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Federal Reserve Bank of Philadelphia

MARCH • APRIL 1988




GOING, GOING, GONE:
SETTING PRICES WITH AUCTIONS
Loretta Mester
The BUSIN ESS REVIEW is published by the
Department of Research six times a year. It is
edited by Judith Farnbach. Artwork is designed
and produced by Dianne Hallowell under the
direction of Ronald B. Williams. The views ex­
pressed herein are not necessarily those of this
Reserve Bank or of the Federal Reserve System.

Auctions are one of the oldest mechanisms for
determining the price of a product. Economists
have begun to explore the conditions under
which alternative forms of auctions are best
used. Since people use various types of auc­
tions to sell everything from great works of art
to Treasury securities to offshore oil drilling
rights, this recent research has real-world
implications for how auctions should be
conducted.

Single-copy subscriptions for
individuals are available without charge. Institu­
tional subscribers may order up to 5 copies.

EXPERIMENTAL ECONOMICS:
PUTTING MARKETS
UNDER THE MICROSCOPE
Herb Taylor

S u b s c r ip t io n s .

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Controlled experiments in simplified settings
have been used to assess how the forces of
supply and demand work in different types of
market arrangements and how the perform­
ance of asset markets is affected by changing
various market conditions, including the exis­
tence of insider information and futures
markets. These experimental methods have
helped to answer such questions as: how many
suppliers are needed to produce a competitive
marketplace, and how quickly does the price of
a product move toward the level that equates
supply and demand?

Investigating How Markets Work: Two Perspectives
Many of us in the United States give little thought to how the prices of the products and financial assets
that we buy are determined. When the price of coffee goes up, people say, "it's the law of supply and
demand." The concepts are as old as economics itself.
Although the U.S. is often characterized as a "capitalist" country where we have "free markets" and
"competition" that allow the forces of supply and demand to set prices for goods and services, many
Americans don't stop to consider how, or whether, such mechanisms actually work. We take for granted
that markets work—at least that they work well enough so that, when we arrive to buy goods or services,
we don't have to stand in line a long time. This is not the case everywhere, however, and some countries,
such as the Soviet Union and China, are actually trying to introduce more market forces of supply and
demand into their economies.
What is it that makes markets function well? And how do alternative types of price-setting mechanisms
perform differently? Economists continue to study these questions, and have been going beyond the
introductory textbook explanation of supply and demand. This issue of the Business Review is devoted to
explaining two approaches used in recent economic research on how markets function. One approach is
empirical, but uses experimental methods—like a lab experiment, it sets up simplified markets in a
laboratory environment and observes how prices adjust to equate supply and demand. The other
approach is theoretical—it models auction markets as strategic games, and finds that the rules of the
game affect how supply and demand determine price.

Richard W. Lang
Senior Vice President & Director of Research

Going, Going, Gone:
Setting Prices With Auctions
Loretta ]. Mester*
Each week when the U.S. Treasury auctions
off billions of dollars of Treasury bills, it is set­
ting prices with a mechanism that is over 2000
years old. Auctions are used to sell a wide range
of objects, from art works to drilling rights to
government contracts—and the stakes are high.
On November 13, 1987, the Wall Street Journal
reported that Van Gogh's "Irises" was auctioned
for a record $53.9 million dollars (beating the
March 1987 record of almost $40 million paid

*Loretta J. Mester is a Senior Economist in the Banking and
Financial Markets Section of the Research Department of
the Federal Reserve Bank of Philadelphia.




for Van Gogh's "Sunflow ers"). On September
30,1980, U.S. oil companies paid $2.8 billion in
an auction for drilling rights on 147 tracts in the
Gulf of Mexico. In another auction, a consor­
tium of Phillips Petroleum and Chevron USA
bid $333.6 million to win the offshore drilling
rights near Point Arguello, California; their bid
was over twice the next highest offer.1

1The drilling rights examples are from Paul R. Milgrom
and Robert J. Weber, "A Theory of Auctions and Competi­
tive Bidding," Econometrica 50 (September 1982), and Marc
Levinson, "Using Science to Bid for Business," Business
Month (April 1987), respectively.

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MARCH/APRIL 1988

BUSINESS REVIEW

The longevity of auctions, the variety of objects
sold through auctions, and the enormous volume
of business done in auctions today point to the
importance of understanding the economics of
auctions. Economists have developed theoreti­
cal models to try to answer a number of ques­
tions about auctions. What are the advantages of
using an auction to set the price of an object?
Which set of auction rules should the seller use?
And given a particular set of auction rules, what
is the buyer's best bidding strategy? The answers
to these questions will be important to anyone
who participates on either side of an auction
transaction, including government procurers,
government debt managers, investors, collec­
tors, and businesses.

determining the prices of goods to be ex­
changed.2 Two other mechanisms are posted
prices and negotiated prices. Retailers usually
post a price for each good they want to sell, and
individual buyers have little choice but to take it
or leave it. Sellers find posted prices inexpen­
sive to manage, but in the short run, they are
inflexible to changes in demand or to changes in
an individual buyer's tastes since there is a lag
between the time the price is set and the product
is sold. Also, posted prices cannot reflect subtle
variations in quality among different units of a
particular product being sold. When prices are
negotiated, both buyers and sellers influence
the price substantially, haggling back and forth.
Manufacturers usually negotiate the price of

FINDING THE RIGHT PRICE
Auctions as Price-Setting Mechanisms. Auc­
tions, which have been used since ancient times
(see 2500 YEARS OF AUCTIONS...AT A
GLANCE), are one of the basic mechanisms for

2This discussion is based upon Paul R. Milgrom, "The
Economics of Competitive Bidding: A Selective Survey," in
Leonid Hurwicz, David Schmeidler, and Hugo Sonnenschein, eds., Social Goals and Social Organization: Essays in
Memory o f Elisha Pazner (Cambridge: Cambridge University
Press, 1985).

2500 Years Of Auctions...At A Glance
One of the earliest reports of an auction was by Herodotus who described the bidding of men for wives
in Babylon around 500 B.C.a This auction was unique since bidding sometimes started at a negative
price.b Some scholars interpret the Biblical story of the sale of Joseph into slavery as an even earlier
reference.0 In ancient Rome, auctions were used in commercial trade and were held in the atrium auctionarium where goods could be displayed prior to sale. Auctions were also used to liquidate property by
Romans in financial straits. Caligula auctioned off family belongings to cover his debts and Marcus
Aurelius held an auction of royal treasures to finance a state deficit. Plundered war booty was often sold
at auction. The most notable auction in Rome was held in 193 A.D. when the Praetorian Guard put the
whole empire up for auction. After killing the previous emperor, the guards announced they would
appoint the highest bidder as the next emperor. Didius Julianus outbid his competitors, but after two
months he was beheaded by Septimius Severus who seized power. (A winner's curse?) In China, auc­
tions were used as early as the 7th century A.D. to sell the belongings of deceased Buddhist monks. In
colonial America auctions were used to liquidate inventories, unload importers' unsold items at the end
of the season, and sell secondhand furniture, farm equipment, and animals. Evidently the auction was
considered a disreputable way of selling goods since the owner's name was usually concealed. The most
infamous auctions in American history were the slave auctions held before the Civil War.

aUnless otherwise noted, the historical facts presented are from Ralph Cassady, Jr., Auctions and Auctioneering
(Berkeley: University of California Press, 1967), Chapter 3.
bMartin Shubik, "Auctions, Bidding, and Markets: An Historical Sketch," in R. Engelbrecht-Wiggans, M. Shubik,
and R. Stark, eds., Auctions, Bidding, and Contracting: Uses and Theory (New York: NYU Press, 1983) p. 39.
cPaul Milgrom, "Auction Theory," p. 1.

