Entry for William Vickrey, prepared for the Dictionary of Scientific BiographyVickrey's Contributions, Vickrey Auction, Public Economics, Asymmetric Information

Ronald M. Harstad

English

Research Papers in Economics

William S. Vickrey (b. Victoria, British Columbia, Canada, 21 June 1914; d. Hastings-
on-Hudson, New York, 11 October 1996), microeconomics, public economics, taxation, 
efficient pricing structures, incentives and private information, game theory, financial 
economics, macroeconomic policy. 
Vickrey earned a B.S. in mathematics from Yale University in 1935, and was 
associated with Columbia University’s Economics Department for nearly all the 
remaining 61 years of his life.  He received an M.A. in 1937 and first taught at Columbia 
that year.  The next six years he worked on taxation and public utility pricing, and was a 
prolific contributor to major economics journals.  World War II interrupted his academic 
career; Vickrey was a conscientious objector, and two years’ public service included 
designing an inheritance tax system for Puerto Rico (he would later design Japan’s 
postwar tax system).  Back in Economics at Columbia, he became a lecturer in 1946, was 
awarded his Ph.D. in 1947, became assistant professor in 1948, associate professor in 
1950, professor in 1958, and McVickar Professor of Political Economy in 1971.  
Emeritus Professor since 1982, he continued to teach occasional courses and interact with 
students and colleagues at seminars and conferences right up to his death. 
Vickrey was ahead of his time in many areas of economics, and it took years, 
sometimes dozens, for the discipline to catch up.  His most lauded works were produced 
by 1961, but not widely cited at first, sometimes not for decades.  He was elected a 
Fellow of the Econometric Society in 1967, received a University of Chicago honorary 
degree in 1979, elected Distinguished Fellow of the American Economic Association in 
1978 and its president in 1992.  1996 was particularly eventful:  election to the National Academy of Sciences in April, award of the Nobel Prize in Economic Science, 
announced October 8
th, and then his death following three hectic days in the resulting 
spotlight. 
An enormous fraction of the last forty years’ theoretical research in microeconomics 
can be characterized as working out details of large ideas that, as his writings make clear, 
were well understood by Vickrey in the 1940s or 50s.  For one, Vickrey is the father of 
the vast literature on the “economics of asymmetric information.”  The Nobel Committee 
called him the first scholar to focus explicitly on the feature that key information is 
privately held by individuals (pursuing their informed self-interest), when exploring 
issues of incentives and the performance of markets, of taxation and of other public 
regulations.   
The Nobel announcement focused on Vickrey’s 1961 paper about auctions, which 
realizes a principal reason for conducting an auction is that critical information about the 
value of an auctioned asset lies in privately held knowledge of or estimates of its value to 
each bidder.  Among many seminal contributions in a full and thoughtful paper, the 
simplest and most noted was introducing the second-price auction, often called the 
“Vickrey auction.”  In it, each bidder privately submits a bid, knowing the rules:  the 
highest bidder will be awarded the asset at a price set by the highest losing bid, i.e., the 
“second price.”  Switching from “pay-your-bid” or first-price auction rules to second-
price rules has startling consequences.  Suppose you know the asset’s worth to you; in a 
first-price auction, you optimally bid below that by an amount that maximizes a 
complicated tradeoff between the probability of winning and the profitability should you 
win. Vickrey’s rules induce you simply to bid your value:  if a rival bids higher, winning would mean unprofitably overbidding; if all rivals bid less, you want to win, and would 
gain nothing from bidding lower.  Second-price rules are thus “incentive-compatible” in 
that bidders do not have to be presumed public-spirited:  each is given an incentive to 
truthfully reveal that price at which he or she is indifferent between obtaining the asset 
and foregoing its purchase.  Information thus learned from a second-price auction can be 
both critical for follow-up decisions (e.g., airwaves auctions yield information about the 
value of making further slices of the electromagnetic spectrum available for commercial 
usages) and otherwise unattainable.  In the model he presents, Vickrey also originates the 
issue of market design—how does a seller or public agency set market rules so as to 
maximize expected revenue, or some other goal?—and establishes that a seller on 
average earns identical revenues from first- and second-price auctions.  Later work has 
found that, in a wide variety of settings with approximately risk-neutral actors, a revenue-
seeking seller will prefer a second-price auction, and an efficiency-seeking seller will 
