A Gentle Introduction to Game Theory / Edition 1

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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.

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Editorial Reviews

Booknews
Based on Stahl's (U. of Kansas-Lawrence) lectures for liberal arts majors, requires no more background than high school algebra and some coordinate geometry. Introduces the theory of two-person games starting from some easy zero-sum games and progressing to proofs of the two-by-two cases of von Neumann's Minimax Theorem and the existence of the Nash Equilibrium. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780821813393
  • Publisher: American Mathematical Society
  • Publication date: 1/28/1999
  • Series: Mathematical World Series , #13
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 176
  • Product dimensions: 6.90 (w) x 9.90 (h) x 0.50 (d)

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  • Anonymous

    Posted November 6, 2006

    excellent introduction for non mathematicians

    This book is quite accessible for the non-mathematician and proves efficiency in the real life for basic problems. It should be known and learnt by every body!

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