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Softcover ISBN:  9780821813393 
Product Code:  MAWRLD/13 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
eBook ISBN:  9781470411923 
Product Code:  MAWRLD/13.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9780821813393 
eBook ISBN:  9781470411923 
Product Code:  MAWRLD/13.B 
List Price:  $94.00 $71.50 
MAA Member Price:  $84.60 $64.35 
AMS Member Price:  $75.20 $57.20 

Book DetailsMathematical WorldVolume: 13; 1999; 176 ppMSC: Primary 90;
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 nonmathematicians. 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.
ReadershipUndergraduates in any area, interested in game theory.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. The formal defintions

Chapter 3. Optimal responses to specific strategies

Chapter 4. The maximin strategy

Chapter 5. The minimax strategy

Chapter 6. Solutions of zerosum games

Chapter 7. $2 \times n$ and $m x\times 2$ games

Chapter 8. Dominance

Chapter 9. Symmetric games

Chapter 10. Pokerlike games

Chapter 11. Pure maximin and minimax strategies

Chapter 12. Pure nonzerosum games

Chapter 13. Mixed strategies for nonzerosum games

Chapter 14. Finding mixed Nash equilibria for $2 \times 2$ nonzerosum games


Additional Material

Reviews

This book is an excellent introduction to the mathematical aspects of game theory for beginners without a background in calculus.
Journal of Mathematical Psychology 
Game theory, in the sense of von Neumann and Morgenstern, studies models of competition in situations of uncertainty. It provides a means for both deriving desirable strategies and explaining naturally occurring behavior; it finds applications ranging from economics and politics to evolutionary biology. All this and its intrinsic human interest (read here how it elucidates the outcome of the Cuban Missile Crisis) make it a favorite undergraduate topic, particularly for students majoring outside mathematics. There is not a faster read in the realm of higher mathematics. Recommended for college libraries. Undergraduates and up.
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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 nonmathematicians. 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.
Undergraduates in any area, interested in game theory.

Chapters

Chapter 1. Introduction

Chapter 2. The formal defintions

Chapter 3. Optimal responses to specific strategies

Chapter 4. The maximin strategy

Chapter 5. The minimax strategy

Chapter 6. Solutions of zerosum games

Chapter 7. $2 \times n$ and $m x\times 2$ games

Chapter 8. Dominance

Chapter 9. Symmetric games

Chapter 10. Pokerlike games

Chapter 11. Pure maximin and minimax strategies

Chapter 12. Pure nonzerosum games

Chapter 13. Mixed strategies for nonzerosum games

Chapter 14. Finding mixed Nash equilibria for $2 \times 2$ nonzerosum games

This book is an excellent introduction to the mathematical aspects of game theory for beginners without a background in calculus.
Journal of Mathematical Psychology 
Game theory, in the sense of von Neumann and Morgenstern, studies models of competition in situations of uncertainty. It provides a means for both deriving desirable strategies and explaining naturally occurring behavior; it finds applications ranging from economics and politics to evolutionary biology. All this and its intrinsic human interest (read here how it elucidates the outcome of the Cuban Missile Crisis) make it a favorite undergraduate topic, particularly for students majoring outside mathematics. There is not a faster read in the realm of higher mathematics. Recommended for college libraries. Undergraduates and up.
CHOICE