**Mathematical World**

Volume: 13;
1999;
176 pp;
Softcover

MSC: Primary 90;

Print ISBN: 978-0-8218-1339-3

Product Code: MAWRLD/13

List Price: $31.00

AMS Member Price: $24.80

MAA member Price: $27.90

**Electronic ISBN: 978-1-4704-1192-3
Product Code: MAWRLD/13.E**

List Price: $31.00

AMS Member Price: $24.80

MAA member Price: $27.90

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# A Gentle Introduction to Game Theory

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*Saul Stahl*

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

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.

#### Readership

Undergraduates in any area, interested in game theory.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## A Gentle Introduction to Game Theory

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Table of Contents ix10 free
- Preface xi12 free
- Chapter 1. Introduction 114 free
- Chapter 2. The formal definitions 1326 free
- Chapter 3. Optimal responses to specific strategies 2538
- Chapter 4. The maximin strategy 3548
- Chapter 5. The minimax strategy 4558
- Chapter 6. Solutions of zero-sum games 5366
- Chapter 7. 2 x n and m x 2 games 7184
- Chapter 8. Dominance 8396
- Chapter 9. Symmetric games 89102
- Chapter 10. Poker-like games 97110
- Chapter 11. Pure maximin and minimax strategies 115128
- Chapter 12. Pure nonzero-sum games 121134
- Chapter 13. Mixed strategies for nonzero-sum games 135148
- Chapter 14. Finding mixed Nash equilibria for 2 x 2 nonzero-sum games 155168
- Bibliography 169182
- Solutions to selected exercises 171184
- Index 175188 free
- Back Cover Back Cover1190