Rustamdjan Hakimov; Heller, C.-Philipp; Kübler, Dorothea; Kurino, Morimitsu
Article — Published Version
How to Avoid Black Markets for Appointments with
Online Booking Systems
American Economic Review
Provided in Cooperation with:
WZB Berlin Social Science Center
Suggested Citation: Rustamdjan Hakimov; Heller, C.-Philipp; Kübler, Dorothea; Kurino, Morimitsu
(2021) : How to Avoid Black Markets for Appointments with Online Booking Systems, American
Economic Review, ISSN 1944-7981, American Economic Association, Nashville, Tenn, Vol. 111, Iss. 7,
pp. 2127-2151,
https://doi.org/10.1257/aer.20191204
This Version is available at:
https://hdl.handle.net/10419/235248
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American Economic Review 2021, 111(7): 2127–2151
https://doi.org/10.1257/aer.20191204
2127
How to Avoid Black Markets for Appointments
with Online Booking Systems
†
By R H, C.-P H, D K,
M K*
Allocating appointment slots is presented as a new application for
market design. Online booking systems are commonly used by pub-
lic authorities to allocate appointments for visa interviews, driver’s
licenses, passport renewals, etc. We document that black markets for
appointments have developed in many parts of the world. Scalpers
book the appointments that are offered for free and sell the slots to
appointment seekers. We model the existing rst-come-rst-served
booking system and propose an alternative batch system. The batch
system collects applications for slots over a certain time period and
then randomly allocates slots to applicants. The theory predicts and
lab experiments conrm that scalpers protably book and sell slots
under the current system with sufciently high demand, but that they
are not active in the proposed batch system. We discuss practical
issues for the implementation of the batch system and its applicabil-
ity to other markets with scalping. (JEL C92, D47)
Allocation problems where money is not used to coordinate supply and demand
have gained the attention of economists in recent decades. Well-known examples
include the assignment of seats at schools and universities. A related problem
* Hakimov: University of Lausanne & WZB Berlin Social Science Center (email: rustamdjan.hakimov@unil.
Center & Technical University Berlin (email: dorothea.kuebler@wzb.eu); Kurino: Keio University, Faculty
of Economics (email: [email protected]). Liran Einav was the coeditor for this article. We would like to
thank three anonymous referees for their insightful and constructive comments and clear guidance. Our special
thanks go to Renke Fahl-Spiewack at the German Foreign Ofce who inspired us to work on this problem. We
are grateful to Nina Bonge who helped us with conducting the experiments as well as Jennifer Rontganger and
Christopher Eyer for copyediting. We thank Georgy Artemov, Péter Biró, Julien Combe, Bob Hammond, Akshay
Arun Moorthy, Alex Nichifor, Siqi Pan, Antonio Romero-Medina, Yasunari Tamada, Masatoshi Tsumagari, Martin
Van der Linden, Suvi Vasama, Tom Wilkening, Zhibo Xu, and participants of the Berlin Behavioral Economics
Workshop, the European Behavioral Economics Meeting (EBEM) at the University of Bonn, the Conference of
Behavioral Economics and the Economics of Inequality at the University of Edinburgh, and seminar participants
at Keio University, Hitotsubashi University, UTS Sydney, University of Melbourne, University of St. Andrews,
ECONtribute Bonn/Cologne, HSE St. Petersburg, DICE at Düsseldorf University, the MiddEX virtual seminar, and
FAIR at the University of Bergen for their valuable comments. Dorothea Kübler gratefully acknowledges nancial
support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through CRC TRR190
“Rationality and Competition” and the Cluster of Excellence “Contestations of the Liberal Script” (EXC2055) as
well as the Leibniz SAW project MADEP. Rustamdjan Hakimov acknowledges nancial support from the Swiss
National Science Foundation project 100018_189152. Morimitsu Kurino acknowledges nancial support from JPS
KAKENHI (grant from Japan Society for the Promotion of Science), and F-MIRAI at the University of Tsukuba.
†
Go to https://doi.org/10.1257/aer.20191204 to visit the article page for additional materials and author
disclosure statements.