4



FEDERAL RESERVE BANK OF PHILADELPHIA

Going, Going, Gone

their inputs with their suppliers and most
people negotiate the price of a car or a house.
While negotiated prices allow all aspects of the
product and situation to be taken into account,
they can be expensive and time-consuming, as
different offers and counteroffers must be con­
sidered one at a time.
The auction mechanism falls somewhere in
between posted and negotiated prices. In auc­
tions, sellers set the rules and prices are deter­
mined by competition among potential buyers.
Auctions are more flexible than posted prices.
Since the price in an auction is set at the same
time the object is sold, it reflects current demand
conditions, the latest information, and the tastes
of the particular consumers who are bidding.
This flexibility is important because a common
feature of the diverse items sold at auction is
their uniqueness. No two oil paintings are the
same even if painted by the same artist; Treasury
bills sold today differ from those sold yesterday
because of constantly changing information
about fiscal and monetary policy as well as other
economic factors. Auctions allow prices to reflect
the unique aspects of goods being sold.
Auctions also differ from negotiated prices—
they are less time-consuming than negotiations
because the seller can compare the offers of
competing buyers simultaneously rather than
having to consider each offer one at a time. More
importantly, once the rules of the auction are
agreed on, sellers remain passive while the buy­
ers determine the price; in other words, sellers
cannot haggle with buyers as they can in nego­
tiations. The seller's preferences only come into
play when the rules of the auction are set. These
auction rules serve as a commitment on the part
of the seller to behave in a certain way; they also
restrict the kind of offers buyers can make. So in
auctions, both buyers and sellers are more con­
strained than in negotiations.
The rules of an auction also show exactly how
a price will be determined so that demand equals
supply. For example, the rules may say the win­
ner must pay an amount equal to the highest bid.
In other markets, where price adjustment is not



Loretta ]. Mester

so clear, economists have found it helpful to
think about the adjustment in terms of auctions.
For example, in a textbook competitive market, a
hypothetical "Walrasian auctioneer" is thought
to call out a price for each good, and then market
participants tell him how much they demand
and how much they want to supply of each good
at that price. The "auctioneer" then adjusts
prices—up for goods whose demand exceeds
supply and down for goods whose supply ex­
ceeds demand—and the whole process con­
tinues until the market reaches equilibrium
where supply equals demand, at which time
trade occurs. No one believes such an auc­
tioneer exists, but the apparatus gives econo­
mists a way of visualizing how prices move to
their equilibrium levels.
Types of Auctions. Auctions are not all alike.
Actually the word itself is something of a mis­
nomer. A udio means increase, but not all auc­
tions involve calling out higher and higher bids.
Auctions may take one of two basic forms, oral
or sealed bid. In oral auctions, bidders hear one
another's bids as they are made and can make
counteroffers; each bidder knows how many
others are bidding. In sealed bid auctions, bid­
ders simultaneously submit one or more bids to
the seller without revealing their bids to one
another. In this case, the bidders do not neces­
sarily know how many other bidders there are.
Two common types of oral auctions are the
English and Dutch auctions. The English auction
is the most common and well-known. The auc­
tioneer raises the price until only one bidder
remains—he wins the good at the price he has
bid. In the Dutch auction (used to sell tulip bulbs
in Holland and fish in Israel), the auctioneer
calls out a high price and then continuously
lowers the price until some bidder stops him
and claims the good at that price.3

3Another type of oral auction, the double auction, is used
on the New York Stock Exchange where many units of a
good are auctioned at one time. Bids and offers are called out
freely and anonymously and can be accepted immediately
so that the market is continuously clearing.

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BUSINESS REVIEW

In each of the different sealed bid auctions,
tne highest bidder wins, but the amount he has
to pay differs. Consider a sealed bid auction of a
plot of land and suppose three bids are
received: $100,000, $99,000 and $98,000. In the
first price auction, what you bid is what you pay if
you win, so the bidder who submitted the
$100,000 bid wins the land and pays $100,000.
In the second price auction, again the highest bid­
der wins but he pays only the amount of the
highest rejected bid, which is $99,000. Why
might a seller use a second price auction? From
this example, it appears he would always get a
higher price by using the first price auction, but
this is not true. The bidders know what kind of
auction they are involved in and adjust their
bids accordingly. Bidders tend to place higher
bids in the second price auction than in the first
price auction, so on the face of it, it is not clear
which auction gives the seller the highest
revenue. Still, the second price auction is rare.
Sealed bid auctions are also used to sell several
units of a good at one time, such as tracts of land
or Treasury bills. Though they appear more
complex because multiple units and bids are
involved, they are basically generalizations of
the single unit first price and second price auc­
tions. To see how these auctions work, suppose
a seller auctions three identical plots of land, and
he gets the following bids:
A submits 3 bids— $100,000 for one plot,
$95,000 for an additional plot, and $92,000
for a third plot
B submits 3 bids— $99,000 for one plot,
$98,500 for an additional plot, and $95,500
for a third plot
C submits 1 bid—$98,000 for one plot
The discriminatory sealed bid auction is like a
first price auction: the highest bidders win and
the winners pay what they bid. Each unit could
be sold at a different price. In our example, the
highest bids (and therefore, the prices paid) and
6 FRASER
Digitized for


MARCH/APRIL 1988

the winners are: $100,000 from bidder A, $99,000
from bidder B, and $98,500 from bidder B again.
Clearly, if two bidders win the same number of
units they need not pay the same total amount
for their winnings.4
In the uniform auction the units are all sold at
the same price which is equal to the highest
rejected bid, as in the second price auction. Since
the winning three bids are $100,000, $99,000,
and $98,500, the highest rejected bid is $98,000,
so bidder A wins one plot of land and bidder B
wins two plots, and they both pay $98,000 per
plot.
During the 1960s a hot debate developed
about whether U.S. Treasury bills should be sold
in a uniform auction or a discriminatory auction.
(See HOW TREASURY BILLS ARE AUC­
TIONED TODAY.) Proponents of the uniform
price auction claimed that, because it was a sim­
pler auction, bid preparation would be less cos­
tly, so more bidders would participate. This
would lead to a larger volume of bills being sold,
more efficient allocations of the bills, and higher
bids. Proponents of the discriminatory auction
claimed the government would obtain higher
revenue via price discrimination.
If the type of auction had no effect on the way
people bid, then the discriminatory auction
would always yield the greater revenue. But
buyers do bid differently depending on the rules
of the auction. Economists are developing theo­
retical models of auction markets to examine the
way bidders behave under various auction rules.
Their results shed some light on why certain
auctions are more common than others, what
auction rules will generate the most revenue

4The Federal Reserve uses the discriminatory auction
when it engages in short-term repurchase agreements with
dealers. The auction sets the interest rate the Fed will earn on
securities it purchases to temporarily increase the banking
system's reserves. The Fed's outright purchases and sales for
the System Account also usually occur through an auction
with security dealers. See The Federal Reserve System Purposes
and Functions (Washington D.C.: Board of G overnors of the
Federal Reserve System, 1984) pp. 38-43.

FEDERAL RESERVE BANK OF PHILADELPHIA

Loretta J. Mester

Going, Going, Gone

How Treasury Bills Are Auctioned Today
Each week the U.S. Treasury uses the discriminatory auction to sell Treasury bills to major buyers. On
Tuesday the Treasury announces, via the Federal Reserve Banks, the amount of 91-day and 182-day bills
it wishes to sell on the following Monday and invites tenders (bids) for specified amounts of these bills.
Tenders are due by 1:00 p.m. Eastern time on the Monday after the announcement, and the Treasury
usually publicizes the results later that afternoon. The bills are issued to the successful bidders on
Thursday.
Two different types of bids can be submitted in the T-bill auction: competitive and noncompetitive.
Competitive bidders include money market banks, dealers, and other institutional investors who buy
large quantities of T-bills. The tenders they submit indicate the amount of bills they wish to purchase and
the price they are willing to pay. They are permitted to submit more than one tender. Noncompetitive
bidders are usually small or inexperienced bidders who indicate the amount of bills they want to
purchase (up to $1,000,000) and agree to pay the quantity weighted average of the accepted competitive
bids.
After all bids are in, first the Treasury sets aside the amount of bills requested by the noncompetitive
bidders. The remainder is allocated among the competitive bidders, beginning with those who bid the
highest price, until the total amount is issued. The price paid by the noncompetitive bidders can then be
calculated based on the competitive bids that were accepted.3
The Treasury bill auction is more complicated than the standard discriminatory auction since the non­
competitive bids are satisfied in full. Consequently, when submitting their bids, the major buyers do not
know the exact amount being auctioned to them. During 1987, an average of around $14 billion of
Treasury bills were auctioned each week.

aSee James F. Tucker, Buying Treasury Securities at Federal Reserve Banks (Federal Reserve Bank of Richmond, Feb­
ruary 1985) for further details.

