Introducing Game Theory and its Applications

Introducing Game Theory and its Applications

by Elliott Mendelson, Mendelson Mendelson
     
 

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

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Overview

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.

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Product Details

ISBN-13:
9781584883005
Publisher:
Taylor & Francis
Publication date:
06/28/2004
Series:
Discrete Mathematics and Its Applications Series, #21
Edition description:
New Edition
Pages:
272
Product dimensions:
6.30(w) x 9.30(h) x 0.80(d)

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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

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