Alvin E. Roth
What Have We Learned from
Market Design?
In the centennial issue of the Economic Journal, I wrote (about game theory) that
the real test of our success will be not merely how well we understand
thegeneral principles that govern economic interactions, but how well we
can bring this knowledge to bear on practical questions of microeco-
nomic engineering…” (Roth, 1991)
Since then, economists have gained significant experience in practical market
design. One thing we learned from this experience is that transactions and institu-
tions matter at a level of detail that economists have not often had to deal with,
and, in this respect, all markets are different. But there are also general lessons.
This essay will consider some ways in which markets succeed and fail by looking at
some common patterns we see of market failures, and how they have been fixed.
This is a big subject, and I will only scratch the surface by concentrating on
markets my colleagues and I helped design in the last few years. My focus will be
different than in Roth (2002), where I discussed some lessons learned in the 1990s.
The relevant parts of that discussion, which I’ll review briefly in the next section,
gathered evidence from a variety of labor market clearinghouses to determine
properties of successful clearinghouses, motivated by the redesign of the clearing-
house for new American doctors.1 Other big market design lessons from the 1990s
concern the design of auctions for the sale of radio spectrum and electricity.2
As we have dealt with more market failures, it has become clear that the histo-
ries of the American and British markets for new doctors, and the market failures
that led to their reorganization into clearinghouses, are far from unique. Other
markets have failed for similar reasons, and some have been fixed in similar ways.
I’ll discuss common market failures we have seen in recent work on more senior
Alvin E. Roth is George Gund Professor of Economics and Business Administration in
the Department of Economics at Harvard University and the Harvard Business
School.
This paper was prepared to accompany the Hahn Lecture delivered by Professor Roth
at the Royal Economic Society meetings on April 11, 2007, at the University of
Warwick. The paper previously appeared in the Economic Journal, 118 (March),
2008, 285-310.
© 2008 Blackwell Publishing Ltd.
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Alvin E. Roth
medical labor markets, and also on allocation procedures that do not use prices,
for school choice in New York City and Boston, and for the allocation of live-donor
kidneys for transplantation. These problems were fixed by the design of appropri-
ate clearinghouses. I’ll also discuss the North American labor market for new econ-
omists, in which related problems are addressed by marketplace mechanisms that
leave the market relatively decentralized.
The histories of these markets suggest a number of tasks that markets and allo-
cation systems need to accomplish to perform well. The failure to do these things
causes problems that may require changes in how the marketplace is organized.
I’ll argue that, to work well marketplaces, need to:
1. Provide thickness—that is, they need to attract a sufficient proportion of poten-
tial market participants to come together ready to transact with one another.
2. Overcome the congestion that thickness can bring, by providing enough time, or
by making transactions fast enough, so that market participants can consider enough
alternative possible transactions to arrive at satisfactory ones.
3. Make it safe to participate in the market as simply as possible, as opposed to
transacting outside of the marketplace, or engaging in strategic behavior that reduces
overall welfare.
I’ll also remark in passing on some other lessons we have started to learn,
namely that:
4. Some kinds of transactions are repugnant, and this can be an important con-
straint on market design.
And, on a methodological note, that:
5. Experiments can play a role, in diagnosing and understanding market failures
and successes, in testing new designs, and in communicating results to policy makers.
This paper will be organized as follows. Section 1 will describe some of the rel-
evant history of markets for new doctors, which at different periods had to deal
with each of the problems of maintaining thickness, dealing with congestion, and
making it safe to participate straightforwardly in the market. In the subsequent
sections I’ll discuss markets in which these problems showed up in different ways.
Section 2 will review the recent design of regional kidney exchanges in the
United States, in which the initial problem was establishing thickness, but in which
problems of congestion, and lately, making it safe for transplant centers to partic-
ipate, have arisen. This is also the market most shaped by the fact that many peo-
ple find some kinds of transactions repugnant: In particular, buying and selling
kidneys for transplantation is illegal in most countries. So, unlike the several labor
markets I discuss in this essay, this market operates entirely without money, which
will cast into clear focus how the “double coincidence of wants” problems that are
most often solved with money can be addressed with computer technology (and
will highlight why these problems are difficult to solve even with money, in mar-
kets like labor markets in which transactions are heterogeneous).
Section 3 will review the design of the school choice systems for New York City
high schools (in which congestion was the immediate problem to be solved), and
the design of the new public school choice system in Boston, in which making it
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What Have We Learned from Market Design?
safe to participate straightforwardly was the main issue. These allocation systems
also operate without money.
Section 4 will discuss recent changes in the market for American gastroenterol-
ogists, who wished to adopt the kind of clearinghouse organization already in
place for younger doctors, but who were confronted with some difficulties in mak-
ing it safe for everyone to change simultaneously from one market organization to
another. This involved making changes in the rules of the decentralized market
that would precede any clearinghouse even once it was adopted.
This will bring us naturally to a discussion of changes recently made in the
decentralized market for new economists in the United States.
1. MARKETS FOR NEW DOCTORS IN THE UNITED STATES,
CANADA, AND BRITAIN3
The first job American doctors take after graduating from medical school is called
a residency. These jobs are a big part of hospitals’ labor force, a critical part of
physicians’ graduate education, and a substantial influence on their future careers.
From 1900 to 1945, one way that hospitals competed for new residents was to try
to hire residents earlier than other hospitals. This moved the date of appointment
earlier, first slowly and then quickly, until by 1945 residents were sometimes being
hired almost two years before they would graduate from medical school and begin
work.
When I studied this in Roth (1984) it was the first market in which I had seen
this kind of “unraveling” of appointment dates, but today we know that unravel-
ing is a common and costly form of market failure. What we see when we study
markets in the process of unraveling is that offers not only become increasingly
early, but also become dispersed in time and of increasingly short duration. So not
only are decisions being made early (before uncertainty is resolved about workers’
preferences or abilities), but also quickly, with applicants having to respond to
offers before they can learn what other offers might be forthcoming.4 Efforts to
prevent unraveling are venerable; for example, Roth and Xing (1994) quote
Salzman (1931) on laws in various English markets from the 13th century con-
cerning “forestalling” a market by transacting before goods could be offered in the
market.5
In 1945, American medical schools agreed not to release information about
students before a specified date. This helped control the date of the market, but a
new problem emerged: hospitals found that if some of the first offers they made
were rejected after a period of deliberation, the candidates to whom they wished
to make their next offers had often already accepted other positions. This led hos-
pitals to make exploding offers to which candidates had to reply immediately,
before they could learn what other offers might be available, and led to a chaotic
market that shortened in duration from year to year, and resulted not only in
missed agreements but also in broken ones. This kind of congestion also has since
been seen in other markets, and in the extreme form it took in the American med-
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Alvin E. Roth
ical market by the late 1940s, it also constitutes a form of market failure (cf. Roth
and Xing 1997, and Avery, Jolls, Roth, and Posner 2007 for detailed accounts of
congestion in labor markets in psychology and law).
Faced with a market that was working very badly, the various American med-
ical associations (of hospitals, students, and schools) agreed to employ a central-
ized clearinghouse to coordinate the market. After students had applied to resi-
dency programs and been interviewed, instead of having hospitals make individ-
ual offers to which students had to respond immediately, students and residency
programs would instead be invited to submit rank order lists to indicate their pref-
erences. That is, hospitals (residency programs) would rank the students they had
interviewed, students would rank the hospitals (residency programs) they had
interviewed, and a centralized clearinghouse—a matching mechanism—would be
employed to produce a matching from the preference lists. Today this centralized
clearinghouse is called the National Resident Matching Program (NRMP).
Roth (1984) showed that the algorithm adopted in 1952 produced a matching
of students to residency programs that is stable in the sense defined by Gale and
Shapley (1962), namely that in terms of the submitted rank order lists, there was
never a student and a residency program that were not matched to each other but
would have mutually preferred to be matched to each other than to (one of) their
assigned match(es). However changes in the market over the years made this more
challenging.
For example, one change in the market had to do with the growing number of
married couples graduating from American medical schools and wishing to be
matched to jobs in the same vicinity. This hadn’t been a problem when the match
was created in the 1950’s, when virtually all medical students were men. Similarly,
the changing nature of medical specialization sometimes produced situations in
which a student needed to simultaneously be matched to two positions. Roth
(1984) showed that these kinds of changes can sometimes make it impossible to
find a stable matching, and indeed, an early attempt to deal with couples in a way
that did not result in a stable matching had made it difficult to attract high levels
of participation by couples in the clearinghouse.
