Lectures on the Theory of Games: (Am-37)

by Kuhn, Harold William

• ISBN13: 9781400829569
• ISBN10: 1400829569
• Copyright: 2009-03-01
• Publisher: Princeton Univ Pr

Summary

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.

Table of Contents

Author's Note	p. vii
Preface	p. ix
What Is the Theory of Games?	p. 1
Notes	p. 3
Matrix Games	p. 5
Two Examples	p. 5
The Definition of a Matrix Game	p. 9
The Fundamental Theorem for 2 x 2 Matrix Games	p. 10
The Geometry of Convex Sets	p. 12
Fundamental Theorem for All Matrix Games	p. 21
A Graphical Method of Solution	p. 24
An Algorithm for Solving All Matrix Games	p. 28
Simplified Poker	p. 36
Notes	p. 45
Appendix	p. 48
Extensive Games	p. 59
Some Preliminary Restrictions	p. 59
The Axiom System	p. 59
Pure and Mixed Strategies	p. 64
Games with Perfect Information	p. 66
A Reduction of the Game Matrix	p. 67
An Instructive Example	p. 70
Behavior Strategies and Perfect Recall	p. 72
Simplified Poker Reconsidered	p. 77
Notes	p. 78
Infinite Games	p. 81
Some Preliminary Restrictions	p. 81
An Illuminating Example	p. 81
Mixed Strategies and Expectation	p. 83
The Battle of the Maxmin versus Supinf	p. 88
The Fundamental Theorem	p. 92
The Solution of Games on the Unit Square	p. 94
Notes	p. 103
Index	p. 105
Table of Contents provided by Publisher. All Rights Reserved.