2128
THE AMERICAN ECONOMIC REVIEW
JULY 2021
involves scheduling appointments at public ofces. Such appointments are provided
for free and are necessary to access many essential public services, such as obtain-
ing a visa or a driver’s license, or renewing a passport. Lately, many authorities
have introduced online booking systems that allow appointment seekers to book
in advance and to avoid queues. Typically, these online booking systems are based
on rst-come-rst-served rules: an authority offers time slots on a website, and
appointment seekers visiting the website can pick any available (not previously
booked) slot.
Such online systems based on rst-come-rst-served rules are vulnerable to
scalping. Scalpers are rms that book slots and sell them to appointment seekers.
Typically, scalpers use software, or bots, to track the system and book slots imme-
diately after they appear. Thus, the rms have a technological advantage when it
comes to booking speed compared to appointment seekers. A black market for
appointment slots implies that the political objective of providing equal access to
the public service, independent of income, may be violated. Moreover, it can be
argued that rms acting as intermediaries prot undeservedly from public services.
1
The vulnerability of the booking system originates from the fact that once slots
become available, they can be booked on a rst-come-rst-served basis. Scalpers
book any open slots with fake names or the names of their customers and sell them.
For appointments booked under fake names, scalpers rst cancel and then immedi-
ately book the slots under the names of their customers. This rebooking of canceled
slots bypasses the barrier imposed by the ID verication of the booking system.
Thus, while it might seem that ID verication would prevent scalping, the scalper’s
advantage of speed in the rst-come-rst-served system effectively circumvents it.
A number of prominent cases have surfaced recently where appointment slots at
public ofces were sold on the market. The introduction of an online booking sys-
tem for appointments with the Irish Naturalisation and Immigration Service Center
in Dublin led to scalping and a collapse of the system.
2
Bots have also been used by
scalpers to book all the slots at the Préfectures in France where foreigners need to
obtain their residence permit. Thus, appointment seekers cannot obtain slots directly
but instead must buy them from the scalpers.
3
Fees of up to US$500 were paid to
scalpers to get an appointment for a visa interview at the German consulates in
Beirut, Tehran, and Shanghai.
4
1
One feature of scalping is that it can help to serve the buyers with the highest valuations. However, we are not
looking for a solution that maximizes the sum of the valuations of appointment seekers who are served. Instead, we
propose a system that guarantees equal access, is ex ante fair by relying on randomization, and is efcient in the
sense that no slots are wasted.
2
Sorcha Pollak, “Bots Used to Block Immigrants in Ireland from Making Visa Appointments,” Irish Times,
https://www.irishtimes.com/news/social-affairs/bots-used-to-block-immigrants-in-ireland-from-making-visa-
appointments-1.3620957 (accessed December 1, 2020).
3
Julia Pascual and Nicolas Corentin, “Titres de séjour: le prospère business de la revente de rendez-vous en pré-
fecture,” Le Monde, https://www.lemonde.fr/societe/article/2019/06/01/titres-de-sejour-le-business-de-la-revente-
de-rendez-vous-en-prefecture-prospere_5470146_3224.html (accessed December 1, 2020).
4
Peter Maxwill, “Ein Termin in der deutschen Botschaft? Das kostet!,” Spiegel, https://www.spiegel.de/politik/
ausland/iran-termine-in-deutscher-botschaft-in-teheran-werden-verkauft-a-1041367.html (accessed December 1,
2020). After the events received press coverage, we were contacted by the German Foreign Ofce to consider the
problem. This was the starting point of our work. An increase in the demand for appointments played a crucial role
in 2014 in Beirut where many Syrian refugees tried to get a visa. The German consulates observed that open slots
were almost immediately taken and that there was a high proportion of no-shows for the booked appointments.
The German Foreign Ofce implemented a number of changes, such as delaying the reopening of slots after their
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Similar problems have been documented for appointments to obtain a driver’s
license at the Department of Motor Vehicles in some states in the United States.
5
In Berlin, appointment slots at public ofces were offered for money on a private
website.
6
In both instances, policymakers have tried to take legal action, but without
success.
Appointments at public hospitals in China can be booked online, and the cost of
service has to be paid at the moment of booking. Scalpers sell these appointments
at prestigious hospitals for up to 50 times their face value.
7
Thus, scalping can also
be protable when people pay for appointments if the price is not determined by
supply and demand.