under different circumstances, and the crucial
role of information.
PLAYING THE GAME:
HOW ECONOMISTS MODEL AUCTIONS
In general, economists model the auction as a
game with the bidders playing against each other.
The point of the game is to win the object at the
lowest possible price; each bidder devises a
strategy with this in mind. The bidder's choice of
strategy depends on what information the bid­
der has. Som e information is available to all the
players, like the rules of the particular auction
being held. But each bidder also has private infor­
mation about how she values the object—that is,
information that only she knows. It is precisely
because the bidders have some private informa­
tion that sellers use an auction to set the price in
the first place. If the seller knew each bidder's
valuation he could just set the price of the object
being sold at the highest valuation and not
bother to hold the auction. The role of private



information is crucial to understanding how
auctions work. The assumptions made in the
theoretical models about the nature of this
private information range along a broad spec­
trum.
Independent Private Values. At one end of
the spectrum, models assume that each bidder
knows for certain how she values the object and
that this information is totally private. The bid­
der's valuation of the object reflects her individual
tastes; only she knows what that value is, and
each bidder can have a different value. Suppose
a painting is being auctioned to bidders who just
want it because it is beautiful and not because
they plan to sell it. (A museum might be this
kind of bidder.) Then each bidder knows for cer­
tain what the painting is worth to herself but not
to the other bidders, and what other bidders
know about the painting will not affect her own
valuation—these bidders are said to have
private values.
Even though the bidders have private values,
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BUSINESS REVIEW

each would like to know how the other bidders
value the item (that is, their private informa­
tion), because this would reveal something about
how they are likely to bid. W hen the bidders'
values are independent, then the value one bidder
places on the painting is not systematically
related to the values the others place on the
object. In this case, a bidder's own valuation of
the painting tells her nothing about the other
bidders' valuations and so nothing about how
they will bid.
Common Values. Models at the other end of
the spectrum assume that the object being auc­
tioned is worth the same to all bidders, but they
are unsure of this value. Bidders have private
information that tells them something about this
true market value of the object, although not
enough to be certain. For example, when the
government announces a lease sale of oil and
gas deposits on offshore public lands, it lets
firms use seismic surveys and off-site drilling to
gather information about the tracts. So different
potential buyers may have different information
about the market value of the tracts when it
comes time to bid. The right to extract the
deposits is worth the same thing to each
bidder—the market value of the oil or gas
actually in the land— so the bidders have com­
mon values. At the time of bidding no bidder
knows this value for sure and each makes an
estimate of the value based on his private infor­
mation.
As in the private values model, a bidder in the
common values model would like to find out
what private information the other bidders
have, because it would tell him something about
how they are likely to bid. But, unlike the private
values model, finding out their private informa­
tion would also reveal something more about
the likely market value of the object, which
is precisely the value he is trying to estimate.
Learning about another bidder's estimate,
which reflects that bidder's private information,
will affect a bidder's own estimate of the object's
market value. Unlike the private values model, a
bidder's beliefs about the value of the object can
Digitized for8 FRASER


MARCH/APRIL 1988

change during the course of an auction as he
sees how other bidders are bidding.
Because the bidders in the common values
model are unsure about the true value of the
object, they are subject to the "winner's curse.”
Suppose one bidder estimates an antique chair
is worth $500 based on his private information,
but all the other bidders estimate its value at no
more than $400. If that one bidder offers $500,
he will win the chair. But by bidding his
estimate, the winner is cursed! Winning con­
veys the message that every other bidder made a
lower estimate of the chair's value, and so, on
average, the winner who has bid his estimate
will pay more than the chair is worth on the
open market.
Bidders can avoid the winner's curse by bid­
ding less than they think the object is worth.
When there are fewer bidders, a bidder can
shade down his bid more without affecting his
probability of winning, because there is less
chance that someone else's bid is just below his.
So the seller can expect a lower price when there
are fewer bidders.
Models and Reality. The independent private
values model and the common values model
describe extreme situations. Most real life
situations are not so simple. For example, in an
art auction, many bidders care about the pain­
ting's resale value as well as its personal value.
Therefore, their values are neither private nor
independent. Likewise, in the mineral rights
auction, the value of the minerals is related to
how efficiently the firm extracts them —the
amount of recoverable minerals may differ for
each firm bidding and so the value of the extrac­
tion rights to each firm is no longer a common
value.5

5Although most theoretical research has concentrated on
the polar case models, Paul Milgrom and Robert Weber have
analyzed a model that includes the independent private
values model and the common values model as special
cases. See Paul Milgrom and Robert Weber, "A Theory of
Auctions...."

FEDERAL RESERVE BANK OF PHILADELPHIA

Going, Going, Gone

A SELLER NEEDS TO KNOW
THE BIDDERS' STRATEGIES...
When a seller gets ready to put his antique car
or his plot of land up for auction, he has to
decide which kind of auction can be expected to
give him the highest price, and this will depend
on how bidders behave. Analyses of theoretical
models of auctions show that several factors will
affect the expected price, such as whether bid­
ders are more likely to have private values or
common values, and how willing the bidders
are to risk not winning the object.
Dutch and First Price Auctions. In theory, bid­
ders behave the same way in the Dutch auction,
where prices are called out in descending order,
as they do in the sealed bid first price auction. So
it does not matter which of these two types the
seller chooses, regardless of whether the situa­
tion is an independent private values one or a
common values one.6
A bidder follows the same strategy in the
Dutch and the first price auctions because in
both auctions he makes the same decision based
on the same information. He knows that if he
wins he has to pay what he bid, and that he wins
only if he bids higher than everyone else. But he
has to decide what to bid without knowing what
the others are going to do. It might seem that the
auctions should differ, since a bidder learns
something about the other bidders' valuations
during the course of the Dutch auction but not
during the first price auction. But the kind of
information he learns had already been incor­
porated into the strategy he chose at the begin­
ning of the Dutch auction, and it is the same
information he uses when choosing his strategy
in the first price auction. In the Dutch auction, a
bidder selects a cutoff price at which he will
claim the object so long as no one else has already
claimed it. As the auctioneer lowers the price,
the bidder hears prices he knows are higher

6However, Paul Milgrom, "The Economics.../' p. 274,
reports that Cox, Roberson, and Smith (in press) have
experimental evidence that seems to refute this.




Loretta ]. Mester

than other bidders' cutoff prices. But this infor­
mation does not lead him to change his own
cutoff price because he chose it understanding
that he wins only if the other bidders have a
lower cutoff value. Likewise, in the sealed bid
first price auction, he selects a price knowing
that it will win the object only if others have
selected a lower price. Therefore, in both the
Dutch auction and the first price auction, all the
bidders will have the same strategy. They shade
down their bids slightly below their valuations
since in these auctions winners pay what they
bid.
English and Second Price Auctions. The
choice between the English and second price
auction, on the other hand, does depend on
whether the bidders know their own private
values or bidders are unsure about the single
common value of the item. In a situation when
bidders have independent private values, both
auctions yield the same outcome. In the English
auction, the bidder keeps raising his bid until
the price equals the value of the object to him, or
until he is the last remaining bidder. Once the
price equals the second highest valuation, the
bidder with the second highest valuation stops
bidding. The remaining bidder (who has the
highest valuation) can claim the object by bid­
ding only very slightly more than the second
highest valuation. In the second price auction,
the bidder simply submits a bid equal to what
the object is worth to himself, since if he wins,
what he pays is beyond his control anyway.
Therefore, in either auction when there are
independent private values, the winner is the
bidder with the highest valuation and the price
he pays is equal to the second highest
valuation.
In a common values situation, where bidders
are unsure of the value of the object being auc­
tioned, the English and second price auctions no
longer lead to the same outcome. This is because
in the English auction a bidder gains two types
of useful information by observing the bids of
others (information he would not know at the
start of the auction). He sees how many bidders
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BUSINESS REVIEW

MARCH/APRIL 1988

have fallen out of the auction (since they have
lower valuations than the price being called)
and he sees at what prices these bidders have
fallen out. If a bidder had a reasonably high
estimate of the value to start with, he gains con­
fidence in this estimate as the bids go up,
especially if many people are still in the bidding;
this weakens the winner's curse and allows
more aggressive bidding than in the sealed bid
auction. So the price paid is likely to be higher in
an English auction than in a sealed bid second
price auction.
...SO HE CAN CHOOSE THE AUCTION
WITH THE HIGHEST EXPECTED REVENUE.
The seller now knows that regardless of the
type of information bidders have (independent
private values or common values), Dutch auc­
tions and first price auctions are expected to
generate the same revenue. He also knows that
with independent private values, English and
second price auctions yield the same expected
revenue, but with common values, the English
auction is expected to be better. (See EXPEC­
TED REVENUE DEPENDS ON TYPE OF
VALUES...)
What about the Dutch and first price auction
as compared with the English and second price
auction? One important factor in determining
which auction yields the highest revenue is how
the bidders feel about the risk of losing. While
each bidder in an auction would like to win, risk
averse bidders tend to up their bids so they will
be more likely to win, while risk neutral bidders
do not.

