John von Neumann - Theory of Games and Economic Behavior

Theory of Games
and Economic Behavior

Theory of Games
and Economic
Behavior

John von Neumann
and Oskar Morgenstern

With an introduction by Harold W. Kuhn
and an afterword by Ariel Rubinstein

SIXTIETH-ANNIVERSARY EDITION

Copyright 1944 by Princeton University Press

Copyright renewed 1972 Princeton University Press

Sixtieth-Anniversary Edition copyright 2004 Princeton University Press

Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540

In the United Kingdom: Princeton University Press, 3 Market Place,

Woodstock, Oxfordshire 0X20 1SY

All Rights Reserved

Second Edition, 1947

Third Edition, 1953

Fourth printing, and first paperback printing, of Sixtieth Anniversary Edition, 2007

Paperback ISBN-13: 978-0-691-13061-3

Paperback ISBN-10: 0-691-13061-2

Library of Congress Control Number 2004100346

ISBN-13: 978-0-691-11993-9

ISBN-10: 0-691-11993-7

British Library Cataloging-in-Publication Data is available

This book has been composed in Baskerville MT, Monotype Century, and Helvetica Condensed

Printed on acid-free paper.

press.princeton.edu

Primed in the United States of America

9 10

Contents

, BY HAROLD W. KUHN

BY JOHN VON NEUMANN AND OSKAR MORGENSTERN

, BY ARIEL RUBINSTEIN

, BY HERBERT A. SIMON

, BY ARTHUR H. COPELAND

, BY LEONID HURWICZ

, BY T. BARNA

, BY WALTER A. ROSENBLITH

, BY PAUL SAMUELSON

, BY PAUL CRUME

, BY E. ROWLAND

, BY CLAUDE CHEVALLEY

, BY WILL LISSNER

, BY JOHN MCDONALD

, BY OSKAR MORGENSTERN

Introduction

HAROLD W. KUHN

Although John von Neumann was without doubt the father of game theory, the birth took place after a number of miscarriages. From an isolated and amazing minimax solution of a zero-sum two-person game in 1713 [1] to sporadic considerations by E. Zermelo [2], E. Borel [3], and H. Steinhaus [4], nothing matches the path-breaking paper of von Neumann, published in 1928 [5].

This paper, elegant though it is, might have remained a footnote to the history of mathematics were it not for collaboration of von Neumann with Oskar Morgenstern in the early 40s. Their joint efforts led to the publication by the Princeton University Press (with a 4,000 subvention from a source that has been variously identified as being the Carnegie Foundation or the Institute for Advanced Study) of the 616-page Theory of Games and Economic Behavior (TGEB).

I will not discuss here the relative contributions of the two authors of this work. Oskar Morgenstern has written his own account [6] of their collaboration, which is reprinted in this volume; I would recommend to the reader the scholarly piece [7] by Robert J. Leonard, who has noted that Morgensterns reminiscence sacrifices some of the historical complexity of the run-up to 1944 and has given a superb and historically complete account of the two authors activities in the relevant period. On balance, I agree with Leonard that had von Neumann and Morgenstern never met, it seems unlikely that game theory would have been developed. If von Neumann played both father and mother to the theory in an extraordinary act of parthenogenesis, then Morgenstern was the midwife.

In writing this introduction, I have several goals in mind. First, I would like to give the reader a sense of the initial reaction to the publication of this radically new approach to economic theory. Then, we shall survey the subsequent development of the theory of games, attempting to explain the apparent dissonance between the tenor of the book reviews and the response by the communities of economists and mathematicians. As a participant in this response (from the summer of 1948), my account is necessarily colored by subjective and selective recollections; this is a fair warning to the reader.

The book reviews that greeted the publication of TGEB were extraordinary, both in quantity and quality; any author would kill for such reviews. Consider the following partial list of the reviews, paying special attention to the length of these reviews, the quality of the journals, and the prominence of the reviewers:

H. A. Simon, American Journal of Sociology (1945) 3 pages

A. H. Copeland, Bulletin of the American Mathematical Society (1945) 7 pages

L. Hurwicz, The American Economic Review (1945) 17 pages

J. Marschak, Journal of Political Economy (1946) 18 pages

T. Barna, Economica (1946) 3 pages

C. Kaysen, Review of Economic Studies (1946) 15 pages

D. Hawkins, Philosophy of Science (1946) 7 pages

J.R.N. Stone, Economic Journal (1948) 16 pages

E. Ruist, Economisk Tidskrift (1948) 5 pages

G. Th. Guilbaud, Economie Applique (1949) 45 pages

E. Justman, Revue dEconomie Politique (1949) 18 pages

K. G. Chacko, Indian Journal of Economics (1950) 17 pages

The quotes from these reviews are a publishers dream. Thus:

Simon encouraged every social scientist who is convinced of the necessity for mathematizing social theoryas well as those unconverted souls who are still open to persuasion on this pointto undertake the task of mastering the Theory of Games.

Copeland asserted: Posterity may regard this book as one of the major scientific achievements of the first half of the twentieth century.

Hurwicz signaled that the techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy and concluded the appearance of a book of the caliber of the Theory of Games is indeed a rare event.

After praising the careful and rigorous spirit of the book, Jacob Marschak concludes: Ten more such books and the progress of economics is assured.

If the quantity of reviews and the quality of the journals in which they were published are impressive, the choice of reviewers and their positions in the social sciences are equally impressive. Two of the reviewers, H. A. Simon and J.R.N. Stone, were awarded Nobel Memorial Prizes in Economics.

The first review to appear was that of Herbert Simon. By his own account [8], he spent most of [his] 1944 Christmas vacation (days and some nights) reading [the TGEB]. Simon knew of von Neumanns earlier work and was concerned that the TGEB might anticipate results in a book that he was preparing for publication.

The first review that was directed at mathematicians was that of A. H. Copeland, a specialist in probability theory and professor at the University of Michigan. Copelands only significant work in social science is the so-called Copeland method for resolving voting problems: simply, it scores 1 for each pairwise win and 1 for each pairwise loss, and declares the alternative with the highest score the winner. His review gave the mathematical community an extremely complete account of the contents of the TGEB. As is typical of almost all of the reviewers, although Copeland pointed to the research challenges opened by the TGEB, he never engaged in research in game theory as such. The only paper in his prolific output that is marginally related to game theory is a joint paper on a one-player game which must be categorized as a game of chance. Copelands principal contribution to game theory consists in the fact that he was Howard Raiffas thesis adviser; the book Games and Decisions, written by Raiffa with R. Duncan Luce (published by Wiley in 1957 and reprinted by Dover Publications in 1989) was the first non-mathematical exposition that made the theory of games accessible to the broad community of social scientists.