The allocation of appointment slots shares some similarities with, but also differs
from, ticket markets for sporting events and concerts as well as air travel tickets. The
organizers of sporting events and concerts often set prices below the market-clearing
price out of fairness or image concerns, and thus face the challenge of resale mar-
kets and scalping. In contrast to these markets, the appointment slots have IDs
attached to them, and scalping occurs despite this feature. We will show how our
proposed booking system for appointments that are free of charge relates to but
differs from solutions proposed for event ticketing (Bhave andBudish 2017, Leslie
andSorensen 2014, Courty 2019). Airline tickets for which scalping is not observed
have IDs attached to them and are allocated through a rst-come-rst-served sys-
tem. However, speed does not matter, since tickets are made available before the
full demand is realized, and airlines do not make canceled tickets available for new
customers at the old price.
We rst study a typical online system for scheduling appointments. We pres-
ent a model of the rst-come-rst-served (“immediate”) system where slots can be
booked instantaneously, and solve for an equilibrium in this system. We demon-
strate that in equilibrium scalpers can protably book and sell slots to appointment
seekers under reasonable parameters of the rst-come-rst-served system.
We propose an alternative system that collects applications in real time, and ran-
domly allocates the slots among applicants (“batch” system). The system works
as follows: a set of slots (batch) is offered, and applications are collected over a
certain time period, e.g., for one day. At the end of the day, all slots in the batch are
allocated to the appointment seekers. Thus, the allocation is in batches, not immedi-
ate as in the rst-come-rst-served system. In the case of excess demand, a lottery
decides who gets a slot. If a slot is canceled, this slot is added to the batch in the next
cancellation, increasing the number of slots, outsourcing the services to private rms, and allocating some slots via
email. However, scalpers are still active. See also “Privatsache Visavergabe” from October 18, 2017.
5
Michael Cabanatuan, “DMV Investigates Startup That Has Disrupted Appointment Process,” San Francisco
Chronicle, https://www.sfchronicle.com/bayarea/article/DMV-investigates-startup-that-has-disrupted-13064509.
php (accessed December 1, 2020).
6
Hannar Beitzer, “Für kostenlose Termine zahlen,” Süddeutsche Zeitung, https://www.sueddeutsche.de/pan-
orama/berliner-buergeraemter-zahlen-fuer-kostenlose-termine-wegen-chaos-1.2581163 (accessed December 1,
2020).
7
Yang Wanli, “Top Medical Authority Says Appointment Scalpers Will Be Punished,” China Daily, http://
www.chinadaily.com.cn/china/2016-01/28/content_23281382.htm (accessed December 1, 2020); and Catherine
Wong, “Ticket Scalpers Selling Hospital Appointments: Beijing Police Arrest 29 Members of Gang Using Ofcial
Booking Apps to Recruit Customers,” South China Morning Post, https://www.scmp.com/news/china/society/
article/1928186/ticket-scalpers-selling-hospital-appointments-beijing-police (accessed December 1, 2020).
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THE AMERICAN ECONOMIC REVIEW
JULY 2021
allocation period, e.g., the following day. Thus, the scalper cannot transfer the slot
from the fake name to the customer by way of cancellations and rebookings.
We show that under reasonable parameter restrictions, the scalper not entering
the market is the unique equilibrium outcome of the batch system. The intuition for
this result is that, keeping the booking behavior of the scalper xed, a seeker has the
same probability of getting a slot when buying from the scalper as when applying
directly. Flooding the market with fake applications increases the probability that
the scalper will receive many slots, but he cannot make sure that he gets slots for
his clients, and he cannot transfer slots to the names of the clients. Thus, given the
booking choice of the scalper, the seekers will always prefer to apply directly if the
price for the scalper’s service is positive.
The batch system has two important features relative to the immediate system:
rst, it eliminates the importance of speed, and second, it prevents the possibility
of transferring the identity of the slots booked under fake names to the names of
the clients through cancellations and rebookings. Both features are necessary to
avoid scalping. To see this, consider two alternative systems where only one of the
two features holds, respectively. First, if the scalper is faster than the seekers but
cannot transfer the identity of slots, he can still protably operate in the market if
seekers ask the scalper to book slots on their behalf (as in our experiment and in the
case of train tickets in India discussed in SectionIIIC). Second, in a batch system
where speed does not matter but bookings do not require identication, the scalper
can ood the market with fake applications, is virtually guaranteed to receive all
slots under fake names, and can sell the slots to seekers in a secondary market. This
holds true for some ticket markets for sporting events and concerts (as discussed in
SectionIIIC).