Risk and Independent Values. In fact, in the
independent private values model when all bid­
ders are risk neutral, the Dutch and first price
auctions give the seller the same revenue, on
average, as the English and second price auc­
tions. That is, while the prices are not always
exactly the same, they are the same on average
over a series of auctions. (This result is not
obvious and remained obscure long after
being proved.7)
If, on the other hand, bidders are risk averse,
then the first price auction (and therefore the
Dutch) gives greater expected revenue than the
second price and English auctions. In either the
second price auction or English auction, risk
averse bidders find it best to bid the same way
they would if they were risk neutral. But in the
first price or Dutch auction, risk averse bidders
find it better to bid higher than they would have
if they were risk neutral, as a kind of insurance
against losing. (They still bid less than their
valuations.) Since with risk neutral bidders, the
expected revenue was the same in the four auc­
tions, it follows that with risk averse bidders, the

7For our more technical readers: Bidders can be thought
of as choosing, through their actions, a probability of win­
ning and a corresponding expected payment. The revenue
equivalence result hinges on the fact drat, in equilibrium, the
probability a bidder with a given valuation wins, is the same
across all auctions in which the winning bidder has the
highest valuation. In the independent private values model,
all four auctions— Dutch, English, first price, and second
price— have this trait. See Paul Milgrom and Robert Weber,
"A Theory of Auctions...," pp. 1092-1093.

Expected Revenue Depends on Type of Values...

c

Common Values

Independent Private Values

English = 2nd Price ^

10



Dutch = 1st Price

English > 2nd Price

)

FEDERAL RESERVE BANK OF PHILADELPHIA

Going, Going, Gone

first price and Dutch auctions yield greater
expected revenue than the second price and
English auctions.
Risk and Common Values. Now suppose
once again that bidders are risk neutral but that
common values describe the situation.8*In this
case, the English auction yields the highest expec­
ted price and revenue, then the second price
auction, and finally the Dutch and first price auc­
tions. This may explain the popularity of the
English auction.
We can rank these auctions using the fact that
the more the price paid by the winning bidder is
linked to the value estimates of the other bid­
ders, the higher this price is expected to be. The
expected price in the English auction is depen­
dent on all the non-winners' value estimates,
since the winner observes the prices at which all
the other bidders have dropped out, and bases
her winning bid on this information. In the
second price auction, the winning price is linked
to only one other value estimate—the second
highest estim ate— since the w inning bidder

8Actually, all that is needed is that the bidders' valuations
be dependent. That is, if a bidder places a high value on the
object, she knows the other bidders are likely to place a high
value on it too. Comm on values is the extreme case since all
bidders are trying to estimate a single common value. (The
estimates conditional on the true value may be independent,
however.)




Loretta ]. Mester

must pay a price equal to the second highest
submitted bid. So the expected revenue in a
second price auction is less than that in an
English auction. In the first price and Dutch auc­
tions, the winning bid is not linked to any other
bidder's value estimate, and these auctions yield
the lowest expected revenue.
Unfortunately, if bidders are risk averse, we
can no longer predict which auction yields the
highest expected revenue in situations with com­
mon values or dependent values. While we
know that the expected revenue from the Dutch
and first price auctions is the same, and the
expected revenue from the English auction sur­
passes that of the second price auction, the com­
plete ranking depends on the degree of risk
aversion of the bidders and on how correlated
their valuations are. (See ...AND ON BIDDERS'
RISK CHARACTERISTICS.)
Implications for Treasury Bill Auctions.
These revenue results shed some new light on
whether the U.S. should continue to use a dis­
crim inatory auction to sell Treasury bills. If the
T-bill auction could be described by an indepen­
dent private values model, then if bidders are
risk neutral it does not matter which type of auc­
tion is used, and if bidders are risk averse the
government earns higher revenue, on average,
using the discriminatory auction (which is like a
first price auction). But the T-bill auction seems
to be more of a common values situation since

11

BUSINESS REVIEW

buyers are interested in the market value of the
bills; so if bidders are risk neutral, the govern­
ment would be better off switching to the uniform
auction (which is like a second price auction). If,
however, bidders are risk averse, we cannot say
which auction would yield the higher expected
revenue. Empirical work has compared the
revenue generated by the uniform price auction
which was used to sell long-term bonds in the
1970s and the discriminatory auction which is
used to sell short-term and medium-term
bonds.9 The results indicate that the uniform
auctions tended to yield higher revenue. This is
consistent with theory when bidders have com­
mon (or dependent) values and are risk neutral.
In sum, what these results tell us is that before
a seller can decide on which auction to use, he
needs to find out in which situation he is likely to
be. Are bidders risk averse or risk neutral? Does
the situation look more like an independent
private values one or a common values one?
Which type of situation it is will depend on the
kind of information the bidders have.
THERE'S STILL A LOT TO LEARN:
THE GAVEL HASN'T FALLEN YET
Economists are just beginning to address
some of the interesting questions about auc­
tions. For example, although we know (at least
in the simple models) the buyers' best strategies
in an auction, we know less about when the
seller will choose an auction as opposed to some
other method to set the price. One reason the
auction is used in a wide variety of situations is
that it is efficient—the winner values the object
more than any of the other bidders (and more
than the seller), and he pays more than others
would have paid. This means that after someone
wins the object in an auction he will not be able
to sell the object at a profit to someone else who
participated in the auction. And the person who
held the auction will not be told by a bidder

9See Paul Milgrom and Robert Weber, "A Theory of Auc­
tions...," p. 1094.

12



MARCH/APRIL 1988

afterward that she would have been willing to
pay more than the winner did. So from the seller's
point of view the auction can give him the
highest price he can expect to receive for the
object.10
Another area of active research concerns the
seller's policy of revealing information about
the object he is auctioning. Whether the seller
benefits from such a policy depends upon the
nature of his information. In some cases, the
seller would gain, on average, from telling all the
bidders his information since this would dec­
rease the advantage some of the bidders have
over others. By revealing his information the
seller can weaken the winner's curse, allowing
bidders to bid more aggressively. This may
explain why auction houses often reveal
appraisals of the objects they sell.11 But recent
work shows that adopting the policy of telling
all kinds of information is not always in the
best interest of the seller.12 And, in fact,
some government agencies conceal information
about the number of firms they have invited to
submit bids in their auctions.13
In general, most of the models studied so far
have been simplifications of real life situations.
Even these simple models have been difficult to
analyze. But the models are becoming more
realistic. Auctions with multiple buyers and
sellers, like the double auction, are being

10Another result that explains the popularity of auctions
is that a seller in a poor bargaining position compared to the
buyers can do almost as well as a seller in a strong bargaining
position by conducting an auction. Also, a seller in a strong
bargaining position sometimes will be better off selling an
object by one of the standard auctions (like sealed bid, or
English) than by any other method. These results are from
Paul Milgrom, "Auction Theory," in Truman F. Bewley, ed.,
Advances in Economic Theory (Cambridge: Cambridge
University Press, 1987), pp. 26-27.
11Paul Milgrom, "The Economics...," p. 287 discusses
this.
12See Steven Matthews, "Com paring Auctions for Risk
Averse Buyers: A Buyer's Point of View," Econometrica, 55
(May 1987), pp. 633-646.
13See R. Preston McAfee and John McMillan in "Auctions
and Bidding," journal of Economic Literature, 25 (June 1987),
p. 720.

FEDERAL RESERVE BANK OF PHILADELPHIA

Going, Going Gone

studied, as are models that assume bidders are
able to collude to keep the price down. In oil and
timber rights auctions the same bidders may
meet again and again and so should learn more
and more about their competitors—this repeti­
tion could facilitate collusion. The research that
has been done suggests that some types of auc­
tions are more susceptible to collusion than
others. In one model, it is shown that collusion is
easier in the English auction than in a sealed bid
auction. This may explain why industrial firms,
whose pool of bidders is often the same time and




Loretta J. Mester

time again, usually solicit sealed bids.14
A different avenue of research being pursued
involves testing the predictions of the theoreti­
cal models. Data from actual auctions are being
analyzed, as are data collected from laboratory
experiments. (See Herb Taylor's article in this
Business Review.) We can expect both empirical
and theoretical advances in the study of auctions
in the future.
14This model is developed by Paul R. Milgrom in "A uc­
tion Theory."