In 1995, I was invited to direct the redesign of the medical match, in response
to a crisis in confidence that had developed regarding its ability to continue to
serve the medical market, and whether it appropriately served student interests. A
critical question was to what extent the stability of the outcome was important to
the success of the clearinghouse. Some of the evidence came from the experience
of British medical markets. Roth (1990, 1991) had studied the clearinghouses that
had been tried in the various regions of the British National Health Service, after
those markets unraveled in the 1960s. A Royal Commission had recommended
that clearinghouses be established on the American model, but since the American
medical literature didn’t describe in detail how the clearinghouse worked, each
region of the NHS adopted a different algorithm for turning rank order lists into
matches, and the unstable mechanisms had largely failed and been abandoned,
while the stable mechanisms succeeded and survived.6
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What Have We Learned from Market Design?
Of course, there are other differences between regions of the British health
service than how they organized their medical clearinghouses, so there was also
room for controlled experiments in the laboratory on the effects of stable and
unstable clearinghouse. Kagel and Roth (2000) report a laboratory experiment
that compared the stable clearinghouse adopted in Edinburgh with the unstable
one adopted in Newcastle, and showed that, holding all else constant, the differ-
ence in how the two clearinghouses were organized was sufficient to account for
the success of the Edinburgh clearinghouse and the failure of the unstable one in
Newcastle.
Roth and Peranson (1999) report on the new clearinghouse algorithm that we
designed, which aims to always produce a stable matching. It does so in a way that
makes it safe for students and hospitals to reveal their preferences.7 The new algo-
rithm has been used by the NRMP since 1998, and has subsequently been adopt-
ed by over three dozen labor market clearinghouses. The empirical evidence that
has developed in use is that the set of stable matchings is very seldom empty.
An interesting historical note is that the use of stable clearinghouses has been
explicitly recognized as part of a pro-competitive market mechanism in American
law. This came about because in 2002, sixteen law firms representing three former
medical residents brought a class-action antitrust suit challenging the use of the
matching system for medical residents. The theory of the suit was that the match-
ing system was a conspiracy to hold down wages for residents and fellows, in vio-
lation of the Sherman Antitrust Act.
Niederle and Roth (2003a) observed that, empirically, the wages of medical
specialties with and without centralized matching in fact do not differ.8 The case
was dismissed after the U.S. Congress passed new legislation in 2004 (contained in
Public Law 108-218), noting that the medical match is a pro-competitive market
mechanism, not a conspiracy in restraint of trade. This reflected modern research
on the market failures that preceded the adoption of the first medical clearing-
house in the 1950s, which brings us back to the main subject of the present paper.9
To summarize, the study and design of a range of clearinghouses in the 1980s
and 1990s made clear that producing a stable matching is an important contribu-
tor to a the success of a labor clearinghouse. For the purposes of the present paper,
note that such a clearinghouse can persistently attract the participation of a high
proportion of the potential participants, and when it does so it solves the problem
of establishing a thick market. A computerized clearinghouse like those in use for
medical labor markets also solves the congestion problem, since all the operations
of the clearinghouse can be conducted essentially simultaneously, in that the out-
come is determined only after the clearinghouse has cleared the market. And, as
mentioned briefly, these clearinghouses can be designed to make it safe for partic-
ipants to reveal their true preferences, without running a risk that by doing so they
will receive a worse outcome than if they had behaved strategically and stated some
other preferences.
In the following sections, we’ll see more about how the failure to perform these
tasks can cause markets to fail.
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Alvin E. Roth
2. KIDNEY EXCHANGE
Kidney transplantation is the treatment of choice for end-stage renal disease, but
there is a grave shortage of transplantable kidneys. In the United States there are
over 70,000 patients on the waiting list for cadaver kidneys, but in 2006 fewer than
11,000 transplants of cadaver kidneys were performed. In the same year, around
5,000 patients either died while on the waiting list or were removed from the list
as “Too Sick to Transplant.” This situation is far from unique to the United States:
In the UK at the end of 2006 there were over 6,000 people on the waiting list for
cadaver kidneys, and only 1,240 such transplants were performed that year.10
Because healthy people have two kidneys and can remain healthy with just one,
it is also possible for a healthy person to donate a kidney, and a live-donor kidney
has a greater chance of long-term success than does one from a deceased donor.
However, good health and good will are not sufficient for a donor to be able to give
a kidney to a particular patient: the patient and donor may be biologically incom-
patible because of blood type, or because the patient’s immune system has already
produced antibodies to some of the donor’s proteins. In the United States in 2006
there were 6,428 transplants of kidneys from living donors (in the UK there were
590).
The total supply of transplantable kidneys (from deceased and living donors)
clearly falls far short of the demand, but it is illegal in almost all countries to buy
or sell kidneys for transplantation. This legislation is the expression of the fact that
many people find the prospect of such a monetized market highly repugnant (see
Roth 2007a).
So, while a number of economists have devoted themselves to the task of
repealing or relaxing laws against compensating organ donors (see, e.g. Becker and
Elias 2007, and the discussion of Elias and Roth 2007), another task that faces a
market designer is how to increase the number of transplants subject to existing
constraints, including those that forbid monetary incentives.
It turns out that, prior to 2004, in just a very few cases, incompatible patient-
donor pairs and their surgeons had managed to arrange an exchange of donor kid-
neys (sometimes called “paired donation”), when the patient in each of two
incompatible patient-donor pairs was compatible with the donor in the other pair,
so that each patient received a kidney from the other’s donor. Sometimes a differ-
ent kind of exchange had also been accomplished, called a list exchange, in which
a patient’s incompatible donor donated a kidney to someone who (by virtue of
waiting a long time) had high priority on the waiting list for a cadaver kidney, and
in return the donor’s intended patient received high priority to receive the next
compatible cadaver kidney that became available. Prior to December 2004 only
five exchanges had been accomplished at the fourteen transplant centers in New
England. Some exchanges had also been accomplished at Johns Hopkins in
Baltimore, and among transplant centers in Ohio. So, these forms of exchange
were feasible and non-repugnant.11 Why had so very few happened?
One big reason had to do with the (lack of) thickness of the market, i.e. the size
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What Have We Learned from Market Design?
of the pool of incompatible patient-donor pairs who might be candidates for
exchange. When a kidney patient brought a potential donor to his or her doctor
to be tested for compatibility, donors who were found to be incompatible with
their patient were mostly just sent home. They were not patients themselves, and
often no medical record at all was retained to indicate that they might be available.
And in any event, medical privacy laws made these potential donors’ medical
information unavailable.
Roth, Sönmez, and Ünver (2004a) showed that in principle a substantial
increase in the number of transplants could be anticipated from an appropriately
designed clearinghouse that assembled a database of incompatible patient-donor
pairs. That paper considered exchanges with no restrictions on their size, and
allowed list exchange to be integrated with exchange among incompatible patient-
donor pairs. That is, exchanges could be a cycle of incompatible patient-donor
pairs of any size such that the donor in the first pair donated a kidney to the patient
in the second, the second pair donated to the third, and so on, until the cycle closed
with the last pair donating to the first. And pairs that would have been interested
in a list exchange in which they donated a kidney in exchange for high priority on
the cadaver waiting list could be integrated with the exchange pool by having them
donate to another incompatible pair in a chain that would end with donation to
the waiting list.
We sent copies of that paper to many kidney surgeons, and one of them, Frank
Delmonico (the medical director of the New England Organ Bank), came to lunch
to pursue the conversation. Out of that conversation, which grew to include many
others (and led to modifications of our original proposals), came the New England
Program for Kidney Exchange, which unites the fourteen kidney transplant centers
in New England to allow incompatible patient-donor pairs from anywhere in the
region to find exchanges with other such pairs.
For incentive and other reasons, all such exchanges have been done simultane-
ously, to avoid the possibility of a donor becoming unwilling or unable to donate
a kidney after that donor’s intended patient has already received a kidney from
another patient’s donor. So, one form that congestion takes in organizing kidney
exchanges is that multiple operating rooms and surgical teams have to be assem-
bled. (A simultaneous exchange between two pairs requires four operating rooms
and surgical teams, two for the nephrectomies that remove the donor kidneys, and
two for the transplantations that immediately follow. An exchange involving three
pairs involves six operating rooms and teams, etc.) Roth et al. (2004a) noted that
large exchanges would arise relatively infrequently, but could pose logistical diffi-
culties.