more often sell to the highest-valuing bidder via a second-price auction. 
Vickrey’s 1961 paper also considered allocation of bundles of goods and services (or 
public projects), and of cost shares, to individuals.  He proposed charging an individual 
the cost to the rest of the economy that resulted from their usage of an endeavor, the basis 
for what is now called the Vickrey-Clarke-Groves mechanism and the extensive literature 
on design of allocation mechanisms for public-good and interrelated-goods problems. 
In proposing a framework for understanding auctions and transacting mechanisms, 
and a simple rule that could improve such markets, Vickrey’s insight that the analyst 
must account for self-interested individuals acting on the basis of private information 
presaged developments that have dominated game theory for the last thirty years.  John Harsanyi characterized “games of incomplete information” in the late 1960s, and was a 
1994 Nobel Laureate for developing techniques that had been correctly used by Vickrey 
in the 1940s and 50s.  Path-breaking studies of situations where individuals seek to 
credibly reveal private information about their own abilities to potential transacting 
partners (“signaling games”) and where firms seek to sort out individuals who are 
privately aware of their own high intellectual or entrepreneurial abilities from those 
without the same skills who nonetheless seek the same opportunities (“screening games”) 
were the subject of the 2001 Nobel Prize to George Akerlof, Michael Spence and Joseph 
Stiglitz; Vickrey demonstrated his understanding of the key insights in their work nearly 
a half-century prior to that award. 
The 1947 book, Agenda for Progressive Taxation, is essentially Vickrey’s doctoral 
dissertation; to this day it contains frontier research in taxation, and its 21 specific 
recommendations remain sound.  It is strikingly original in its conception that taxes 
distort incentives to engage in taxed transactions, primarily earning income, and that 
individuals’ responses to taxes are based on information (about their abilities in 
alternative occupations and willingnesses to undertake efforts) unknowable to 
government.  It is this original idea which James Mirrlees carries to an explicit 
characterization a quarter century later, in work that led the Nobel Committee to make 
him the co-laureate with Vickrey in 1996. 
Concern for human welfare was Vickrey’s driving force.  In his 1945 paper, 
“Measuring Marginal Utility by Reactions to Risks,” and his 1947 Agenda, Vickrey 
develops a basis for relating social preferences over alternatives to individuals’ 
preferences.  In so doing, he lays a part of the foundation for Kenneth Arrow’s dissertation, “Social Choice and Individual Welfare,” which Vickrey supervised, and 
which was the focal work in the Nobel announcement of the 1972 laureate to Arrow.  The 
Nobel award to Amartya Sen in 1998 also cited work elaborating ideas initiated in these 
writings by Vickrey. 
For all the research in theoretical economics that has elaborated on his original ideas, 
Vickrey himself was totally focused on practical applications, interested in theoretical 
models only to rest practical solutions on an underlying logic.  In the late 1930’s, he 
proposed the principle that taxation should attempt to be neutral with respect to decisions 
as to when to realize a gain in income, and published a full-fledged system for doing so in 
1939, “Averaging of Income for Income Tax Purposes.” 
His most extensive involvement, though, was in suggesting principles for efficient 
provision of public utilities, and in coming up with inventive, practical mechanisms to 
fulfill these principles.  The theoretical side involved reaching a subtle understanding of 
the correct marginal cost to attribute to usage of utilities:  what is society’s economic cost 
to have one more car traveling that roadway at that hour, or of one more subway rider 10 
minutes ahead of peak demand?  In 1948, Vickrey suggested that seats on airplanes 
should be purchased on a futures market where prices fluctuated depending on the 
forecast between demand for seats and supply of seats as the date of the flight 
approached.  Four decades later, airlines began to develop yield management software 
that quotes prices essentially in imitation of such a market.  A big difference is that the 
airlines choose to sell nontransferable and largely nonrefundable tickets; Vickrey 
proposed resellable tickets with a penalty to discourage speculation. Two years’ study of patterns of subway ridership led to the 1952 monograph, “The 
Revision of the Rapid Transit Fare Structure of the City of New York.”  Vickrey found 
that marginal-cost pricing implied prices at the very peak of demand five times the off-
peak minimum, with substantial savings available if a regular commuter adjusted his 
schedule as little as 15 minutes away from peak.  Serious savings in the cost of rolling 
stock could result from aggregate commuter responses.  In the first of classic examples of 