13

Philadelphia/RESEARCH

Working Papers
The Philadelphia Fed's Research Department occasionally publishes working papers based on the current
research of staff economists. These papers, dealing with virtually all areas within economics and finance, are
intended for the professional researcher. The 21 papers added to the Working Papers Series in 1987 are listed
below.
A list of all available papers may be ordered from WORKING PAPERS, Department of Research, Federal
Reserve Bank of Philadelphia, 10 Independence Mall, Philadelphia, Pennsylvania 19106. Copies of papers may
be ordered from the same address. For overseas airmail requests only, a $2.00 per copy prepayment is
required.
No. 87-1

Paul Calem, "Deposit Market Segmentation: The Case of MMDAs and Super-NOWs." (Super­
sedes No. 86-3, "MMDAs, Super-NOWs, and the Differentiation of Bank Deposit Products.")

No. 87-2

John J. Merrick, Jr., "Volume Determination in Stock and Stock Index Futures Markets: An
Analysis of Arbitrage and Volatility Effects."

No. 87-3

Richard P. Voith, "Compensating Variation in Wages and Rents."

No. 87-4

John J. Merrick, Jr., "Price Discovery in the Stock Market."

No. 87-5/R

Loretta J. Mester, "Testing for Expense Preference Behavior Using Cost Data." (Revision of
No. 87-5).

No. 87-6

Paul Calem and Janice Moulton, "Competitive Effects of Interstate Bank Mergers and
Acquisitions."

No. 87-7

Joel Houston, "The Policy Implications of the Underground Economy."

No. 87-8

Mitchell Berlin and Paul Calem, "Financing, Commitment, and Entry Deterrence."

No. 87-9

Joel F. Houston, "Estimating the Size and Implications of the Underground Economy."

No. 87-10

Joel F. Houston, "Participation in the Underground Economy: A Theoretical Analysis."

No. 87-11

John J. Merrick, Jr., "Hedging with Mispriced Futures."

No. 87-12

Linda Allen, Stavros Peristiani and Anthony Saunders, "Bank Size, Collateral and Net Purchase
Behavior in the Federal Funds Market: Empirical Evidence."

No. 87-13

John J. Merrick, Jr., "Portfolio Insurance With Stock Index Futures."

No. 87-14

John F. Boschen and Leonard O. Mills, "Tests of the Relation Between Money and Output in the
Real Business Cycle Model."

No. 87-15

Anthony Saunders and Stanley Sienkiewicz, "The Hedging Performance of ECU Futures
Contracts."

No. 87-16

John J. Merrick, Jr., "Early Unwindings and Rollovers of Stock Index Futures Arbitrage Programs:
Analysis and Implications for Predicting Expiration Day Effects."

No. 87-17

Paul Calem, "On Estimating Technical Progress and Returns to Scale."

No. 87-18

Richard Voith, "Commuter Rail Ridership: The Long and Short Haul."

No. 87-19

Mark J. Flannery and Aris A. Protopapadakis, "From T-Bills to Common Stocks: Investigating
the Generality of Intra-Week Return Seasonality."

No. 87-20

Behzad T. Diba and Herschel I. Grossman, "Rational Bubbles in Stock Prices?"

No. 87-21

Brian J. Cody, "Exchange Controls and the Foreign Exchange Market: A Model of Political
Risk."




Experimental Economics:
Putting Markets under the Microscope
Herb Taylor*
There is a famous joke about a physicist, an
engineer, and an economist shipwrecked on a
desert island with only a can of beans to eat. "I
can help open it," volunteers the physicist. "I'll
start a small fire, put the can in it, and compute
how long it will take for the can to explode."
"G reat!" says the engineer, "I can calculate the

*Herb Taylor is a Research Officer and Economist in the
Research Department of the Federal Bank of Philadelphia.
The author thanks Vernon L. Smith for his informative dis­
cussion and very useful comments on an earlier draft.




trajectory that the beans will take and where we
should stand to catch them ." "Wait a minute!"
the economist interrupts. "You fellows are ap­
proaching this whole thing the wrong way...First,
assume we have a can opener..."
Economists are notorious for making assump­
tions—assumptions that are at once crucial to
their analysis and completely unrealistic. An
economist discussing the bond market assumes
that all market participants are "perfectly rational";
an economist analyzing the oil industry assumes
that energy markets are "in equilibrium." Even
15

BUSINESS REVIEW

economists recognize that not everyone is per­
fectly rational and that markets are probably
never in equilibrium. Yet they stand by analyses
based on such assumptions. Why?
Economists contend that it is pointless to argue
over the realism of their assumptions. First of all,
developing a theory always requires making
some simplifying assumptions, and economists
theorizing about complex human interactions
are bound to make simplifying assumptions that
seem exceptionally "unrealistic." But economists
have a logistical problem as well. More realistic
assumptions—"som e people are rational" or
"markets eventually settle at an equilibrium
under the right circum stances"—will not
improve economists' analysis unless economists
can be more specific. How many people is
"some"? How do the "irrational" people behave?
How long is "eventually"? What are "the right
circumstances" for an equilibrium? And for
economists to go out into the marketplace and
collect the data they need to answer these ques­
tions is a hopeless task. They cannot assemble
enough information about how market par­
ticipants think, choose, act, and react. They can­
not control for the many factors that make one
market different from another, and each market
different from one day to the next. So it would
seem that economists have little choice but to
stick with admittedly unrealistic assumptions
and hope that they are reasonable enough to
produce some realistic conclusions and predic­
tions about the way the econom y performs.
Now some economists are trying a fresh ap­
proach to evaluating the assumptions economists
so routinely make about the way markets operate.
By constructing and observing relatively simple
"experim ental" markets operating under con­
trolled conditions, they can see and test and
measure the impact that different economic en­
vironments and different institutional arrange­
ments have on market performance. Experi­
mental economics is still young, but it has al­
ready demonstrated that taking a closer look at
simpler structures opens up new ways to improve
and refine economists' analyses and predictions.
16



MARCH/APRIL 1988

ECONOMISTS ENVISION HOW MARKETS
WORK IN PRINCIPLE...
Think of any good or service—Ford Escorts or
visits to the dentist. Over any time period, we
can observe some quantity of this product being
bought at some average price. For instance, we
may find that in February, 2,127 Escorts were
sold at an average price of $11,359. In the mind
of an economist, both the price and the quantity
that we see result from the workings of "the
market" for Escorts in February. But what is this
"m arket" and how does it work to determine the
price and quantity sold?
The market for a product is comprised of
those considering buying the product (the
demanders), those willing to provide it (the sup­
pliers), and the social arrangements and insti­
tutions that bring them together (the market
mechanism). Typically, economists' analysis of
the market includes a discussion of the factors
affecting the overall demand for the product, the
overall supply of it, and how the two are recon­
ciled.
Generally the public's demand for a product
is held to depend on its price, prices of related
products, the income level of potential cus­
tomers, and their tastes and preferences. The
demand curve (Figure 1) illustrates a basic idea
about market demand—the higher the price of a
product, the smaller the quantity consumers
will want to buy.
Suppliers' willingness to make a product
available is usually held to depend on the price
they can get for the product, the cost of the labor,
raw materials, and other factors needed to pro­
duce it, and the available technology. The sup­
ply curve (Figure 1) illustrates a basic notion
about market supply—the higher the price of a
product, the larger the quantity producers will
be willing to make available.
Having laid out demand and supply con­
ditions in the market, econom ists add the as­
sumption that the market settles at a price which
clears it of any unmet demands or unwanted
supplies. This assumption gives economists a
theory about the price and quantity of the proFEDERAL RESERVE BANK OF PHILADELPHIA