These logistical difficulties loomed large in our early discussions with sur-
geons, and out of those discussions came the analysis in Roth, Sönmez, and Ünver
(2005a) of how kidney exchanges might be organized if only two-way exchanges
were feasible. The problem of two-way exchanges can be modeled as a classic prob-
lem in graph theory, and, subject to the constraint that exchanges involve no more
than two pairs, efficient outcomes with good incentive properties can be found in
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Alvin E. Roth
computationally efficient ways. When the New England Program for Kidney
Exchange was founded in 2004 (Roth et al. 2005b), it used the matching software
that had had been developed to run the simulations in Roth et al. (2005a,b), and it
initially attempted only two-way matches (while keeping track of the potential
three-way matches that were missed). This was also the case when Sönmez, Ünver,
and I started running matches for the Ohio-based consortium of transplant cen-
ters that eventually became the Alliance for Paired Donation.12
However, some transplants are lost that could have been accomplished if three-
way exchanges were available. In Saidman, Roth, Sönmez, Ünver and Delmonico
(2006) and in Roth, Sönmez, and Ünver (2007), we showed that to get close to the
efficient number of transplants, the infrastructure to perform both two- and three-
way exchanges would have to be developed, but that once the population of avail-
able patient-donor pairs was large enough, few transplants would be missed if
exchanges among more than three pairs remained difficult to accomplish. Both the
New England Program for Kidney Exchange and the Alliance for Paired Donation
have since taken steps to be able to accommodate three-way as well as two-way
exchanges. Being able to deal with the (six operating room) congestion required to
accomplish three-way exchanges has the effect of making the market thicker, since
it creates more exchange possibilities.
As noted above, another way to make the market thicker is to integrate
exchange between pairs with list exchange, so that exchange chains can be consid-
ered, as well as cycles. This applies as well to how the growing numbers of non-
directed (altruistic) donors are used. A non-directed (ND) donor is someone who
wishes to donate a kidney without having a particular patient in mind (and whose
donor kidney therefore doesn’t require another donor kidney in exchange). The
traditional way to utilize such non-directed donors was to have them donate to
someone on the cadaver waiting list. But as exchanges have started to operate, it
has now become practical to have the ND donor donate to some pair that is will-
ing to exchange a kidney, and have that pair donate to someone on the cadaver
waiting list. Roth, Sönmez, Ünver, Delmonico and Saidman (2006) report on how
and why such exchanges are now done in New England. As in traditional exchange,
all surgeries are conducted simultaneously, so there are logistical limits on how
long a chain is feasible. But we noted that, when a chain is initiated by a ND donor,
it might be possible to relax the constraints that all parts of the exchange be simul-
taneous, because
if something goes wrong in subsequent transplants and the whole ND-
chain cannot be completed, the worst outcome will be no donated kid-
ney being sent to the waitlist and the ND donation would entirely bene-
fit the KPD [kidney exchange] pool. (Roth et al. 2006, p. 2704).
That is, if a conventional exchange were done in a non-simultaneous way, and if
the exchange broke down after some patient-donor pair had donated a kidney but
before they had received one, then that pair would not only have lost the promised
transplant, but also have lost a healthy kidney. In particular, the patient would no
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What Have We Learned from Market Design?
longer be in position to exchange with other incompatible patient-donor pairs.
But in a chain that begins with an ND donor, if the exchange breaks down before
the donation to some patient-donor pair has been made (because the previous
donor in the chain becomes unwilling or unable to donate), then the pair loses the
promised transplant, but is no worse off than they were before the exchange was
planned, and in particular they can still exchange with other pairs in the future. So,
while a non-simultaneous ND chain of donations could create an incentive to
break the chain, the costs of a breach would be less than in a pure exchange, and
so the benefits (in terms of longer chains) are worth exploring. The first such non-
simultaneous “Never Ending” Altruistic Donor (NEAD) chain was begun by the
Alliance for Paired Donation in July 2007. A week after the first patient was trans-
planted from an altruistic (ND) donor, her husband donated a kidney to another
patient, whose mother later donated her kidney to a third patient whose daughter
donated (simultaneously) to a fourth patient, whose sister is, as I write, now wait-
ing to donate to another patient whose incompatible donor will be willing to “pass
it forward” (Rees et al. 2007).13
To summarize the progress to date, the big problem facing kidney exchange
prior to 2004 was the lack of thickness in the market, so that incompatible patient-
donor pairs were left in the difficult search for what Jevons famously described as
a double coincidence of wants (Jevons 1876; Roth et al. 2007). By building a data-
base of incompatible patient-donor pairs and their relevant medical data, it
became possible to arrange more transplants, using a clearinghouse to maximize
the number (or some quality- or priority-adjusted number) of transplants subject
to various constraints. The state of the art now involves both two- and three-way
cyclical exchanges and a variety of chains, either ending with a donation to some-
one on the cadaver waiting list or beginning with an altruistic non-directed donor,
or both. While large simultaneous exchanges remain logistically infeasible, the fact
that almost all efficient exchanges can be accomplished in cycles of no more than
three pairs, together with clearinghouse technology that can efficiently find such
sets of exchanges, substantially reduces the problem of congestion in carrying out
exchanges. And, for chains that begin with non-directed donors, the early evidence
is that some relaxation of the incentive constraint that all surgeries be simultane-
ous seems to be possible.
There remain some challenges to further advancing kidney exchange that are
also related to thickness, congestion, and incentives.
Some patients have many antibodies, so that they will need very many possi-
ble donors to find one who is compatible. For that reason and others, it is unlike-
ly that purely regional exchanges, such as presently exist, will provide adequate
thickness for all the gains from exchange to be realized. Legislation has recently
been passed in the U.S. House and Senate to remove a potential legal obstacle to a
national kidney exchange.14 Aside from expanding kidney exchange to a national
scale, another way to increase the thickness of the market would be to make kid-
ney exchange available not just to incompatible patient-donor pairs, but also to
those who are compatible but might nevertheless benefit from exchange.15
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Regarding congestion, while some of the congestion in terms of actually con-
ducting transplants has been addressed, there is still congestion associated with the
time it takes to test for immunological incompatibility between patients and
donors who (based on available tests) are matched to be part of an exchange. That
is, antibody production can vary over time, and so a patient and donor who appear
to be compatible in the database may not in fact be. Because it now sometimes
takes weeks to establish this, during which time other exchanges may go forward,
sometimes exchanges are missed that could have been accomplished if the tests for
compatibility could be done more quickly, so that the overall pattern of exchanges
could have been adjusted.
And as regional exchanges have grown to include multiple transplant centers,
a new issue has come to the fore concerning how kidney exchange should be
organized to give transplant centers the incentive to inform the central exchange
of all of their incompatible patient-donor pairs. Consider a situation in which
transplant center A has two pairs that are mutually compatible, so that it could
perform an in-house exchange between these two pairs. If the mutual compatibil-
ities are as shown in Figure 1a, then if these two pairs exchange with each other,
only those two transplants will be accomplished. If instead the pairs from trans-
plant center A were matched with the pairs from the other centers, as shown in
Figure 1a, four transplants could be accomplished (via exchanges of pair A1 with
pair B, and pair A2 with C).
Double-headed arrows indicate that the connected pairs are compatible for
exchange, i.e. the patient in one pair is compatible with the donor in the other.
Pairs A1 and A2 are both from transplant center A, pairs B and C are from differ-
ent transplant centers. Transplant center A, which sees only its own pairs, can con-
duct an exchange among its pairs A1 and A2 since they are compatible, and, if it
does so, this will be the only exchange, resulting in two transplants. However, if in
Figure 1a transplant center A makes its pairs available for exchange with other cen-
ters, then the exchanges will be A1 with B and A2 with C, resulting in four trans-
plants. However, in Figure 1b the suggested exchange might be A1 with B, which
would leave the patient in A2 without a transplant. Faced with this possibility (and
not knowing if the situation is as in 1a or 1b), transplant center A might choose to
transplant A1 and A2 by itself, without informing the central exchange.
But, note that if the situation had been that of Figure 1b, then transplant cen-
ter A runs the risk that if it informs the central exchange of its pairs, then the rec-
ommended exchange will be between A1 and B, since B has high priority (e.g. B is
a child). This would mean that pair A2 did not get a kidney, as they would have if
A1 and A2 had exchanged inhouse. So, the situation facing transplant center A, not
knowing what pairs will be put forward for exchange by the other transplant cen-
ters, is that it can assure itself of doing two transplants for its patients in pairs A1
and A2, but it is not guaranteed two transplants if it makes the pairs available for
exchange and the situation is as in Figure 1b. If this causes transplant centers to
withhold those pairs they can transplant by themselves, then a loss to society
results in case the situation is as in Figure 1a. (In fact, if transplant centers with-
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What Have We Learned from Market Design?
Figures 1a and 1b. Double headed arrows indicate that the connected pairs are
compatible for exchange, i.e. the patient in one pair is compatible with the donor
in the other. Pairs A1 and A2 are both from transplant center A, pairs B and C are
from different transplant centers. Transplant center A, which sees only its own
pairs, can conduct an exchange among its pairs A1 and A2 since they are compat-
ible, and, if it does so, this will be the only exchange, resulting in two transplants.
However, if in Figure 1a transplant center A makes its pairs available for exchange
with other centers, then the exchanges will be A1 with B and A2 with C, resulting
in four transplants. However in Figure 1b the suggested exchange might be A1 with
B, which would leave the patient in A2 without a transplant. Faced with this pos-
sibility (and not knowing if the situation is as in 1a or 1b) transplant center A
might choose to transplant A1 and A2 by itself, without informing the central
exchange.
hold those pairs they can exchange in-house, then primarily hard-to-match pairs
will be offered for exchange, and the loss will be considerable.)
One remedy is to organize the kidney exchange clearinghouse in such a way
that guarantees center A that any pairs it could exchange in-house will receive
transplants.
This would allow the maximal number of transplants to be achieved in situa-
tion 1a, and it would mean that in situation 1b the exchange between A1 and A2
would be made (and so the high priority pair B would not participate in exchange,
just as they would not have if pairs A1 and A2 had not been put forward). This is
a bit of a hard discussion to have with surgeons who find it repugnant that, for
example, the child patient in pair B would receive lower priority than pairs A1 and
A2 just because of the accident that they were mutually compatible and were being
treated at the same transplant center. (Needless to say, if transplant center A with-
holds its pairs and transplants them in-house, they effectively have higher priority
than pair B, even if no central decision to that effect has been made.) But this is an
issue that will have to be resolved, because the full participation of all transplant
centers substantially increases the efficiency of exchange.
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Note that, despite all the detailed technical particulars that surround the
establishment of kidney exchange programs, and despite the absence of money in
the kidney exchange market, we can recognize some of the basic lessons of market
design that were also present in designing labor market clearinghouses. The first
issue was making the market thick, by establishing a database of patient-donor
pairs available to participate in exchange. Then issues of congestion had to be dealt
with, so that the clearinghouse could identify exchanges involving sufficiently few
pairs (initially two, now three) so that they could be accomplished simultaneous-
ly. Simultaneity is related to making sure that everyone involved in an exchange
never has an incentive not to go forward with it, but as exchanges have grown to
include multiple transplant centers, there are also incentive issues to be resolved in
making it safe for a transplant center to enroll all of its eligible pairs in the central
exchange.
3. SCHOOL CHOICE
Another important class of allocation problems in which no money changes hands
is the assignment of children to big-city public schools, based both on the prefer-
ences of students and their families, and on the preferences of schools, or on city
priorities. Because public school students must use whatever system local author-
ities establish, establishing a thick market is not the main problem facing such sys-
tems. (Although how well a school choice system works may influence how many
children ultimately attend city schools). But how well a school-choice system
works still has to do with how effectively it deals with congestion, and how safe it
makes it for families to straightforwardly reveal their preferences.
My colleagues and I were invited to help design the current New York City high
school choice program chiefly because of problems the old decentralized system
had in dealing with congestion. In Boston we were invited to help design the cur-
rent school choice system because the old system, which was itself a centralized
clearinghouse, did not make it safe for families to state their preferences.16 In both
Boston and New York City the newly designed systems incorporate clearinghous-
es to which students (and, in New York City, schools) submit preferences. Although
another alternative was considered in Boston, both Boston and New York City
adopted clearinghouses similar to the kinds of stable clearinghouses used in med-
ical labor markets (powered by a student-proposing deferred acceptance algo-
rithm), adapted to the local situations. For my purpose in the present paper I’ll
skip any detailed discussion of the clearinghouse designs, except to note that they
make it safe for students and families to submit their true preferences. Instead, I’ll
describe briefly what made the prior school choice systems congested or risky.17
In New York City, well over 90,000 students a year must be assigned to over 500
high school programs. Under the old system, students were asked to fill out a rank
order list of up to five programs. These lists were then copied and sent to the
schools. Subject to various constraints, schools could decide which of their appli-
cants to accept, waitlist, or reject. Each applicant received a letter from the New
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What Have We Learned from Market Design?
York City Department of Education with the decisions of the schools to which she
had applied, and applicants were allowed to accept no more than one offer, and
one waitlist. This process was repeated: after the responses to the first letter were
received, schools with vacant positions could make new offers, and after replies to
the second letter were received, a third letter with new offers was sent. Students
not assigned after the third step were assigned to their zoned schools, or assigned
via an administrative process. There was an appeals process, and an “over the
counter” process for assigning students who had changed addresses, or were oth-
erwise unassigned before school began.
Three rounds of processing applications to no more than five out of more than
500 programs by almost 100,000 students was insufficient to allocate all the stu-
dents. That is, this process suffered from congestion (in precisely the sense
explored in Roth and Xing 1997): not enough offers and acceptances could be
made to clear the market. Only about 50,000 students received offers initially,
about 17,000 of whom received multiple offers. And when the process concluded,
approximately 30,000 students had been assigned to a school that was nowhere on
their choice list.
Three features of this process particularly motivated the NYCDOE desire for a
new matching system. First were the approximately 30,000 students not assigned
to a school they had chosen. Second, students and their families had to be strate-
gic in their choices. Students who had a substantial chance of being rejected by
their true first choice school had to think about the risk of listing it first, since, if
one of their lower choice schools took students’ rankings into account in deciding
on admissions, they might have done better to list it first. (More on this in a
moment, in the discussion of Boston schools.) Finally, the many unmatched stu-
dents, plus those who may not have indicated their true preferences (and the con-
sequent instability of the resulting matching), gave schools an incentive to be
strategic: a substantial number of schools managed to conceal capacity from the
central administration, thus preserving places that could be filled later with stu-
dents unhappy with their assignments.
As soon as New York City adopted a stable clearinghouse for high school
matching (in 2003, for students entering high school in 2004), the congestion
problem was solved; only about 3,000 students a year have had to be assigned
administratively since then, down from 30,000 (and many of these are students
who for one reason or another fail to submit preference lists). In addition, in the
first three years of operation, schools learned that it was no longer profitable to
withhold capacity, and the resulting increase in the availability of places in desir-
able schools resulted in a larger number of students receiving their first choices,
second choices, and so forth from year to year. Finally, as submitted rank order lists
have begun to more reliably reflect true preferences, these have begun to be used
as data for the politically complex process of closing or reforming undesirable
schools (Abdulkadiroglu, Pathak, and Roth, 2005 and 2007).
In Boston, the problem was different. The old school choice system there made
it risky for parents to indicate their true first choice school if it was not their local
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school. The old system was simple in conception: parents ranked schools, and the
old Boston algorithm tried to give as many families as possible their first choice
school. In case the capacity of a school was less than the number of students who
ranked it first, ties were broken by giving priority to students who had siblings in
the school, or who lived within walking distance, or, finally, who had been assigned
a good lottery number. After these assignments were made, the old Boston algo-
rithm tried to match as many remaining students as possible with their second
choice school, and so on. The difficulty facing families was that, if they ranked a
popular school first and weren’t assigned to it, they might find that by the time
they were considered for their second choice school, it was already filled with peo-
ple who had ranked it first. So, a family that had a high priority for their second
choice school (e.g. because they lived close to it), and could have been assigned to
it if they had ranked it first, might no longer be able to get in if they ranked it sec-
ond.