The rst feature of the batch system, namely eliminating the relevance of
speed, parallels the proposal by Budish, Cramton, and Shim (2015) to replace
continuous-time trading at nancial exchanges with frequent batch auctions. Similar
to Budish, Cramton, andShim (2015), we show that an allocation system where
speed determines the priorities creates an advantage for the scalper. In our setup,
however, there is an additional drawback to speed: it makes ID verications irrel-
evant, which is novel. While batch auctions transform competition on speed into
competition on price, the batch booking system transforms competition on speed
into equal access via lotteries. For equal access via lotteries to be effective, ID
checks are needed: these checks are not necessary when an auction is used to elim-
inate scalping.
Based on a parameterized version of the model, we conducted a set of lab exper-
iments. We nd that the scalpers’ choices in the experiment are in line with the the-
oretical predictions: scalpers only persistently and protably enter the market in the
immediate system when demand is high, i.e., when there are enough appointment
seekers to cover the scalper’s costs. Furthermore, in line with the theory, the exper-
iments show that the proposed batch system does not allow the scalpers to make a
prot, and that market entry is rare. Finally, the batch system leads to higher average
welfare for the seekers than the immediate system, as predicted.
For the actual implementation of the proposed batch system, certain features of
the design are crucial. We discuss these practicalities such as the length of the time
interval in which applications for a batch of slots are possible in SectionIII. We also
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discuss possible alternative measures to ght scalping and show that they do not
preclude scalping under the rst-come-rst-served system or have other undesirable
features. Finally, we discuss a range of other markets with scalping, such as train
tickets, limited edition sneakers, and tickets for sporting events, and consider the
potential usefulness of the batch system in these cases. The main takeaway is that
the applicability of the batch system depends on whether identity checks can be
implemented.
Related Literature.—The importance of speed in high-frequency trading has led
to enormous investments in fast data connections around the world. This feature
relates our contribution to a proposal for the redesign of nancial exchanges by
Budish, Cramton, andShim (2015), as discussed above.
8
Our paper speaks to the literature on the sale and resale of tickets for sporting
events, concerts, popular restaurants, etc. Marketing tools introduced by the orga-
nizers of sporting events have blurred the difference between primary and secondary
markets (for a survey, see Courty 2017). Courty (2019) proposes a centralized ticket
exchange where fans can return tickets that are then randomly allocated to other
fans.
Often, economists take the development of secondary markets as evidence of
underpricing by the original seller and therefore suggest increasing prices or run-
ning auction-like mechanisms to prevent secondary market sellers from prot-
ing. Auctions can be used for ticket sales to reduce arbitrage prots, as in Bhave
and Budish (2017). Alternatively, random allocations of tickets priced below the
market-clearing rate are used, for instance, for the soccer World Cup nal, for
Wimbledon, and for some baseball games in the MLB. More generally, Chakravarty
andKaplan (2013) show that lotteries can be an optimal allocation rule when no
payments are collected.
Speed can be decisive in online auctions where sniping aims at minimizing the
time between the bid and the end of the auction. While sniping can be addressed by
endogenous or unknown auction closing times (Roth andOckenfels 2002; Ockenfels
andRoth 2006; Ariely, Ockenfels, andRoth 2005; Malaga etal. 2010), the scalping
of appointments cannot be prevented by keeping the exact time of the release of new
slots unknown. The software monitoring the booking websites all but guarantees
that the scalper will get every available slot.
When there is no possibility of monetary transfers, the assignment of appoint-
ment slots is a house allocation problem studied in the matching literature (Shapley
andScarf 1974, Hylland andZeckhauser,1979, Abdulkadiro g
̆
lu andSönmez 1998).
9
The existing models cannot analyze the emergence of black markets, and we there-
fore present a new model. Finally, this paper is part of a growing experimental lit-
erature on matching markets surveyed by Roth (2016) and Hakimov and Kübler
(2020), as well as experimental work on the role of market intermediaries for cor-
ruption and collusion, as in Cason (2000) and Drugov, Hamman, andSerra (2014).