Experimental Economics

duct that we observe. The price we observe is
the market-clearing price; the quantity we observe
is the quantity that people want to buy and sell at
that price (P* and Q* in Figure 2).
Behind the assumption that the market for a
product always clears is the economists' vision
of a market as a place swarming with potential
buyers and sellers, each well-informed, each
operating independently, and each bidding
against all others in an effort to make trades. In
such a competitive environment, a product's
price is persistently pushed toward its market­
clearing level. A price above the market-clearing
level (say at Pa in Figure 3) induces suppliers to
produce more of the product than consumers
want to buy, and the competition for customers
forces suppliers to cut their prices. A price below
the market-clearing level (say at Pb in Figure 3)
makes consumers want to buy more of the pro­
duct than producers are willing to make avail­
able, and competition for the relatively scarce
product induces some potential customers to
offer a higher price for it. Only at the market­
clearing price, where consumers want to buy
exactly as much of the product as suppliers want
to produce, do the incentives for buyers and
sellers to adjust prices disappear.
...BUT IT'S HARD TO SEE
HOW MARKETS WORK IN REALITY
If market competition were really keen enough
to bring markets quickly into equilibrium at the
competitive price, then assuming that markets
were always at their competitive equilibrium
would be no problem. But real world markets
are not the all-out bidding wars among teeming
numbers of competitors that economic theory
posits. A few products are indeed offered by
large numbers of small producers, but many—
like autos and breakfast cereals—are supplied
by a handful of large producers, and some—like
computers and fast-food hamburgers—are pro­
vided by a few small producers and one giant.
Trading practices and procedures often differ
from the theoretical ideal, too. In the stock mar­
ket traders bombard each other with bids and



Herb Taylor

Figure 1
Price

Figure 2
Price

Figure 3
Price

Quantity

17

BUSINESS REVIEW

offers; but in the retail car market a salesman and
a customer negotiate a price one-on-one; and in
the grocery market the store clerk simply posts
the price, leaving shoppers to choose between
buying at that price and not buying at all. Com­
petition may ultimately push most markets
toward a competitive equilibrium. But undoubt­
edly some features of real world markets slow
the adjustment process, and some may even
block it entirely. If so, then economists could
improve their analysis by developing more real­
istic theories about how markets work.
Unfortunately, as a practical matter, econo­
mists have not made a great deal of progress in
assessing how a market's characteristics affect
its performance. It is not that they haven't
thought long and hard about such issues. The
theory of how a monopoly producer would res­
trict the supply of a product to keep its price
above competitive levels dates back to the 1830s.
Over the years, economists have also con­
sidered how markets supplied by just a few pro­
ducers (oligopolists) might behave, and they
have developed many alternative theories along
the way. And recently economists have gone on
to develop whole new theories of how different
auction formats and negotiating strategies might
affect market outcomes as well.1 But it has pro­
ven difficult for economists to assess the accuracy
of these theories or to choose among the com­
peting ones. And they have been able to offer
few answers to questions like how other trading
rules affect market performance, or how long it
takes for a market to come to an equilibrium, or
what path prices take on the way.
The problem is that economists have been
trying to improve and refine their ideas about
how markets work solely on the basis of what
they observe in real world markets. These mar­
kets are usually so large and complicated that it
is difficult—and sometimes impossible—for
economists to collect the information or exeriFor a more complete discussion of auctions and other
trading arrangements, see Loretta Mester's "Going, Going,
Gone: Setting Prices in Auction Markets" in This Issue.

18



MARCH/APRIL 1988

cise the control that they need to test their ideas.
Picture an economist trying to learn more about
how product markets work by focusing on the
burger business. She cannot hope to survey
every fast-food producer and potential fast-food
customer closely enough to get an accurate pic­
ture of supply and demand conditions in the
market, so she cannot be sure what the competi­
tive burger price would be. And she cannot add
two new burger chains to the industry or tem­
porarily switch from a posted-price to an auc­
tion format at McDonald's to see how such
changes affect a market's performance.
CONTROLLED EXPERIMENTS BRING PRO­
DUCT MARKETS INTO SHARPER FOCUS...
Economists trying to learn about how markets
operate by observing existing real world markets
are hobbled by their inability to observe or con­
trol the many factors at work there. Experimen­
tal economists get around the problem by setting
up small markets with simple structures in which
they can control for all of the relevant factors and
then observe how people act in these controlled
economic environments.
Setting up an Experimental Product Market.
The key to researchers' control over supply and
demand conditions in experimental markets is
their ability to establish trade in an abstract
commodity—one with no physical characteris­
tics. Such a commodity is itself worthless; its
only value is the value that the researchers induce
by offering to redeem units of it for cash after the
market closes. Using this “induced value" ap­
proach, a researcher can control exactly how
many units of the commodity participants will
want to buy and sell at any price.2

2The induced value theory upon which the design of
experimental markets is based is presented by Vernon L.
Smith in "Experimental Economics: Induced Value Theory,"
American Economic Review (May 1976) pp. 274-279. Smith's
"Microeconomic Systems as an Experimental Science,"
American Economic Review (December 1982) pp. 923-955 is a
presentation of the experimental markets methodology and
results which is considered the standard.

FEDERAL RESERVE BANK OF PHILADELPHIA

Experimental Economics

Herb Taylor

In a typical experiment, the researcher divides
the market participants into demanders and
suppliers. Before the market opens, she tells the
demanders that any units of the commodity they
buy during the trading period can be turned in
for cash after the market closes. She then gives
each demander a schedule indicating the redemp­
tion value of each unit he purchases in the market.
Demander A's redemption schedule, for exam­
ple, may indicate that the first unit of the com­
modity that he buys in the market can be re­
deemed for $.60, the second can be redeemed
for $.50, the third for $.40, and so on. Likewise,
the researcher informs the suppliers that after
the market closes she will charge them for any
units of the commodity that they sell during the
trading period. She then gives each supplier a
schedule indicating how much each unit he sells
in the market will cost him afterwards. Supplier
Z's cost schedule, for instance, may tell him that
he will be charged $.20 for the first unit he sells,
$.40 for the second unit, $.60 for the third, and so

deal with a number of potential customers dur­
ing the marketing period, but he must deal with
them one at a time. Usually in a posted-price
market, each seller decides on the price he will
charge before the market opens and he cannot
change it during the market period. In some
posted-price experiments, the buyers of the
commodity are required to decide what price
they will pay in advance and they cannot change
during the market period.
Once the trading rules are settled, trading
begins. A trading period can last anywhere from
five to twenty minutes. Usually there are eight
or so participants in the market, sometimes more.
Often they are college students, though working
businesspeople have participated. Sometimes
trading takes place in a single room; many times
participants are scattered around at different
locations and communicate over computer ter­
minals. Negotiated-price markets have been
conducted both using private booths to allow
face-to-face contact and using telephones.
on. In m arkets for real w orld com m odities, each
During a trading period, no money or com­
market participant knows the value that he him­ modities actually change hands. When a deman­
self puts on the commodity, but not the value der and supplier come to an agreement, the
others put on it. To mimic this feature in experi­ researcher records the price and quantity at
mental markets, each demander knows only his which the transaction is completed. When the
own redemption schedule and each supplier market closes, the researcher computes each par­
only his own cost schedule. Setting the redemp­ ticipants' gains for the session. For instance, if
tion and cost schedules in this way establishes Demander A and Supplier Z above happened to
precisely the supply and demand conditions in make their first transaction of the market period
the market. (See CONTROLLING THE MARKET with each other, with Z selling A one unit at $.45,
WITH THE "INDUCED VALUE" APPROACH, then at the end of the period A would be credited
pp. 20-21.)
with $.15 (= $.60 — $.45) on the deal and Z
Before the trading period begins the researcher would be credited with $.25 (= $.45 — $.20). If Z
also announces the trading rules. Prices may be agreed to sell A a second unit at that price, A
established in one of three basic ways: auction, would be credited with an additional $.05 (=$.50
negotiation, or posting. Auctions allow the most — $.45) and Z would gain with an additional
interaction between buyers and sellers, negotia­ $.05 (= $.45 — $.40) as well.
tion somewhat less, and posted prices the least.
Once the gains from the first trading session
The auction format most often used in experi­ have been computed, the researcher usually
mental markets is the "double" auction, where runs several more trading periods under the
both buyers and sellers are free to announce same market conditions to see how market
bids and offers to the market at any time. In the behavior evolves. The researcher then may alter
negotiated price format, buyers and sellers bar­ some aspect of the market's structure in order to
gain with each other one-on-one. A seller may observe the impact of that change on the market




19

BUSINESS REVIEW

MARCH/APRIL 1988

Controlling the Market with the "Induced Value" Approach
Creating Demand and Supply Schedules
Participants in experimental markets are trading an abstract commodity of no intrinsic value. The
researcher creates market demand for the commodity by giving each designated demander a redemp­
tion schedule and creates market supply by giving each designated supplier a cost schedule.
To create the typical looking experimental market demand schedule, the researcher could give three
demanders the following redemption schedule:
Redemption Schedule
for the:
the researcher will pay you:
1st unit you buy
$.60
2nd unit you buy
$.50
3rd unit you buy
$.40
4th unit you buy
$.30
The researcher now knows that if the commodity is available in the market at a price between $.50 and
$.60, each demander will make a profit on the first unit he buys, but he will lose money on the second. So,
presuming that demanders prefer more money to less, each will demand exactly one unit of the com­
modity at a market price in that range. Market demand, then, will be exactly three units in the $.50 to $.60
price range. Similar reasoning produces the rest of the market demand schedule.
To create the typical-looking experimental market supply schedule, the researcher could give three
suppliers the following cost schedule:

Cost Schedule
the researcher will charge you:
for the:
$.20
1st unit you sell
$.40
2nd unit you sell
$.60
3rd unit you sell
$.80
4th unit you sell
The researcher now knows that if the market price of the commodity is between $.20 and $.40, each sup­
plier makes a profit on the first unit he sells, but he loses money on the second. So as long as the suppliers
prefer more money to less, each will offer exactly one unit of the commodity for sale at a market price in
that range. Market supply is therefore three units in the $.20 to $.40 price range. Similar reasoning pro­
duces the rest of the market supply schedule.
The demand and supply schedules created by the researcher for this hypothetical experimental market
establish a competitive equilibrium price range of $.40 to $.50, indicated by the intersection of the two
schedules in that range.
Price
$.80 $.70

-

$.60
$.50

-

$.40

-

Supply

i

-■

$.30

-

$.20

-

$.10

—

20



Demand

Quantity
9

12

15

FEDERAL RESERVE BANK OF PHILADELPHIA

Experimental Economics

Herb Taylor

The Results of a Typical Market Experiment
In this particular experiment, the researcher, Vernon Smith, used the induced value approach to
create the supply and demand conditions shown in the far left panel below. Under these conditions, the
competitive market theory predicts that eight units of the commodity will be exchanged at a price of
$2.10. The next two panels report what actually happened when the market was put into operation in
two separate experiments of five trading periods each. In these experiments market participants bought
and sold one unit of the commodity per "transaction". The number of units exchanged, as measured
along the horizontal axis by the number of transactions, turned out to be somewhere between seven and
nine in every period. The prices at which buyers and sellers transacted, as measured along the vertical
axis, varied widely during the early trading periods of each experiment; but by the last period of each
experiment, all transactions were at or near the $2.10 equilibrium price.

NOTE: These results were originally reported in Vernon Smith "Bidding and Auctioning Institutions: Experimental
Results," Bidding and Auctioning for Procurement and Allocation, ed. Yakov Amihud, New York University Press (1976)
pp. 43-63. The figure appears with the permission of New York University Press.

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BUSINESS REVIEW

outcome, everything else constant. W hen all of
the market experiments have been run, the mar­
ket participants are paid their total gains from
the session in cash.
Some Results of Market Experiments. Perhaps
the most comforting result to come from experi­
mental market studies is the strong tendency for
auction markets to achieve the market-clearing
price and quantity predicted by the competitive
market model. A double auction market with a
few buyers and sellers usually provides enough
competition to drive the commodity price to its
theoretical equilibrium price within a couple of
trading periods. It seems that only a monopoly
supplier can prevent the price of a product from
declining to the competitive level in an auction
market.3
On the other hand, results from experimental
markets operating under different trading rules
are less supportive of the competitive market
paradigm. Negotiated price markets seem to
converge less quickly and less directly to the
competitive equilibrium than auction markets.
Posted-price markets are even slower to adjust
and may not converge to the competitive out­
come at all. Generally when suppliers post the
prices at which they will sell, the average price
tends to stabilize above the competitive equilib­
rium level. W hen demanders post the prices
they will pay, prices tend to stay below their
competitive equilibrium level.
There is little in the way of formal theory to
explain why a market's performance varies with
its trading rules, but experimental economists
have ventured the hypothesis that information
flows play a key role. As we move from a postedprice to a negotiated-price to an auction-price
format, market participants have a greater and

■frhis summary of experimental results is based heavily on
a classic review of the literature in this area by Charles R.
Plott, "Industrial Organization Theory and Experimental
Econom ics/' Journal o f Economic Literature (December 1982)
pp. 1485-1527. Another, somewhat more technical, sum­
mary is by Vernon L. Smith, "Experimental Methods in the
Political Economy of Exchange," Science (October 1986) pp.
167-173.

22 FRASER
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MARCH/APRIL 1988

greater opportunity to observe the terms on
which others are trading and offering to trade.
Access to this type of information seems to speed
the market's convergence to the competitive
outcome. Nonetheless, the impact of informa­
tion on market performance is subtle. In one
experiment, for instance, market participants'
knowledge of each other's cost and redemption
schedules impeded the convergence to a com­
petitive price. In another experimental market,
the researcher's release of data on suppliers'
profits seemed to help them keep prices above
the competitive level.
Controlled market experiments are not only
helping economists isolate the conditions under
which markets achieve a competitive equilib­
rium, they are also helping economists sort out
what is happening when they do not. For instance,
monopolists in experim ental posted-price
markets seem to achieve the higher price and
restricted quantity that traditional theory sug­
gests a profit-maximizer should, though con­
vergence to this situation may take quite a few
trading periods. Other experiments with small
numbers of suppliers in non-auction markets
suggest that oligopolists sometimes find some
arrangement for collusion so that they can boost
joint profits. For instance, when researchers ran
experiments designed to mimic the major fea­
tures of a barge transportation market and the
market for a gasoline additive in order to address
some regulatory issues, they found that ad­
herence to certain rules for posting prices in
these industries enabled suppliers to maintain
higher than competitive prices.
Researchers have also used market experi­
ments to strike out in new directions as they try
to refine economists' understanding of the way
markets operate. In a very practical example,
one study physically separated suppliers and
demanders of the commodity and then intro­
duced a group of "m iddlem en" who spent one
period in the suppliers' room buying and the
next period in the demanders' room selling.
They found that a market with a number of
"m iddlemen" was relatively quick to achieve a
FEDERAL RESERVE BANK OF PHILADELPHIA

Experimental Economics

competitive equilibrium. Broader in their impli­
cations are the data from experimental markets
which suggest that different supply and demand
conditions produce different patterns of adjust­
ment to equilibrium: when the market demand
curve has a steep slope, for instance, prices tend
to start out above the equilibrium price and then
decline. Economists have just begun testing some
rudimentary theories that attempt to explain
these kinds of patterns.4*
...AND HELP CLARIFY HOW ASSETS ARE
PRICED IN FINANCIAL MARKETS
When economists turn their attention from
product markets to financial markets, con­
siderations like buyers' tastes and sellers' oper­
ating costs move into the background and
expectations play the major role. In financial
markets buyers and sellers are trading IOUs—
promises of future money payments—and pre­
sumably the prices at which they are willing to
trade are dictated by their expectations about
the value of those future payments.
According to the efficient markets theory,
competition among well-informed market par­
ticipants always drives a financial asset's current
market price to a level which reflects the best
possible forecast of its future payment stream.
So the current price of a share of IBM stock, for
instance, presumably would represent the best
available evaluation of the dividend stream that
IBM will pay in the future. Likewise, if financial
markets are efficient, then the current price of an
AT&T bond represents the best possible evalua­
tion of AT&T's promise to make the interest
payments and pay the face value.
At least until recently, many econom ists
maintained that financial markets were efficient,

4Vem on L. Smith, "Experimental Auction Markets and
the Walrasian Hypothesis," Journal of Political Economy
(August 1965) pp. 387-393 reports on a study of con­
vergence paths to equilibrium in an experimental market.
The study involving middlemen is reported by Charles R.
Plott and Jonathan T. Uhl in "Competitive Equilibrium with
Middlemen: An Empirical Study," Southern Economic Journal
(April 1981) pp. 1063-1071.