As a consequence, many families were faced with difficult strategic decisions,
and some families devoted considerable resources to gathering relevant informa-
tion about the capacities of schools, how many siblings would be enrolling in
kindergarten, etc. Other families were oblivious to the strategic difficulties, and
sometimes suffered the consequences; if they listed popular schools for which they
had low priority, they were often assigned to schools they liked very little.
In Boston, the individual schools are not actors in the school choice process,
and so there was a wider variety of mechanisms to choose from than in New York.
My colleagues and I recommended two possibilities that were strategy-proof (in
the sense that they make it a dominant strategy for students and families to sub-
mit their true preferences), and which thus would make it safe for students to sub-
mit their true preferences (Abdulkadiroglu, Pathak, Sönmez, and Roth 2005 and
2007).18 This proved to be decisive in persuading the Boston School Committee to
adopt a new algorithm. Then Superintendent of Schools Thomas Payzant wrote, in
a 2005 memo to the School committee:
The most compelling argument for moving to a new algorithm is to
enable families to list their true choices of schools without jeopardizing
their chances of being assigned to any school by doing so.
Superintendent Payzant further wrote:
A strategy-proof algorithm levels the playing field by diminishing the
harm done to parents who do not strategize or do not strategize well.
Making the school choice system safe to participate in was critical in the decision
of Boston Public Schools to move from a clearinghouse that was not strategy-proof
to one that was. Different issues of safety were critical in the market for
Gastroenterologists, discussed next.
4. GASTROENTEROLOGISTS19
An American medical graduate who wishes to become a gastroenterologist first
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What Have We Learned from Market Design?
completes three years of residency in internal medicine, and then applies for a job
as a fellow in gastroenterology, a subspecialty of internal medicine.20 The market
for gastroenterology fellows was organized via a stable labor market clearinghouse
(a “match”) from 1986 through the late 1990s, after which the match was aban-
doned (following an unexpected shock to the supply and demand for positions in
1996; see Mckinney, Niederle, and Roth 2005). This provided an opportunity to
observe the unraveling of a market as it took place. From the late 1990s until 2006,
offers of positions were made increasingly far in advance of employment (moving
back to almost two years in advance, so that candidates were often being inter-
viewed early in their second year of residency). Offers also became dispersed in
time, and short in duration, so that candidates faced a thin market. One conse-
quence was that the market became much more local than it had been, with gas-
troenterology fellows more likely to be recruited at the same hospital at which they
had worked as a resident (Niederle and Roth 2003; Niederle, Proctor, and Roth
2006).
Faced with these problems, the various professional organizations involved in
the market for gastroenterology fellows agreed to try to resume using a centralized
clearinghouse, to be operated one year in advance of employment. However, this
raised the question of how to make it safe for program directors and applicants to
wait for the clearinghouse, which would operate almost a year later than hiring had
been accomplished in the immediate past. Program directors who wanted to wait
for the match worried that if their competitors made early offers, then applicants
would lose confidence that the match would work and consequently would accept
those early offers. That is, in the first year of a match, applicants might not yet feel
safe to reject an early offer in order to wait for the match. Program directors who
worried about their competitors might thus be more inclined to make early offers
themselves.
The gastroenterology organizations did not feel able to directly influence the
hiring behavior of programs that might not wish to wait for the match.
Consequently, we recommended that policies be adopted that would allow appli-
cants who wished to wait for the match to more effectively deal with early offers
themselves (Niederle, Proctor, and Roth 2006). We modeled our recommendation
on the policies in place in the American market for graduate school admission. In
this market, a policy (adopted by the large majority of universities) states that
offers of admission and financial support to graduate students should remain open
until April 15:
Students are under no obligation to respond to offers of financial sup-
port prior to April 15; earlier deadlines for acceptance of such offers vio-
late the intent of this Resolution. In those instances in which a student
accepts an offer before April 15, and subsequently desires to withdraw
that acceptance, the student may submit in writing a resignation of the
appointment at any time through April 15. However, an acceptance given
or left in force after April 15 commits the student not to accept another
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Alvin E. Roth
offer without first obtaining a written release from the institution to
which a commitment has been made. Similarly, an offer by an institution
after April 15 is conditional on presentation by the student of the written
release from any previously accepted offer. It is further agreed by the
institutions and organizations subscribing to the above Resolution that a
copy of this Resolution should accompany every scholarship, fellowship,
traineeship, and assistantship offer.
(See http://www.cgsnet.org/portals/0/pdf/CGSResolutionJune2005.pdf.)
This of course makes early exploding offers much less profitable. A program that
might be inclined to insist on an against-the-rules early response is discouraged
from doing so, because they can’t “lock up” a student to whom they make such an
offer, because accepting such an offer does not prevent the student from later
receiving and accepting a preferred offer.21
A modified version of
this policy was adopted by all four major
Gastroenterology professional organizations, the American Gastroenterological
Association (AGA), the American College of Gastroenterology (ACG), the
American Society for Gastrointestinal Endoscopy (ASGE), and the American
Association for the Study of Liver Diseases (AASLD), regarding offers made before
the (new) match. Their resolution states, in part,
The general spirit of this resolution is that each applicant should have an
opportunity to consider all programs before making a decision and be
able to participate in the Match. … It therefore seeks to create rules that
give both programs and applicants the confidence that applicants and
positions will remain available to be filled through the Match and not
withdrawn in advance of it. This resolution addresses the issue that some
applicants may be persuaded or coerced to make commitments prior to,
or outside of, the Match. … Any applicant may participate in the match-
ing process … by … resigning the accepted position if he/she wishes to
submit a rank order list of programs … The spirit of this resolution is to
make it unprofitable for program directors to press applicants to accept
early offers, and to give applicants an opportunity to consider all offers.
The gastroenterology match for 2007 fellows was held June 21, 2006, and succeed-
ed in attracting 121 of the 154 eligible fellowship programs (79%). 98% of the
positions offered in the match were filled through the match, and so it appears that
the gastroenterology community succeeded in making it safe to participate in the
match, and thus in changing the timing and thickness of the market, while using a
clearinghouse to avoid congestion.
The policies adopted by gastroenterologists prior to their match make clear
that market design in this case consists not only of the “hardware” of a centralized
clearinghouse, but also rules and understandings that constitute elements of “mar-
ket culture.” This leads us naturally to consider how issues of timing, thickness, and
congestion are addressed in a market that operates without any centralized clear-
inghouse.
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What Have We Learned from Market Design?
5. MARKET FOR NEW ECONOMISTS
The North American market for new Ph.D.s in economics is a fairly decentralized
market, with some centralized marketplace institutions, most of them established
by the American Economics Association (AEA).22 Some of these institutions are of
long standing, while others have only recently been established. Since 2005 the
American Economic Association has had an Ad Hoc Committee on the Job
Market, charged with considering ways in which the market for economists might
be facilitated.23
Roughly speaking, the main part of this market begins each year in the early
fall, when economics departments advertise for positions. Positions may be adver-
tised in many ways, but a fairly complete picture of the academic part of the mar-
ket can be obtained from the AEA’s monthly publication, Job Openings for
Economists (JOE), which provides a central location for employers to advertise and
for job seekers to see who is hiring (http://www.aeaweb.org/joe/). Graduate stu-
dents nearing completion of their Ph.D.s answer the ads by sending applications,
which are followed by letters of reference, most typically from their faculty advi-
sors.24
Departments often receive several hundred applications (because it is easy for
applicants to apply to many schools), and junior recruiting committees work
through the late fall to read applications, papers, and letters, and to seek informa-
tion through informal networks of colleagues, to identify small subsets of appli-
cants they will invite for half-hour preliminary interviews at the annual AEA meet-
ing in early January. This is part of a very large annual set of meetings of the Allied
Social Science Associations, which consist of the AEA and almost 50 smaller asso-
ciations. Departments reserve suites for interviewing candidates at the meeting
hotels, and young economists in new suits commute up and down the elevators,
from one interview to another, while recruiting teams interview candidates one
after the other, trading off with their colleagues throughout long days. While the
interviews in hotel suites are normally pre-arranged in December, the meetings
also host a spot market, in a large hall full of tables, at which both academic and
non-academic employers can arrange at the last minute to meet with candidates.
The spot market is called the Illinois Skills Match (because it is organized in con-
junction with the Illinois Department of Employment Security).