8
Relatedly, batch and serial processing of offers in decentralized labor markets are studied by Roth andXing
(1997), where batch processing helps to overcome congestion and thus improves market outcomes.
9
Experiments on house allocation and random serial dictatorship haven been conducted by Chen andSönmez
(2002); Guillen andKesten (2012); and Hugh-Jones, Kurino, andVanberg (2014).
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I. The Model
We build a simple model of appointment allocation in the presence of scalpers,
focusing on how design choices can reduce the protability of scalping. The proofs
of all results are in online Appendix Section A.
There are n (appointment) seekers, indexed by i ∈
{
1, … , n
}
, who need a ser-
vice from a central authority. The central authority meets the seekers face-to-face to
provide the service, and offers m (appointment) slots. The m slots can be obtained
by any agent, not only the seekers. We represent non-appointment-seeking agents by
one rm, called the scalper.
10
A booking system operated by a central authority is a procedure to allocate m
slots to applicants. A system accepts applications with applicant IDs. ID checks are
performed during the appointment, that is, the correct name and passport number
have to be in the system. A seeker can submit at most one application for a slot with
her ID, as the booking system can detect multiple entries of the same name. We
assume that the scalper can costlessly create fake IDs that do not refer to any exist-
ing appointment seekers. He has to replace them with the IDs of seekers in order to
sell the slots. The central authority cannot distinguish true seekers from fake seekers
based on the application for a slot.
Each seeker i has a value of v
i
of obtaining an appointment for any of the m
slots. This value is the seeker’s private information and is called her type. Each v
i
is
independently and identically distributed along some interval [ v
¯
, v
–
] according to the
commonly known distribution function F where v
¯
> 0 . We normalize the value of
getting no slot to zero, and assume that F has a continuous density f ≡ F ′ with full
support.
There is a (black) market for scalping in which the scalper can enter or remain
inactive. The entry cost is c > 0 .
11
If the scalper decides to enter the market, he can
submit as many applications to the booking system as he wants, up to Q . Here, Q
represents the capacity constraint of the scalper to create fake applications. For
analytical simplicity, we assume that Q is sufciently large so that Q > n . In the
market the scalper sets the monopoly price for the service of procuring a slot for
a seeker. We denote by p the price paid by a seeker to the scalper. We assume that
the set of feasible prices is a compact set included in the set of positive numbers,
denoted by ⊆ ℝ
++
.
Seekers observe the price and decide whether to buy a slot from the scalper.
Under any booking system, if the scalper successfully secures a slot for a seeker, the
seeker obtains the slot. If not, the scalper reimburses the seeker for the price she has
paid. How slots are booked depends on which system is in place.
10
We refer to the scalper by the male personal pronoun and to a seeker by the female personal pronoun.
11
We assume that the cost is xed, and can be interpreted as an investment in the technology, i.e., the program-
ming of bots that search for and book slots. In our model, the game lasts for one period. In reality, the scalper might
be active for many periods if the cost for the scalping technology was paid once. However, the booking systems
include captchas and other security features and are constantly updated. Thus, scalpers have to regularly invest in
the software. Scalpers may also have to pay wages to persons who sell slots to customers, which is another source
of costs accruing in every period.
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Each seeker i ’s payoff depends on her valuation and the price, as well as whether
she obtains a slot:
seekeri’s payoff =
{
v
i
if she obtains a slot directly,
v
i
− p
if she buys a slot at pricepfrom the scalper,
0
if she does not obtain a slot.
The scalper obtains no utility from an appointment slot, but can prot from selling
slots to the seekers. His payoff from selling m ′ ∈
{
0, … , m
}
slots to the seekers is
scalper’s payoff =
{
m ′ p − c
if he sells m ′ slots to seekers,
0
if he is not active.
We assume that the seekers and the scalper are risk neutral.
Under any system, a seeker can either apply for a slot directly or buy the service
of the scalper, not both. The former is called a direct applicant, while the latter
is called a buyer. Let n
b
be the number of buyers, and n
d
be the number of direct
applicants, such that n
b
+ n
d
= n . The number of applications by the scalper is
denoted by n
s
where n
s
≤ Q , and s is the number of slots secured by the scalper
where s ≤ n
s
. The likelihood that the scalper gets s slots and the likelihood of a
direct applicant getting a slot depends on the booking system in place.
