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A Gentle Introduction to Game Theory (Mathematical World, Vol. 13) (Mathematical World)
Journal of Mathematical Psychology This book is an great introduction to the mathematical aspects of game theory for beginners without a background in calculus. Book Description The mathematical theory of games was first developed as a model for situations of conflict, whether actual or recreational. It gained widespread recognition when it was applied to the theoretical study of economics by von Neumann and Morgenstern in Theory of Games and Economic Behavior in the 1940s. The later bestowal in 1994 of the Nobel Prize in economics on Nash underscores the important role this theory has played in the intellectual life of the twentieth century. This volume is based on courses given by the author at the University of Kansas. The exposition is "gentle" because it requires only some knowledge of coordinate geometry; linear programming is not used. It is "mathematical" because it is more concerned with the mathematical solution of games than with their applications. Existing textbooks on the topic tend to focus either on the applications or on the mathematics at a level that makes the works inaccessible to most non-mathematicians. This book nicely fits in between these two alternatives. It discusses examples and completely solves them with tools that require no more than high school algebra. In this text, proofs are provided for both von Neumann's Minimax Theorem and the existence of the Nash Equilibrium in the $2 \times 2$ case. Readers will gain both a sense of the range of applications and a better understanding of the theoretical framework of these two deep mathematical concepts. Reader Reviews This book is an appropriate gift for a teenager with a taste for mathematics. Highly accessible, requiring some algebra, but not much more, the book introduces the deceptively simple mathematical subject of game theory. First of all, it indicates what is =meant= by a game -- something more akin to rock, paper, scissors, than monopoly or chess. Game theory (in a way like chaos theory) is seriously mis-named; the games played tend to be ones that are simple models of economic choice or political strategizing. This is why research in game theory has led to the Nobel Prize in Economics for more than one person. In any case, I used this book as a resource in a discrete math class for teenaged students who were extremely interested in math. It was intended for non-math majors in college, but I think it would work very well as enrichment in the high school classroom (or even middle school -- one can use it in developing an application for algebra). After learning the rudiments of game theory, I thought to apply the concept to =The Weakest Link=, and found that, as a game, it is far more complicated than what you'll find in this book. Still, this is just a starting point. There are plenty of avenues to explore beyond what is covered in here, but one can get bogged down with all the different types of situations that have been treated in game theory. Comment | | (Report this)
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