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Lectures on the Theory of Games (AM-37) : Annals of Mathematics Studies - Harold William Kuhn

Lectures on the Theory of Games (AM-37)

Annals of Mathematics Studies

Paperback

Published: 26th January 2003
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This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games. Harold Kuhn first presented these lectures at Princeton University in 1952. They succinctly convey the essence of the theory, in part through the prism of the most exciting developments at its frontiers half a century ago. Kuhn devotes considerable space to topics that, while not strictly the subject matter of game theory, are firmly bound to it. These are taken mainly from the geometry of convex sets and the theory of probability distributions.

The book opens by addressing "matrix games," a name first introduced in these lectures as an abbreviation for two-person, zero-sum games in normal form with a finite number of pure strategies. It continues with a treatment of games in extensive form, using a model introduced by the author in 1950 that quickly supplanted von Neumann and Morgenstern's cumbersome approach. A final section deals with games that have an infinite number of pure strategies for the two players.

Throughout, the theory is generously illustrated with examples, and exercises test the reader's understanding. A historical note caps off each chapter. For readers familiar with the calculus and with elementary matrix theory or vector analysis, this book offers an indispensable store of vital insights on a subject whose importance has only grown with the years.

Author's Notep. vii
Prefacep. ix
What Is the Theory of Games?p. 1
Notesp. 3
Matrix Gamesp. 5
Two Examplesp. 5
The Definition of a Matrix Gamep. 9
The Fundamental Theorem for 2 x 2 Matrix Gamesp. 10
The Geometry of Convex Setsp. 12
Fundamental Theorem for All Matrix Gamesp. 21
A Graphical Method of Solutionp. 24
An Algorithm for Solving All Matrix Gamesp. 28
Simplified Pokerp. 36
Notesp. 45
Appendixp. 48
Extensive Gamesp. 59
Some Preliminary Restrictionsp. 59
The Axiom Systemp. 59
Pure and Mixed Strategiesp. 64
Games with Perfect Informationp. 66
A Reduction of the Game Matrixp. 67
An Instructive Examplep. 70
Behavior Strategies and Perfect Recallp. 72
Simplified Poker Reconsideredp. 77
Notesp. 78
Infinite Gamesp. 81
Some Preliminary Restrictionsp. 81
An Illuminating Examplep. 81
Mixed Strategies and Expectationp. 83
The Battle of the Maxmin versus Supinfp. 88
The Fundamental Theoremp. 92
The Solution of Games on the Unit Squarep. 94
Notesp. 103
Indexp. 105
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780691027722
ISBN-10: 0691027722
Series: Annals of Mathematics Studies
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 120
Published: 26th January 2003
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 0.94
Weight (kg): 0.17