with two-person non-zero-sum games, where the total value held by the two players is not a constant. The last chapter deals with n-person games, which are difficult to analyze, but are the most interesting because they are closest to life. Success in n-person games almost always requires the formation of a cooperative, in the sense that there is the potential for a coalition that can dominate everyone else.
What I enjoyed the most about this book was the examples and the problems. At the start of the chapters, there is a set of questions that introduce the material, and they are answered at the end of the chapter. In between, the explanations are clear, with a minimum of formulas. I also enjoyed the sections on the various "games" of voting, such as how does a body of legislators decides how to fund projects when each has their pet project that they want to acquire the funding for. It explains some of the labyrinthine features of the congressional process and why it is possible for a deadlock state to develop.
This is one of the best general introductions to game theory that I have seen, the worked problems take you through the features of the games in a step-by-step manner that is very easy to understand.
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