Lectures on the Theory of Games

by Kuhn, Harold William

• ISBN13: 9780691027722
• ISBN10: 0691027722
• Format: Paperback
• Copyright: 2003-01-06
• 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	vii
Preface	ix
What Is the Theory of Games?	1	(4)
Notes	3	(2)
Matrix Games	5	(54)
Two Examples	5	(4)
The Definition of a Matrix Game	9	(1)
The Fundamental Theorem for 2 x 2 Matrix Games	10	(2)
The Geometry of Convex Sets	12	(9)
Fundamental Theorem for All Matrix Games	21	(3)
A Graphical Method of Solution	24	(4)
An Algorithm for Solving All Matrix Games	28	(8)
Simplified Poker	36	(23)
Notes	45	(3)
Appendix	48	(11)
Extensive Games	59	(22)
Some Preliminary Restrictions	59	(1)
The Axiom System	59	(5)
Pure and Mixed Strategies	64	(2)
Games with Perfect Information	66	(1)
A Reduction of the Game Matrix	67	(3)
An Instructive Example	70	(2)
Behavior Strategies and Perfect Recall	72	(5)
Simplified Poker Reconsidered	77	(4)
Notes	78	(3)
Infinite Games	81	(24)
Some Preliminary Restrictions	81	(1)
An Illuminating Example	81	(2)
Mixed Strategies and Expectation	83	(5)
The Battle of the Maxmin versus Supinf	88	(4)
The Fundamental Theorem	92	(2)
The Solution of Games on the Unit Square	94	(11)
Notes	103	(2)
Index	105