Herb Taylor

but the October stock market crash has created
some doubts. It is hard to imagine that informed
market participants' best estimate of all future
stock dividends could plummet by 20 percent in
one day. The crash helped resuscitate a compet­
ing theory that financial markets are subject to
speculative bubbles that burst. An asset's price
can be bid up above its intrinsic value—the value
of its expected future payout—today because
some market participants believe that others
will be willing to pay still more for it tomorrow.
For a while this belief is self-sustaining and the
market booms, but eventually participants lose
faith that prices can rise further and the market
crashes.
Are financiai markets efficient? Do real world
asset prices simply reflect a well-informed mar­
ket's expectation about assets' future payout
stream? Or are financial markets subject to
booms and busts unrelated to changes in assets'
intrinsic values? Ironically, studies of real-world
financial markets cannot offer much in the way
of direct answers to these important real world
questions. Measuring market expectations is at
the core of the problem. There are too many
market participants, the possible future con­
tingencies they must evaluate are too complex,
and the constant inflow of new information
changes their outlook too quickly for all of their
expectations to be measured. But experimental
market methods can be used to get at some
answers. In an experimental asset market, the
researcher can specify the payout stream of the
financial asset, control the flow of relevant infor­
mation to market participants, and then observe
both individual and market responses. Such
experiments have been run and have produced
some interesting results.
Constructing an Experimental Asset Market.
Experimental asset market designs are essen­
tially multiperiod versions of experimental
commodity price designs. In a typical experi­
ment, the researcher issues each market partici­
pant some certificates which entitle the holder
to dividends to be paid out at the end of each
"week" of the market "year." The market "week"
23

BUSINESS REVIEW

is actually a trading session lasting several
minutes; a market "year" may consist of two,
three, or more market "w eeks." Each participant
is told what the dividend payout will be on any
certificate that she holds at the end of a period,
or at least told the probability distribution of the
dividends—for instance, trader C may be told
that for any certificate she holds at the end of
"w eek" two she has a 50-percent chance of
receiving a $1.00 dividend and a 50-percent
chance of receiving no dividend. Participants
are not told what payouts the other traders can
expect.
The experimenter also announces the trading
rules: usually experimental asset markets are
organized as double auctions, just as a realworld exchange would be. Trading then begins.
The experiment usually runs for several market
"years" with the researcher recording all bids,
offers, and transactions. The experiment can
then be repeated with some alteration in experi­
mental design in order to provide data about the
impact that changing some feature of the finan­
cial environment has on the market outcome.
Experimental Evidence about Asset Market
Behavior. Results from simple asset market
experiments are consistent with the idea that
asset markets are efficient.5 But efficiency seems
to be a fragile attribute. Studies have shown that
relatively minor modifications to a simple design
can easily destroy efficiency in an experimental
asset market.
In the most basic asset market designs, the
experimental market is run for several "years"
of two or three "weeks" each, with the same weekly
distribution of dividends every year. In these
cases, traders tend to pick up the pattern in

5Two frequently cited studies of experimental asset mar­
kets are: Robert Forsythe, Thomas R. Palfrey, and Charles R.
Plott, "Asset Valuation in an Experimental Market" Econometrica (May 1982) pp. 537-567; and Daniel Friedman, Glenn
W. Harrison, and Jon W. Salmon, "The Informational
Efficiency of Experimental Asset Markets" journal of Political
Economy 92(3) (1984) pp. 349-408. Both articles lay out their
methodology very clearly and both present results which
support the efficient markets hypothesis.

24FRASER
Digitized for


MARCH/APRIL 1988

market prices quickly. After a few market years,
each week's asset prices settle at levels consis­
tent with the expected value of market par­
ticipants' dividend streams over the rest of the
market year. But in an experiment where the
dividend distributions are systematically
shifted from year to year, asset prices do not
converge to efficient levels and fail to follow any
discernible pattern. More dramatically, a batch
of experiments in which the market year was
simply extended to fifteen or more weeks con­
sistently produced a speculative "boom -bust"
cycle for the first couple of years. It seems that
when an asset's maturity is a long way off, market
participants lose sight of the dividend payments
the asset is expected to yield over its lifetime and
focus instead on the potential for reselling the
asset at a higher price later. Only when the asset's
time of maturity draws near does its expected
payout become the focus of traders' attention.
So there is a pronounced tendency for asset
price bubbles to arise early in the market year,
and for these bubbles to burst at the end as
prices plunge to the efficient market price. In
some of these experiments the subjects were
businesspeople, not students, suggesting that it
is lack of experience with a particular market
situation, not an overall lack of business experi­
ence, which contributes to the speculative
market behavior.6*
Variations in experimental asset market design
have produced some other interesting pieces of
evidence about the way financial markets work.
In one set of experiments, some traders were
given "inside information" about what future

6The nonconvergence results are reported by Arlington
W. Williams and Vernon L. Smith in "Cyclical DoubleAuction Markets with and without Speculators," Journal of
Business (January 1984) pp 1-33. The boom-bust cycles are
reported by Smith, G erry L. Suchanek, and Williams,
"Bubbles, Crashes and Endogenous Expectations in Experi­
mental Asset Markets," Working Paper No. 86-2, Depart­
ment of Economics, University of Arizona (forthcoming in
Econometrica). After the recent stock market crash, Professor
Smith's experimental asset market work was discussed in
The Wall Street Journal (November 1 6 ,1 9 8 7 ) p. 51.

FEDERAL RESERVE BANK OF PHILADELPHIA

Experimental Economics

dividends on the certificates would be. The
researchers found that such information was
quickly reflected in the asset's market price. In
several experiments, futures markets were added
to allow traders to buy and sell certificates for
delivery one or two "w eeks" in the future. Here
researchers found that the addition of futures
markets reduces price volatility and speeds the
convergence to efficient pricing in the spot mar­
ket. In another interesting twist, market par­
ticipants were prescreened and divided into two
groups, more risk averse and less. Each group
participated in an experimental asset market of
identical design. From this experiment, the
researchers concluded that less risk averse
traders, those who might be termed speculators,
make prices more volatile, but also help the
market achieve an efficient asset price more
quickly.7
CONCLUSION
Experimental econom ics—observing the be­
havior of subjects in controlled market environ­
ments—is giving economists the opportunity to
test their assumptions and theories about market
outcomes in ways that the more traditional
studies of "real world" markets cannot. Much of
the experimental work that has been done so far
is supportive of traditional economic theory. For
instance, economists' standard assumptions that
product markets are competitive and that asset
markets are efficient are consistent with much of
the evidence from experimental markets. On
the other hand, experimental work has also
demonstrated that there are some important

7Charles R. Plott and and Shyam Sunder, "Efficiency of
Experimental Security Markets with Insider Information:
An Application of Rational Expectations Models," Journal of
Political Economy (1982) 90(4) pp. 663-698 investigate the
impact of inside information. The previously cited studies
by Forsythe, Palfrey and Plott and by Friedman, Harrison
and Salmon introduce futures markets to their experiments.
The role of risk-aversion was addressed by James S. Ang and
Thomas Schwarz, "Risk Aversion and Information Struc­
ture: An Experimental Study of Price Variability in the Securi­
ties M arkets," Journal of Finance Quly 1985) pp. 825-844.




Herb Taylor

gaps and shortcomings in standard economic
theory. Observing the behavior of experimental
markets underscores the fact that market adjust­
ments are not always quick, smooth, or certain.
Taking a more positive perspective, experi­
mental economics not only points out the need
to develop economic theory, but also helps
economists frame new theories and provides
the tools for testing them. For instance, market
experiments have demonstrated that market
information influences individuals' expec­
tations and decisions in complex ways. But
experiments have also provided some data to
help refine econom ists' theories about indi­
viduals' expectations formation and decision­
making processes. Some of this work has taken a
look at some of the traditional expectations
hypotheses in economics; some has tapped into
psychologists' and other social scientists'
theories of learning and decisionmaking.8
Experimental economics is a relatively new
tool that researchers have developed to take a
closer look at the way markets operate. So far
they have put some relatively simple market
structures under this new "microscope," but
seeing even these simple structures up close is
changing their perspective on how real world
markets function.9

8 Arlington W. Williams, "The Formation of Price Forecasts
in Experimental Markets," Journal of Money, Credit and Bank­
ing (Februafy 1987) pp. 1-18, reports on attempts to survey
market participants' expectations and model them directly.
The evidence of adaptive expectations formation that
Williams found is consistent with the notion that repetition
of a market situation facilitates achieving the efficient markets
outcome. The Journal of Business 59(4) pt. 2 (October 1986),
in a special issue containing the proceedings of a conference
entitled "The Behavioral Foundations of Economic Theory,"
gives some indications of how experimental economists'
work ties into that of other behavioral scientists.
9 Alvin E. Roth, "Laboratory Experimentation in Economics,"

Economics and Philosophy 1986(2) pp. 245-273 presents an
enlightening perspective on the potential contributions of
experimental economics as well as a thought-provoking dis­
cussion of some recent experimental results. Ken Binmore,
"Experimental Economics," European Economic Review
(1987) pp. 257-264 makes a thoughtful case for the useful­
ness of experimental economics.

25

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