These meetings make the early part of the market thick, by providing an easy
way for departments to quickly meet lots of candidates, and by allowing candidates
to efficiently introduce themselves to many departments. This largely controls the
starting time of the market.25 Although a small amount of interviewing goes on
beforehand, it is quite rare to hear of departments that make offers before the
meetings, and even rarer to hear of departments pressing candidates for replies
before the meetings.26
But while the preliminary-interviewing part of the market is thick, it is con-
gested. A dedicated recruiting committee might possibly be able to interview thir-
ty candidates, but not a hundred, and hence can meet only a small fraction of the
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available applicants. Thus the decision of who to interview at the meetings is an
important one, and for all but elite schools a strategic one as well. That is, while a
relatively few departments at the top of the pecking order can simply interview the
candidates they like best, a lower ranked department that uses all its interview slots
to interview the same candidates who are interviewed by the elite schools is likely
to find that it cannot convert its initial interviews into new faculty hires. Thus,
most schools have to give at least some thought not only to how much they like
each candidate, but to how likely it is that they can successfully hire that candidate.
This problem is only made more difficult by the fact that students can easily apply
for many positions, so the act of sending an application does not itself send a
strong signal of how interested the candidate might be. The problem may be par-
ticularly acute for schools in somewhat special situations, such as liberal arts col-
leges, or British and other non-American universities in which English is the lan-
guage of instruction, since these may be concerned that some students who strong-
ly prefer positions at North American research universities may apply to them only
as insurance.
Following the January meetings, the market moves into a less organized phase,
in which departments invite candidates for “flyouts,” day-long campus visits dur-
ing which the candidate will make a presentation and meet a substantial portion
of the department faculty and perhaps a dean. Here too, the market is congested,
and departments can fly out only a small subset of the candidates they have inter-
viewed at the meetings, because of the costs of various sorts.27 This part of the
market is less well coordinated in time: some departments host flyouts already in
January, while others wait until later. Some departments try to complete all their
flyouts before making any offers, while others make offers while still interviewing.
And some departments make offers that come with moderate deadlines of two
weeks or so, which may nevertheless force candidates to reply to an offer before
knowing what other offers might be forthcoming.28
By late March, the market starts to become thin. For example, a department
that interviewed twenty people at the meetings, invited six for flyouts, made offers
to two, and was rejected by both may find that it is now difficult to assess which
candidates who it did not interview may still be on the market. Similarly, candi-
dates whose interviews and flyouts did not result in job offers may find it difficult
to know which departments are still actively searching. To make the late part of the
market thicker, the first thing our AEA job market committee did was to institute
a “scramble” webpage through which departments with unfilled positions and
applicants still on the market could identify each other (see Guide to the
Economics
at
http://www.aeaweb.org/joe/scramble/guide.pdf.) For simplicity, the scramble web
page was passive (i.e. it didn’t provide messaging or matching facilities), it simply
announced the availability of any applicant or department who chose to register.
The scramble webpage operated for the first time in the latter part of the 2005-
2006 job market, when it was open for registrants between March 15 and 20, and
was used by 70 employers and 518 applicants (of which only about half were new,
Scramble
Market
Job
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What Have We Learned from Market Design?
2006 Ph.D.s). It was open only briefly, so that its information provided a snapshot
of the late market, which didn’t have to be maintained to prevent the information
from becoming stale.
The following year our committee sought to alleviate some of the congestion
surrounding the selection of interview candidates at the January meetings by
introducing a signaling mechanism through which applicants could have the AEA
transmit to no more than two departments a signal indicating their interest in an
interview at the meetings. The idea was that by limiting applicants to two signals,
each signal would have some information value that might not be contained mere-
ly in the act of sending a department an application, and that this information
might be helpful in averting coordination failures.29
The signaling mechanism operated for the first time in December 2006, and
about 1,000 people used it to send signals.30
Both the scramble and the signaling facility attracted many users, although it
will take some time to assess their performance. Like the JOE and the January
meetings, they are marketplace institutions that attempt to help the market pro-
vide thickness and deal with congestion.
6. DISCUSSION
In the tradition of market design, I have concentrated on the details of particular
markets, from medical residents and fellows to economists, and from kidney
exchange to school choice. But, despite their very different details, these markets,
like others, struggle to provide thickness, to deal with the resulting congestion, and
to make it safe and relatively simple to participate. While the importance of thick
markets has been understood by economists for a long time, my impression is that
issues of congestion, safety, and simplicity were somewhat obscured when the pro-
totypical market was thought of as a market for a homogeneous commodity.31
Thickness in a market has many of the properties of a public good, so it is not
surprising that it may be hard to provide it efficiently, and that free riders have to
be resisted, whether in modern markets with a tendency to unravel, or in medieval
markets with rules against “forestalling.” Notice that providing thickness blurs the
distinction between centralized and decentralized markets, since marketplaces—
from traditional farmers’ markets, to the AEA job market meetings, to the New
York Stock Exchange—provide thickness by bringing many participants to a cen-
tral place. The possibility of having the market perform other centralized servic-
es, as clearinghouses or signaling mechanisms do, has only grown now that such
central places can also be electronic, on the Internet or elsewhere. And issues of
thickness become if anything more important when there are network externali-
ties or other economies of scope.32
Congestion is especially a problem in markets in which transactions are het-
erogeneous, and offers cannot be made to the whole market. If transactions take
even a short time to complete, but offers must be addressed to particular partici-
pants (as in offers of a job, or to purchase a house), then someone who makes an
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offer runs the risk that other opportunities may disappear while the offer is being
considered. And even financial markets (in which offers can be addressed to the
whole market) experience congestion on days with unusually heavy trading and
large price movements, when prices may change significantly while an order is
being processed, and some orders may not be able to be processed at all. As we have
seen, when individual participants are faced with congestion, they may react in
ways that damage other properties of the market, e.g. if they try to gain time by
transacting before others.33
Safety and simplicity may constrain some markets differently than others.
Parents engaged in school choice may need more of both than, say, bidders in very
high value auctions of the sort that allow auction experts to be hired as consult-
ants. But even in billion dollar spectrum auctions, there are concerns that risks to
bidders may deter entry, or that unmanageable complexity in formulating bids and
assessing opportunities at each stage may excessively slow the auction.34
Somewhere in between, insider trading laws with criminal penalties help make
financial markets safe for non-insiders to participate. And if it is risky to partici-
pate in the market, individual participants may try to manage their risk in ways
that damage the market as a whole, such as when transplant centers withhold
patients from exchange, or employers make exploding offers before applicants can
assess the market, or otherwise try to prevent their trading counterparties from
being able to receive other offers.35
In closing, market design teaches us both about the details of market institu-
tions and about the general tasks markets have to perform. Regarding details, the
word “design” in “market design” is not only a verb, but also a noun, so economists
can help to design some markets, and profitably study the design of others. And I
have argued in this essay that among the general tasks markets have to perform,
difficulties in providing thickness, dealing with congestion, and making participa-
tion safe and simple are often at the root of market failures that call for new mar-
ket designs.
I closed my 1991 EJ article (quoted in the introduction) on a cautiously opti-
mistic note that, as a profession, we would rise to the challenge of market design,
and that doing so would teach us important lessons about the functioning of mar-
kets and economic institutions. I remain optimistic on both counts.
Acknowledgements
The work I report here is a joint effort of many colleagues and coauthors. I pay
particular attention here to work with Atila Abdulkadiroglu, Muriel Niederle,
Parag Pathak, Tayfun Sönmez, and Utku Ünver.
I’ve also benefited from many
conversations on this topic with Paul Milgrom (including two years teaching
together a course on Market Design). This work has been supported by grants
from the NSF to the NBER.
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What Have We Learned from Market Design?
Endnotes
1. Roth and Peranson (1999).
2. See e.g. Cramton (1997), Milgrom (2000), Wilson (2002), and, particularly, Milgrom
(2004)Following that literature to the present would involve looking into modern designs for
package auctions, see e.g. Cramton, Shoham, and Steinberg (2006), and Milgrom (2007).
3. The history of the American medical market given here is extracted from more detailed accounts
in Roth (1984, 2003, 2007).
4. On the costs of such unraveling in some markets for which unusually good data have been avail-
able, see Niederle and Roth (2003b) on the market for gastroenterology fellows, and Fréchette,
Roth, and Ünver (2007) on the market for post-season college football bowls. For some other
recent unraveled markets, see Avery, Fairbanks, and Zeckhauser (2003) on college admissions; and
Avery, Jolls, Posner, and Roth (2001) on appellate court clerks. For a line of work giving theoreti-
cal insight into some possible causes of unraveling, see Li and Rosen (1998), Li and Suen (2000),
Suen (2000), and Damiano et al. (2005).
5. “Thus at Norwich no one might forestall provisions by buying, or paying ‘earnest money’ for them
before the Cathedral bell had rung for the mass of the Blessed Virgin; at Berwick-on-Tweed no
one was to buy salmon between sunset and sunrise, or wool and hides except at the market-cross
between 9 and 12; and at Salisbury persons bringing victuals into the city were not to sell them
before broad day.” Unraveling could be in space, as well as in time. Salzman also reports (p132)
that under medieval law markets could be prevented from being established too near to an exist-
ing market, and also, for markets on rivers, nearer to the sea. “Besides injury through mere prox-
imity, and anticipation in time, there might be damage due to interception of traffic… “Such inter-
ception was more usual in the case of water-borne traffic. In 1233 Eve de Braose complained that
Richard fitz- Stephen had raised a market at Dartmouth to the injury of hers at Totnes, as ships
which ought to come to Totnes were stopped at Dartmouth and paid customs there. No decision
was reached, and eight years later Eve’s husband, William de Cantelupe, brought a similar suit
against Richard’s son Gilbert. The latter pleaded that his market was on Wednesday and that at
Totnes on Saturday; but the jury said that the market at Dartmouth was to the injury of Totnes,
because Dartmouth lies between it and the sea, so that ships touched there and paid toll instead
of going to Totnes; and also that cattle and sheep which used to be taken to Totnes market were
now sold at Dartmouth; the market at Dartmouth was therefore disallowed.”
6. The effects of instability were different in Britain than in the U.S., because positions in Britain
were assigned by the National Health Service, and so students were not in a position to receive
other offers (and decline the positions they were matched to) as they were in the U.S. Instead, in
Britain, students and potential employers acted in advance of unstable clearinghouses. For exam-
ple Roth (1991) reports that in Newcastle and Birmingham, it became common for students and
consultants (employers) to reach agreement in advance of the match, and then submit only each
other’s name on their rank order lists.
7. Abstracting somewhat from the complexities of the actual market, the Roth-Peranson algorithm
is a modified student-proposing deferred acceptance algorithm (Gale and Shapley, 1962, see Roth,
2007b). In simple markets, this makes it a dominant strategy for students to state their true pref-
erences (see Roth, 1982, 1985, Roth and Sotomayor, 1990). Although it can’t be made a dominant
strategy for residency programs to state their true preferences (Roth, 1985; Sonmez, 1997), the fact
that the medical market is large turns out to make it very unlikely that residency programs can do
any better than to state their true preferences. This was shown empirically in Roth and Peranson
(1999), and has more recently been explained theoretically by Immorlica and Mahdian (2005) and
Kojima and Pathak (2007).
8. Bulow and Levin (2006) sketch a simple model of one-to-one matching in which a centralized
clearinghouse, by enforcing impersonal wages (i.e. the same wage for any successful applicant)
could cause downward pressure on wages (see also Kamecke 1998). Subsequent analysis suggests
more skepticism about any downward wage effects in actual medical labor markets. See, for exam-
ple, Kojima (2007) which shows that the Bulow-Levin results don’t follow in a model in which
hospitals can employ more than one worker, and Niederle (forthcoming) who shows that the
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Alvin E. Roth
results don’t follow in a model that includes the facility that the medical match offers to hospitals
that wish to fill more of one kind of position if they fail to fill enough positions of another kind.
Crawford (forthcoming) considers how the deferred acceptance algorithm of Kelso and Crawford
(1982) could be adapted to adjust personal wages in a centralized clearinghouse, see also Artemov
(forthcoming).
9. See Roth (2003). The law states in part: “Congress makes the following findings: For over 50 years,
most United States medical school seniors and the large majority of graduate medical education
programs (popularly known as `residency programs’) have chosen to use a matching program to
match medical students with residency programs to which they have applied. … “Before such
matching programs were instituted, medical students often felt pressure, at an unreasonably early
stage of their medical education, to seek admission to, and accept offers from, residency programs.
As a result, medical students often made binding commitments before they were in a position to
make an informed decision about a medical specialty or a residency program and before residen-
cy programs could make an informed assessment of students’ qualifications. This situation was
inefficient, chaotic, and unfair and it often led to placements that did not serve the interests of
either medical students or residency programs.
“The original matching program, now operated by the independent non-profit National Resident
Matching Program and popularly known as `the Match’, was developed and implemented more
than 50 years ago in response to widespread student complaints about the prior process. …
“The
Match uses a computerized mathematical algorithm… to analyze the preferences of students and
residency programs and match students with their highest preferences from among the available
positions in residency programs that listed them. Students thus obtain a residency position in the
most highly ranked program on their list that has ranked them sufficiently high among its pref-
erences. … “Antitrust lawsuits challenging the matching process, regardless of their merit or lack
thereof, have the potential to undermine this highly efficient, pro-competitive, and long-standing
process. The costs of defending such litigation would divert the scarce resources of our country’s
teaching hospitals and medical schools from their crucial missions of patient care, physician train-
ing, and medical research. In addition, such costs may lead to abandonment of the matching
process, which has effectively served the interests of medical students, teaching hospitals, and
patients for over half a century. “… It is the purpose of this section to—confirm that the antitrust
laws do not prohibit sponsoring, conducting, or participating in a graduate medical education
residency matching program, or agreeing to do so; and ensure that those who sponsor, conduct
or participate in such matching programs are not subjected to the burden and expense of defend-
ing against litigation that challenges such matching programs under the antitrust laws.”
10. For U.S. data see http://www.optn.org/data/ (accessed 8/13/07).
For UK data, see
http://www.uktransplant.org.uk/ukt/statistics/calendar_year_statistics/pdf/yearly_statis-
tics_2006.pdf (accessed 8/13/07).
11. See Rapoport 1986, Ross et al. 1997, Ross and Woodle 2000, for some early discussion of the pos-
sibility of kidney exchange, and Delmonico 2004, and Montgomery et al. 2005 for some early
reports of successful exchanges.
12. The New England Program for Kidney Exchange has since integrated our software into theirs,
and conducts their own matches. The Alliance for Paired Donation originally used our software,
and as the size of the exchange pool grew larger, the basic (integer programming) algorithms
were rewritten in software that can handle much larger numbers of pairs, by Abraham, Blum,
and Sandholm (2007). Roth et al. (2005a,b) were also widely distributed to transplant centers (as
working papers in 2004). The active transplant program at Johns Hopkins has also begun to use
software similar in design to that in Roth et al. (2004b, 2005a), to optimize pairwise matches, see
Segev et al. (2005).
13. Increasing the number of patients who benefit from the altruism of a non-directed donor may
also increase the willingness of such donors to come forward. After recent publicity of the first
NEAD chain on ABC World News Tonight [see http://utoledo.edu/utcommcenter/kidney/], the
Alliance for Paired Donation has had over 100 registrations on its website of people who are
offering to be altruistic living non-directed donors (Rees, personal communication).
140
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What Have We Learned from Market Design?
14. The proposed bill (H.R. 710 introduced on 1/29/07 and passed in the House on 3/7/07 and S.
487 introduced on 2/1/07 and passed in the Senate February 15, 2007) is ‘’To amend the National
Organ Transplant Act to clarify that kidney paired donations shall not be considered to involve
the transfer of a human organ for valuable consideration.’’. Kidney exchange is also being organ-
ized in the UK; see
out on July 4, 2007 (see the BBC report at
15. For example, a compatible middle aged patient-donor pair, and an incompatible patient-donor
pair in which the donor is a 25 year old athlete could both benefit from exchange. Aside from
increasing the number of pairs available for exchange, this would also relieve the present short-
age of donors with blood type O in the kidney exchange pool, caused by the fact that O donors
are only rarely incompatible with their intended recipient. Simulations on the robust effects of
adding compatible patient-donor pairs to the exchange pool are found in Roth, Sönmez and
Ünver (2004a and 2005b), and in Gentry et al. 2007.