how far he went to demonstrate the practicality of his recommendations, Vickrey 
constructed a prototype of an electromechanical turnstile that automatically implemented 
shifting prices.  Similar turnstiles came into widespread use three dozen years later, but 
only small steps in the direction of Vickrey’s suggested wide variations in price about 
peak load times have yet arrived. 
His 1959 study of road use around Washington, DC led to the Congressional Report, 
“Statement on the Pricing of Urban Street Use.”  Again, he found that careful calculation 
of social marginal costs led to highly differentiated road tariffs according to traffic 
congestion.  Vickrey, though, was appalled at the notion of adding to traffic congestion to 
collect tolls, and railed against tollbooths, urging the development of a system where 
small radio transmitters would transmit vehicle or driver IDs over a distance of a few 
feet, and a computerized system connected to roadbed receivers would calculate 
liabilities and bill drivers periodically.  A few years afterward, Vickrey was challenged 
that the system he proposed was infeasible.  He responded in typical fashion:  in the mid-
1960’s, he first built a rudimentary computer in his home and connected it to a radio 
receiver, then limited himself to a $3 budget for parts with which he built a small radio 
transmitter placed under the hood of his car.  He could then show anyone who asked a printout of the times his own car went up or down his driveway.  After a 1970s seminar, I 
asked and was shown one printout.  As someone who practiced the concern for efficiency 
in transportation that he preached, Vickrey rarely used his car:  he almost always took the 
train into Manhattan, then “commuted” the blocks from the station and across 
Columbia’s campus to his office on rollerskates. 
Vickrey’s 1963 “Pricing in Urban and Suburban Transport” is to this day regarded as 
the most important paper in the history of urban transport economics.  Departure times of 
commuters are endogenous variables in the model, reacting to personal tastes, plans, and 
predicted commuting tie-ups.  The Belgian economist Jacques Drèze evaluates “That 
model has received strong empirical support from detailed traffic flow studies, and has 
changed the way traffic engineers think about the problem,” and notes, remarkably, that 
Vickrey’s system of tolls varying with traffic densities “leaves commuters at least as well 
off as before, so that the toll revenues come free.”  Vickrey applied similar reasoning to 
develop efficient pricing structures for telephone services, electricity, water supply, fire 
protection, parks and recreational services, and education. 
For the last decade of his life, Vickrey’s attention returned to macroeconomic policy, 
a subject he had analyzed in a 1963 book, Metastatics and Macroeconomics.  Like his 
other pursuits, that book broke new ground by expecting that macroeconomic policy 
ought to be derived from an understanding of the economy grounded in equilibrium 
models of microeconomic behavior.  Indeed, some of the real business cycle modeling 
honored in the 2004 Nobel award to Finn Kydland and Edward Prescott has its first 
musings in Vickrey’s early analyses. Vickrey’s macroeconomics theme reflected his overriding concern for human 
welfare:  he considered inflation minor relative to unemployment, since the burden of 
above-minimal unemployment fell on the poor.  He argued (in his 1963 book and in 
eleven papers 1986 and later) that over a considerable range of levels of employment, 
lower unemployment did not create higher inflation, hence both fiscal and monetary 
policy should address unemployment, with subsidiary policies addressing inflation.  As 
always, he had inventive recommendations for such policies. 
The acclaim Vickrey’s work eventually attained was to him secondary; he was more 
concerned with whether practical recommendations of more efficient methods were 
adopted.  On a half-dozen occasions in the 1990s, most notably his 1993 Presidential 
Address to the Atlantic Economic Society, Bill Vickrey, somewhat jovially but with 
some melancholy, pronounced himself a failed innovator. 
I have been among scores of economists to experience presenting a seminar while 
Bill Vickrey is to all appearances asleep, only to have him suddenly ask a more 
penetrating question than any seemingly more attentive audience member can muster.  
Then, too, I join those described in the American Economic Association’s 1978 
Distinguished Fellow citation: 
Many of us have had the experience of thinking we were the first to show the 
neutrality of a particular tax scheme, to prove the incentive characteristics of a 
particular bidding institution, to deduce the redistributive implications of the 
expected utility hypothesis, to invent a demand-revealing process, and so on, only to 
find that William S. Vickrey had done it earlier—sometimes much earlier—and whereas our ‘original contribution’ may have contained minor or even substantive 
errors, Vickrey had done it correctly. 
 
