Introducing Game Theory and Its Applications

ISBN-13: 9781584883005 / Angielski / Twarda / 2004 / 272 str.

Laurie Kelly; Elliott Mendelson; Mendelson Mendelson

Opis

The first text to present a simple, intelligent guide to game theory, this book introduces concepts from areas such as economics using applications, game theoretic notions, and research results. The author presents game theory in an intelligible manner for those who do not have a strong background in the field of business or economics. Unlike other textbooks currently on the market that presuppose a knowledge of economics or finance, this book contains a broad base of applications that appeal to a broader audience but requires a minimal background in calculus, probability, and linear algebra. It contains a review the material on probability that readers need prior to taking a course on game theory.

Recenzje

"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

Spis treści

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

O autorze

Elliott Mendelson