The timeline of the game under any booking system is summarized in Figure 1.
Panel A shows the sequence of actions in case the scalper enters the market while
panel B shows the sequence in case he does not. The timing of the game is as follows.
• In t = 0 , seekers learn their valuations privately.
• In t = 1 , the scalper chooses whether to enter the market, which is observable.
If he enters, the scalper sets the price for a slot that is observable, and the game
continues at t = 2 (panel A of Figure1). If the scalper does not enter the mar-
ket, the game continues at t = 3 (panel B of Figure1).
• In t = 2 , if the scalper has entered the market, the seekers simultaneously
decide whether to buy a slot from the scalper or apply for slots directly through
the booking system. The number of buyers is observable for the scalper.
• In t = 3 , if the scalper has entered the market, he chooses the number of appli-
cations n
s
up to capacity Q for the booking system. Those seekers who did not
buy the scalper’s service apply directly to the booking system. The number of
such seekers is denoted by n
d
. If the scalper did not enter, all seekers apply for
slots directly, and thus n
d
= n and n
s
= s = 0 .
• In t = 4 , the booking system is run and payoffs are realized.
The order of moves regarding the booking of slots by the scalper and the buying
decisions of seekers is not crucial for our main results, and we discuss the conse-
quences of changing the order for each booking system in what follows.
The strategy of the scalper determines whether he enters the market and at which
price he offers the slots. It also determines the number of his applications for each
combination of price p and number of buyers n
b
. Every seeker observes the scalper’s
decision regarding entry and price, and then decides whether to buy from the scalper
or to apply for a slot directly.
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We will solve for a symmetric Bayesian Nash equilibrium, or a symmetric equi-
librium in which all seekers use a symmetric strategy, i.e., a strategy that depends
only on types and prices, not on the names of seekers.
A. Immediate Booking System
The immediate system models a rst-come-rst-served online booking system.
In such a system, an application is only observable for the designer if it results in
the booking of a slot. Thus, the maximum number of observable applications is m ,
i.e., n
s
+ n
d
≤ m .
12
The scalper has a technological advantage over the seekers in
the sense that he can secure himself any number of slots up to the total supply with
the help of bots, s = n
s
≤ m . Importantly, the scalper can transfer these slots to
seekers who must pay for his service. This is possible by canceling the slot with the
fake ID and then immediately rebooking it under the name of the seeker.
13
For the sake of simplicity, we model the possibility of cancellations and rebookings
by having the scalper book the slots after he knows the demand of seekers (including
their IDs). This modeling assumption makes cancellations and rebookings unneces-
sary since the scalper knows which seekers are buying from him in a given period.
At the same time, unlike in the real world when seekers observe that there is no
12
This does not preclude a situation of excess demand. However, seekers who do not get a slot directly or
through the scalper cannot be observed.
13
Note that even if the canceled slots are freed up with a delay, a policy that has been adopted by the German
consulates to deter scalping, the scalper will be faster than the seekers in booking them once they appear in the
system. Moreover, the scalper knows for sure that the slot will be offered at some point, early enough for rebooking,
since otherwise the canceled slot is wasted.
t = 0
t = 1
t = 2 t = 4
t = 3
Booking system, supply
of slots, and the number of
seekers are revealed; seekers
learn their valuations.
Scalper learns how many slots
he sold and decides on number
of applications; seekers
who did not buy apply directly.
Scalper enters the market
and sets the price.
Seekers learn the price
and decide to buy or not.
Final payoffs
are realized.
System determines allocation
t = 0
t = 1
t = 2 t = 4
t = 3
Booking system, supply
of slots, and the number of
seekers are revealed; seekers
learn their valuations.
Seekers apply directly.
Scalper decides not
to enter the market.
No actions. Final payoffs
are realized.
System determines allocation
Panel A. Timeline if scalper enters the market
Panel B. Timeline if scalper does not enter the market
F1. T T G
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HAKIMOV ET AL.: BLACK MARKETS AND ONLINE BOOKING SYSTEMS
VOL. 111 NO. 7
possibility of getting a slot except through the scalper, under our modeling assump-
tion appointment seekers need to decide whether to buy before observing the scalp-
er’s actions. Hence, they have to anticipate that the scalper will book all the slots.