BIBLIOGRAPHY 
I. ORIGINAL WORKS. A bibliography of Vickrey’s nine books, 166 other publications, 
and 61 unpublished articles is in the 1994 book listed below.  Among the most 
significant are “Averaging of Income for Income Tax Purposes,” in Journal of 
Political Economy, 47 (1939), 379-397; “Measuring Marginal Utility by Reactions to 
Risks,” in Econometrica, 13 (1945), 319-33; Agenda for Progressive Taxation (New 
York, 1947); “Some Objections to Marginal Cost Pricing,” in Journal of Political 
Economy, 56 (1948), 218-38; The Revision of the Rapid Transit Fare Structure of the 
City of New York (1952, Technical monograph no. 3, finance project, Mayor's 
Committee for Management Survey of the City of New York); “The Economizing of 
Curb Parking Space,” in Traffic Engineering Magazine, Nov. 1954; “A Proposal for 
Revising New York's Subway Fare Structure,” in Journal of the Operations 
Research Society of America, 3 (1955), 38-68; “Statement on the Pricing of Urban 
Street Use,” in Hearings: U.S. Congress, Joint Committee on Metropolitan 
Washington Problems, 11 Nov., 1959, 466-77; “Reaching a Balance Between Mass 
Transit and Provision for Individual Automobile Traffic,” ibid., 478-507; 
“Counterspeculation, Auctions, and Competitive Sealed Tenders,” in Journal of 
Finance, 16 (1961), 8-37; “Pricing in Urban and Suburban Transport,” in American 
Economic Review, 52 (1963), 452-65; “General and Specific Financing of Urban Services,” in H. G. Shaller, ed., Public Expenditure Decisions in the Urban 
Community (Washington, 1963), 62-90; Metastatics and Macroeconomics (new 
York, 1964); “Responsive Pricing of Public Utilities Services,” in Bell Journal of 
Economics and Management Sciences, 2 (1971), 337-46; “The City as a Firm,” in M. 
S. Feldstein and R. F. Inman, eds., The Economics of Public Services (New York, 
1977), 334-43;  “Today's Task for Economists,” in American Economic Review, 82 
(1993), 1-10; “My Innovative Failures in Economics,” in Atlantic Economic Journal, 
March 1993, 1-9; Public Economics, Selected Papers by William Vickrey, 
(Cambridge, 1994). 
II. SECONDARY LITERATURE.  Edward H. Clarke, “Multipart Pricing of Public 
Goods,” in Public Choice, 11 (1971), and Theodore Groves, “Incentives in Teams,” in 
Econometrica, 41 (1973), 617-31, are later contributions developing the Vickrey-Clarke-
Groves mechanism.  Jacques Drèze, “William S. Vickrey,” in Biographical Memoirs, 
National Academies Press, available at 
http://www.nap.edu/html/biomems/wvickrey.html, is a biography by a noted economist. 
RONALD M. HARSTAD 

334-43; “Today's Task for Economists,”

A bibliography of Vickrey’s nine books, 166 other publications, and 61 unpublished articles is in the 1994 book listed below. Among the most significant are “Averaging of Income for Income Tax Purposes,”

Multipart Pricing of Public Goods,”

William S. Vickrey

http://economics.missouri.edu/working-papers/2005/wp0519_harstad.pdf

William S. Vickrey

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics