Game Theory

Mathematical Models of Conflict

By: A. J. Jones

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Paperback | 1 December 2000

At a Glance

Paperback
300 Pages

Edition Type
New edition

Dimensions(cm)
24.77 x 17.78 x 1.91

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$357.25

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Written engagingly and with agreeable humour, this book balances a light touch with a rigorous yet economical account of the theory of games and bargaining models. It provides a precise interpretation, discussion and mathematical analysis for a wide range of "game-like" problems in economics, sociology, strategic studies and war.

There is first an informal introduction to game theory, which can be understood by non-mathematicians, which covers the basic ideas of extensive form, pure and mixed strategies and the minimax theorem. The general theory of non-cooperative games is then given a detailed mathematical treatment in the second chapter. Next follows a "first class" account of linear programming, theory and practice, terse, rigorous and readable, which is applied as a tool to matrix games and economics from duality theory via the equilibrium theorem, with detailed explanations of computational aspects of the simplex algorithm.

The remaining chapters give an unusually comprehensive but concise treatment of cooperative games, an original account of bargaining models, with a skillfully guided tour through the Shapley and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.

Balances a light touch with a rigorous yet economical account of the theory of games and bargaining models
Shows basic ideas of extensive form, pure and mixed strategies, the minimax theorem, non-cooperative and co-operative games, and a ''first class'' account of linear programming, theory and practice
Based on a series of lectures given by the author in the theory of games at Royal Holloway College

Industry Reviews

Begins with saddle points and maximax theorem results. Readers should be able to solve simple two-person zero-sum games. It analyses non-cooperative games (Nash equilibrium), linear programming and matrix games, and co-operative games (Edgeworth trading model). Detailed solutions are provided to all problems., Choice

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Author's Preface	p. ix
Glossary of Symbols	p. xii
The name of the game	p. 1
Introduction	p. 1
Extensive Forms And Pure Strategies	p. 2
Normal Forms And Saddle Points	p. 8
Mixed Strategies And The Minimax Theorem	p. 17
Dominance Of Strategies	p. 21
2 x n And Symmetric Games	p. 24
Other Kinds Of Two Person Zero Sum Games	p. 33
Problems For Chapter 1	p. 40
Chapter References	p. 45
Non-cooperative Games	p. 47
Extensive Forms And Equilibrium N-Tuples	p. 47
Normal Forms And Mixed Strategy Equlibria	p. 54
Discussion Of Equilibria	p. 61
Preliminary Results For 2-Person Zero Sum Games	p. 63
The Minimax Theorem For Matrix Games	p. 67
Properties Of Matrix Games	p. 73
Simplified 2-Person Poker	p. 81
Continuous Games On The Unit Square	p. 87
Problems For Chapter 2	p. 94
Chapter References	p. 98
Linear Programming and Matrix Games	p. 100
Introduction	p. 100
Preliminary Results	p. 106
Duality Theory	p. 109
The Geometric Situation	p. 117
Extreme Points Of The Feasible Region	p. 123
The Shapley-Snow Procedure For Games	p. 126
Mixed Constraints, Slack Variables, And The Tableau	p. 136
The Pivot Operation	p. 140
Artificial Variables	p. 147
Problems For Chapter 3	p. 157
Chapter References	p. 160
Cooperative games	p. 161
Utilities And Scales Of Measurement	p. 161
Characteristic Functions	p. 164
Imputations	p. 174
Strategic Equivalence	p. 177
Dominance Of Imputations	p. 182
von Neumann-Morgenstern Solutions	p. 188
The Edgeworth Trading Model	p. 195
The Shapley Value	p. 202
Problems For Chapter 4	p. 206
Chapter References	p. 208
Bargaining Models	p. 210
Introduction	p. 210
Graphical Representation Of Games And Status Quo Points	p. 211
The Nash Bargaining Model	p. 215
The Threat Game	p. 221
Shapley And Nash Solutions For Bimatrix Games	p. 224
Other Bargaining Models	p. 231
Problems For Chapter 5	p. 235
Chapter References	p. 236
Fixed Point Theorems	p. 237
References	p. 238
Some Poker Terminology	p. 239
Solutions to problems	p. 242
	p. 242
	p. 255
	p. 267
	p. 272
	p. 275
Index	p. 281
Table of Contents provided by Syndetics. All Rights Reserved.

Game Theory

Mathematical Models of Conflict

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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