16. The invitation to meet with Boston Public Schools came after a newspaper story recounted the
difficulties with the Boston system, as described in Abdulkadiro?lu and Sönmez 2003, For sub-
sequent explorations of the old Boston system, see Chen and Sonmez 2006, Ergin and Sonmez
2006, Pathak and Sonmez 2007, Abdulkadiro?lu, Pathak, Roth, and Sönmez (2007).
17. The description of the situation in New York is from Abdulkadiro?lu, Pathak and Roth (2005);
for Boston see Abdulkadiro?lu and Sönmez (2003), Abdulkadiro?lu, Pathak, Roth, and Sönmez,
(2005, 2007).
18. In addition to the student proposing deferred acceptance algorithm that was ultimately adopt-
ed, we proposed a variation of the “top trading cycles” algorithm originally explored in Shapley
and Scarf (1974), which was shown to be strategy-proof in Roth (1982b), and which was extend-
ed, and explored in a school choice context, in Abdulkadiro?lu and Sönmez (1999, 2003).
19. A much more thorough treatment of the material in this section is given in Niederle and Roth
(2008).
20. The American system of residents and fellows is similar but not precisely parallel to the system
in the UK of house officers and registrars, which has also recently faced some problems of mar-
ket design.
21. Niederle and Roth (2007) study in the laboratory the impact of the rules that govern the types
of offers that can be made (with or without a very short deadline) and whether applicants can
change their minds after accepting an early offer. In the uncongested laboratory environments
we studied, eliminating the possibility of making exploding offers, or making early acceptances
non-binding, prevents the markets from operating inefficiently early.
22. This is not a closed market, as economics departments outside North America also hire in this
market, and as American economics departments and other employers often hire economists
educated elsewhere. But a large part of the market involves new American Ph.D.s looking for aca-
demic positions at American colleges and universities. See Cawley (2006) for a description of the
market aimed at giving advice to participants, and Siegfried and Stock (2004) for some descrip-
tive statistics.
23. Its members are Alvin E. Roth (chair), John Cawley, Philip Levine, Muriel Niederle, and John
Siegfried, and the committee has received assistance from Peter Coles, Ben Greiner, and Jenna
Kutz.
24. These applications are usually sent through the mails, but now often also via email and on web
pages set up to receive them. Applicants typically apply to departments individually, by sending
a letter accompanied by their curriculum vitae and job market paper(s) and followed by their let-
ters of reference.
25. The situation is different in Europe, for example, where hiring is more dispersed in time. In an
attempt to help create a thicker European market, the Royal Economic Society held a “PhD pre-
sentations event” for the first time in late January (2006), Felli and Sutton (2006) remark that
“The issue of timing, unsurprisingly, attracted strong comment…”
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Alvin E. Roth
26. While the large scale interviewing at the annual meetings has not been plagued by gradual unrav-
eling, some parts of the market have broken off.
In the 1950’s, for example, the American
Marketing Association used to conduct job market meetings at the time of the ASSA meetings,
but for a long time it has held its job market in August, a year before employment will begin, with
the result that assistant professors of marketing are often hired before having made as much
progress on their dissertations as is the case for economists (Roth and Xing, 1994).
27. These costs arise both not only because budgets for airfares and hotels may be limited, but also
because faculties’ faculties quickly become fatigued after too many seminars and recruiting din-
ners.
28. In 2002 and 2003 Georg Weizsacker, Muriel Niederle, Dorothea Kubler and I conducted surveys
of economics departments regarding their hiring practices, asking in particular about what kinds
of deadlines, if any, they tended to give when they made offers to junior candidates. Loosely
speaking, the results suggested that departments that were large, rich, and elite often did not give
any deadlines (and sometimes were able to make all the offers they wanted to make in parallel,
so that they would not necessarily make new offers upon receiving rejections). Less well endowed
departments often gave candidates deadlines, although some were in a position to extend the
deadline for candidates who seemed interested but needed more time.
29. For a simple conceptual example of how a limited number of signals can improve welfare, con-
sider a market with two applicants and two employers, in which there is only time for each
employer to make one offer, and each applicant can take at most one position. Even if employ-
ers and applicants wish only to find a match, and have no preference with whom they match,
there is a chance for signals to improve welfare by reducing the likelihood of coordination fail-
ure. In the absence of signals, there is a symmetric equilibrium in which each firm makes an
offer to each worker with equal probability, and at this equilibrium, half the time one worker
receives two offers, and so one worker and one employer remain unmatched. If the workers are
each permitted to send one signal beforehand, and if each worker sends a signal to each firm with
equal probability, then if firms adopt the strategy of making an offer to an applicant who sends
them a signal, the chance of coordination failure is reduced from one half to one quarter. If
workers have preferences over firms, the welfare gains from reducing coordination failure can be
even larger. For recent treatments of signaling and coordination, see Coles and Niederle (2007),
Lee and Schwarz (2007a,b), Lien (2007), and Stack (2007). See also Abdulkadiroglu, Che, and
Yasuda (2007), who discuss allowing applicants to influence tie-breaking by signaling their pref-
erences in a centralized clearinghouse that uses a deferred acceptance algorithm.
30. The document “Signaling
in
for
Interviews
Job Market,”
the Economics
at
http://www.aeaweb.org/joe/signal/signaling.pdf includes the following bits of advice: “Advice to
Departments: Applicants can only send two signals, so if a department doesn’t get a signal from
some applicant, that fact contains almost no information. (See advice to applicants, below, which
suggests how applicants might use their signals). But because applicants can send only two sig-
nals, the signals a department does receive convey valuable information about the candidate’s
interest. A department that has more applicants than it can interview can use the signals to help
break ties for interview slots, for instance. Similarly, a department that receives applications from
some candidates who it thinks are unlikely to really be interested (but might be submitting many
applications out of excessive risk aversion) can be reassured of the candidate’s interest if the
department receives one of the candidate’s two signals. A department that receives a signal from
a candidate will likely find it useful to open that candidate’s dossier and take one more look,
keeping in mind that the candidate thought it worthwhile to send one of his two signals to the
department. Advice to Applicants: The two signals should not be thought of as indicating your
top two choices. Instead, you should think about which two departments that you are interested
in would be likely to interview you if they receive your signal, but not otherwise (see advice to
departments, above). You might therefore want to send a signal to a department that you like but
that might otherwise doubt whether they are likely to be able to hire you. Or, you might want to
send a signal to a department that you think might be getting many applications from candidates
somewhat similar to you, and a signal of your particular interest would help them to break ties.
142
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What Have We Learned from Market Design?
You might send your signals to departments to whom you don’t have other good ways of signal-
ing your interest.
31. Establishing thickness, in contrast, is a central concern even in financial markets, see for exam-
ple the market design (“market microstructure”) discussions of how markets are organized at
their daily openings and closings, e.g. Biais, Hillion and Spatt 1999 on the opening call auction
in the Paris Bourse and Kandel, Rindi, and Bosetti 2007 on the closing call auctions in the Borsa
Italiana and elsewhere.
32. Thickness has received renewed attention in the context of software and other “platforms” that
serve some of the functions of marketplaces, such as credit cards, which require large numbers
of both consumers and merchants (see e.g. Evans and Schmalensee, 1999 and Evans, Hagiu and
Schmalensee, 2006; and see Rochet and Tirole 2006, who concentrate on how the price structure
for different sides of the market may be an important design feature.
33. The fact that transactions take time may in some markets instead inspire participants to try to
transact very late, near the market close, if that will leave other participants with too little time
to react. See e.g. the discussion of very late bids (“sniping”) on eBay auctions in Roth and
Ockenfels (2002) and Ariely, Ockenfels, and Roth (2005).
34. Bidder safety lies behind discussions both of the “winner’s curse” and collusion (cf. Kagel and
Levin 2002, Klemperer, 2004) as well as of the “exposure problem” that faces bidders who wish
to assemble a package of licences in auctions that do not allow package bidding (see e.g. Milgrom
2007). And simplicity of the auction format has been addressed in experiments prior to the con-
duct of some FCC auctions, see e.g. Plott (1997). Experiments have multiple uses in market
design, not only for investigation of basic phenomena, and small-scale testing of new designs,
but also in the considerable amount of explanation, communication, and persuasion that must
take place before designs can be adopted in practice.
35. For example, Roth and Xing (1994) report that in 1989 some Japanese companies scheduled
recruiting meetings on the day an important civil service exam was being given, to prevent their
candidates from also applying for government positions.
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