Table Of ContentDISCOVERING PRICES
KENNETH J. ARROW LECTURE SERIES
KENNETH J. ARROW LECTURE SERIES
Kenneth J. Arrow’s work has so deeply shaped the course of
economics for the past sixty years that, in a sense, every modern
economist is his student. His ideas, style of research, and breadth
of vision have been a model for generations of the boldest, most
creative, and most innovative economists. His work has yielded
seminal theorems in areas such as general equilibrium theory,
social choice theory, and endogenous growth theory, proving
that simple ideas have profound effects. The Kenneth J. Arrow
Lecture Series highlights economists from Nobel laureates to
groundbreaking younger scholars, whose work builds on Arrow’s
scholarship as well as his innovative spirit. The books in the series
are an expansion of the lectures that are held in Arrow’s honor at
Columbia University.
The lectures have been supported by Columbia University’s
Committee on Global Thought, Program for Economic Research,
Center on Global Economic Governance, and Initiative for Policy
Dialogue.
Creating a Learning Society: A New Approach to Growth,
Development, and Social Progress, Joseph E. Stiglitz
and Bruce C. Greenwald
The Arrow Impossibility Theorem, Eric Maskin
and Amartya Sen
Speculation, Trading, and Bubbles, José A. Scheinkman
Moral Hazard in Health Insurance, Amy Finkelstein
Creating a Learning Society: A New Approach to Growth,
Development, and Social Progress, Reader’s Edition,
Joseph E. Stiglitz and Bruce C. Greenwald
DISCOVERING
PRICES
AUCTION DESIGN IN
MARKETS WITH COMPLEX
CONSTRAINTS
PAUL MILGROM
COLUMBIA UNIVERSITY PRESS
NEW YORK
Columbia University Press
Publishers Since 1893
New York Chichester, West Sussex
cup.columbia.edu
Copyright © 2017 Columbia University Press
All rights reserved
Library of Congress Cataloging-in-Publication Data
Names: Milgrom, Paul R. (Paul Robert), 1948- author.
Title: Discovering prices : auction design in markets with complex
constraints / Paul Milgrom.
Description: New York : Columbia University Press, 2017. |
Series: Kenneth J.
Arrow lecture series | Includes bibliographical references and index.
Identifiers: LCCN 2016046839 (print) | LCCN 2017003117 (ebook) |
ISBN 9780231175982 (cloth : alk. paper) |
ISBN 9780231544573 (electronic)
Subjects: LCSH: Auctions—Mathematical models. |
Auction theory. | Prices—Mathematical models.
Classification: LCC HF5476 .M549 2017 (print) |
LCC HF5476 (ebook) | DDC 381/.1701—dc23
LC record available at https://lccn.loc.gov/2016046839
Columbia University Press books are printed on permanent
and durable acid-free paper.
Printed in the United States of America
Cover design: Noah Arlow
For Eva forever
CONTENTS
Preface ix
1 INTRODUCTION 1
2 (NEAR-)SUBSTITUTES, PRICES,
AND STABILITY 63
3 VICKREY AUCTIONS AND SUBSTITUTION 133
4 DEFERRED-ACCEPTANCE AUCTIONS
AND NEAR-SUBSTITUTES 167
5 CONCLUSION 201
Notes 205
References 213
Index 217
PREFACE
T
his monograph expands on a lecture honoring Kenneth
Arrow that I delivered at Columbia University on
November 17, 2014. My mandate was to give a lecture build-
ing upon one of Arrow’s many contributions to economics;
an easy task, since his theorizing has carved such a broad
path within economics. Previous lecturers had spoken about
welfare economics and social choice theory, health econom-
ics, the economics of innovation, financial economics, and
much more.
This monograph is inspired in part by a different area of
Ken’s work, which focuses on general equilibrium theory and
the associated price-determination processes. As tradition-
ally conceived, general equilibrium theory develops some of
the oldest ideas in economics, dating back to Adam Smith.
Was Smith right to think that prices can be used to guide
resource allocation, even when there is a vast array of differ-
ent goods? Can the famous “invisible hand” of the market
help buyers and seller discover market-clearing prices—ones
at which supply and demand are in perfect balance?
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PREFACE
In the neoclassical tradition of general equilibrium the-
ory to which Arrow contributed, these questions were posed
within particular formal models. In those, the products for
which prices would be quoted are part of the formulation.
No attention is paid to why those particular products are the
ones the economy is trading. Much of the analysis also sup-
poses that goods are divisible (roughly true for units of sugar
and rice, but less so for cars and houses) and that production
takes no advantage of economies of scale. Further, in nearly
all such models, only two kinds of constraints are acknowl-
edged: resource constraints, limiting demand not to exceed
supply, and sometimes incentive constraints, ensuring that
participants are willing both to provide accurate planning
information and to follow the dictates of the resulting plan.
Given hypothetical markets satisfying these assumptions,
the models are used to pose questions about the efficiency
or inefficiency of equilibrium. The answers that are true in
the formal model inform our understanding of real markets.
In recent years, a very different approach to the study
of prices and decentralized systems has begun to develop
among computer scientists. It focuses on a set of issues that
economic models mostly push aside. One is that discover-
ing efficient resource allocations could require unrealisti-
cally vast amounts of communication among participants,
challenging the capacity even of modern communications
channels. A second is that, even if all the necessary informa-
tion were available, computing efficient allocations might
take too much time, even on very fast computers. In these
models, there may be scale economies, and prices that clear
all the markets may not exist. In markets that look like that,
x
(cid:81) (cid:81)
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