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Game Theory : Mathematical Models of Conflict - A. J. Jones

Game Theory

Mathematical Models of Conflict


Published: 15th December 2000
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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

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

Author's Prefacep. ix
Glossary of Symbolsp. xii
The name of the gamep. 1
Introductionp. 1
Extensive Forms And Pure Strategiesp. 2
Normal Forms And Saddle Pointsp. 8
Mixed Strategies And The Minimax Theoremp. 17
Dominance Of Strategiesp. 21
2 x n And Symmetric Gamesp. 24
Other Kinds Of Two Person Zero Sum Gamesp. 33
Problems For Chapter 1p. 40
Chapter Referencesp. 45
Non-cooperative Gamesp. 47
Extensive Forms And Equilibrium N-Tuplesp. 47
Normal Forms And Mixed Strategy Equlibriap. 54
Discussion Of Equilibriap. 61
Preliminary Results For 2-Person Zero Sum Gamesp. 63
The Minimax Theorem For Matrix Gamesp. 67
Properties Of Matrix Gamesp. 73
Simplified 2-Person Pokerp. 81
Continuous Games On The Unit Squarep. 87
Problems For Chapter 2p. 94
Chapter Referencesp. 98
Linear Programming and Matrix Gamesp. 100
Introductionp. 100
Preliminary Resultsp. 106
Duality Theoryp. 109
The Geometric Situationp. 117
Extreme Points Of The Feasible Regionp. 123
The Shapley-Snow Procedure For Gamesp. 126
Mixed Constraints, Slack Variables, And The Tableaup. 136
The Pivot Operationp. 140
Artificial Variablesp. 147
Problems For Chapter 3p. 157
Chapter Referencesp. 160
Cooperative gamesp. 161
Utilities And Scales Of Measurementp. 161
Characteristic Functionsp. 164
Imputationsp. 174
Strategic Equivalencep. 177
Dominance Of Imputationsp. 182
von Neumann-Morgenstern Solutionsp. 188
The Edgeworth Trading Modelp. 195
The Shapley Valuep. 202
Problems For Chapter 4p. 206
Chapter Referencesp. 208
Bargaining Modelsp. 210
Introductionp. 210
Graphical Representation Of Games And Status Quo Pointsp. 211
The Nash Bargaining Modelp. 215
The Threat Gamep. 221
Shapley And Nash Solutions For Bimatrix Gamesp. 224
Other Bargaining Modelsp. 231
Problems For Chapter 5p. 235
Chapter Referencesp. 236
Fixed Point Theoremsp. 237
Referencesp. 238
Some Poker Terminologyp. 239
Solutions to problemsp. 242
p. 242
p. 255
p. 267
p. 272
p. 275
Indexp. 281
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9781898563143
ISBN-10: 1898563144
Series: Horwood Series in Mathematics & Applications
Audience: General
Format: Paperback
Language: English
Number Of Pages: 286
Published: 15th December 2000
Publisher: Elsevier Science & Technology
Country of Publication: GB
Dimensions (cm): 23.37 x 16.0  x 1.65
Weight (kg): 0.47
Edition Type: New edition