Introducing Game Theory and its Applications: 1st Edition (Hardback) book cover

Introducing Game Theory and its Applications

1st Edition

By Elliott Mendelson

Chapman and Hall/CRC

272 pages | 27 B/W Illus.

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Hardback: 9781584883005
pub: 2004-07-03
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pub: 2016-02-03
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Description

The mathematical study of games is an intriguing endeavor with implications and applications that reach far beyond tic-tac-toe, chess, and poker to economics, business, and even biology and politics. Most texts on the subject, however, are written at the graduate level for those with strong mathematics, economics, or business backgrounds.

In a clear and refreshing departure from this trend, Introducing Game Theory and its Applications presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the author begins with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solution. Here the author presents the simplex method, based on linear programming, for solving these games and develops within his presentation the required background in linear programming. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory.

This book will not only satisfy the curiosity of those whose interest in the subject was piqued by the 1994 Nobel Prize awarded to Harsanyi, Nash, and Selten. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.

Reviews

"This is an important contribution - one that will make demand for this book high. The value of the book can be seen in three distinct characteristics. First, the book does not skimp on providing full details of the theorems (and accompanying proofs) that underpin the strategic study of games. …At a minimum, this book is a wonderful source of games for classroom exercises. …A better understanding of the theory of those games is fundamental to any empirical enterprise, and Introducing Game Theory and Its Applications provides a fine starting point for interested students."

-Interfaces, Andrew B. Whitford, University of Georgia

"In this introductory textbook aimed at anyone trying to understand the implications and applications of game theory, Mendelson provides basic methods for various games that relate to mathematics, economics and business."

-Columbia College Today

"It can be recommended to readers with a limited mathematical knowledge who are interested in game theory and its applications in economics, political science and biology."

-EMS Newsletter, March 2005

Table of Contents

Introduction

COMBINATORIAL GAMES

Definition of Combinatorial Game

The Fundamental Theorem for Combinatorial Games

Nim

Hex and Other Games

Tree Games

Grundy Functions

Bogus Nim-Sums

TWO-PERSON ZERO-SUM GAMES

Games in Normal Form

Saddle Points and Equilibrium Pairs

Maximin and Minimax

Mixed Strategies

2 x 2 Matrix Games

2 x n, m x 2, and 3 x 3 Matrix Games

Linear Programming. Von Neumann's Theorem

THE SIMPLEX METHOD. THE FUNDAMENTAL THEOREM OF DUALITY. SOLUTION OF TWO-PERSON ZERO-SUM GAMES.

Slack Variables. Perfect Canonical Linear Programming Problems

The Simplex Method

Pivoting

The Perfect Phase of the Simplex Method

The Big M Method

Bland's Rules to Prevent Cycling

Duality and the Simplex Method

Solution of Game Matrices

Proofs of Facts 1-4

NON-ZERO-SUM GAMES AND k-PERSON GAMES

The General Setting

Nash Equilibria

Graphical Method for Finding Nash Equilibria for 2 ´ 2 Matrices

Inadequacies of Nash Equilibria in Non-Zero-Sum Games. Cooperative Games

The Nash Arbitration Procedure

Games with Two or More Players

Coalitions

Games in Coalition Form

The Shapley Value

Strategic Equivalence

Stable Sets

APPENDICES

Finite Probability Theory

Utility Theory

Nash's Theorem

Answers to Selected Exercises

Bibliography

INDEX

About the Series

Discrete Mathematics and Its Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT036000
MATHEMATICS / Combinatorics