14
After the scalper has made his bookings, all remaining slots are assigned to the
direct applicants if there are enough slots available. Otherwise, the remaining slots
are randomly assigned to them. More formally, the assignment is determined as fol-
lows: if the number of buyers is smaller than or equal to the number of slots secured
by the scalper, i.e., n
b
≤ s , each buyer will get a slot for sure and
(
s − n
b
)
slots lead
to no-shows; otherwise (if n
b
> s ), s slots are randomly distributed to n
b
buyers
such that each gets a slot with probability s/ n
b
. The residual supply of m − n
s
slots
is distributed randomly among the direct applicants. Thus, each direct applicant
gets a slot with a probability of ( m − n
s
)/ n
d
. Any remaining open slots are freely
disposed of.
PROPOSITION 1 (Equilibrium in the Immediate System): Let p
∗
be the price that
maximizes the prot of the scalper Π
(
p
)
. In the immediate booking system, there
exists a symmetric equilibrium where on the equilibrium path the following occurs.
15
(i) If Π
(
p
∗
)
≥ 0 , the scalper enters the market, sets price p
∗
, and makes m
applications. Moreover, each seeker follows the symmetric strategy in which
a type above p
∗
buys the service from the scalper, and a type below p
∗
applies
directly and receives a slot with zero probability.
(ii) If Π
(
p
∗
)
< 0 , the scalper does not enter the market, and all seekers apply
directly.
In the equilibrium of the immediate system, the scalper enters the market if the
entry cost is not too high. If the scalper enters, he will book all slots. Then, the only
possibility for seekers to get a slot is to buy it from the scalper.
Example.—Consider a market with 20 seekers competing for 15 slots. The val-
uations of the seekers are uniformly distributed on the interval
[
10,100
]
. The entry
cost is 100. In equilibrium, the scalper enters the market with the prot-maximizing
price of 51 where prices are restricted to be integers. All seekers with valuations
above 51 buy his service. The scalper books all 15 slots with an expected prot of
454. The expected number of slots sold is 10.9, which implies that, on average, 4.1
slots remain unassigned, leading to no-shows despite excess demand.
While the overall welfare of the booking system is not our main interest, we can
distinguish three effects of scalping on welfare in the immediate system. (i) The
entry cost for the scalper creates a deadweight loss. (ii) If there are more seekers
14
When the order of moves is reversed (i.e., the scalper books rst, and the seekers then observe the remaining
slots and decide whether to buy), it is equally straightforward for a scalper to make a prot. This does not require
scalpers to be able to cancel and rebook slots under different names, as shown by the example in SectionIIIC.
15
The scalper’s prot is given as
Π
(
p
)
=
{
∑
k=0
m
(
n
k
)
F
n−k
(
p
)
(
1 − F
(
p
)
)
k
pk − c
if m ≥ n,
∑
k=0
m
(
n
k
)
F
n−k
(
p
)
(
1 − F
(
p
)
)
k
pk +
∑
k=m+1
n
(
n
k
)
F
n−k
(
p
)
(
1 − F
(
p
)
)
k
pm − c
if m < n.
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than slots, the presence of the scalper may improve the allocative efciency. The
reason is that without the scalper, the slots are allocated randomly to seekers, irre-
spective of their valuation. If the scalper is active, only seekers with a high valuation
will obtain slots. (iii) The price charged by the scalper creates inefciencies due to
slots being wasted if there are fewer seekers with a valuation above the price than
available slots.
B. Batch Booking System
We propose the batch booking system as an alternative to the immediate system.
Under the batch system, the central authority collects and pools applications with
IDs during a certain time interval. At the end of the interval, the m slots are allocated
randomly to the applicants. The number of applications is not constrained by the
supply of slots, since the allocation of slots takes place after the period of collect-
ing applications. The batch system eliminates the importance of speed, since the
random allocation gives every applicant the same chance independent of when
she applied within the given time interval. Thus, the scalper has no technological
advantage relative to the seeker, except that he can submit Q applications, while
seekers can submit only one. All canceled slots are allocated in the next or later
batches.
Although the allocation of slots in the batch system takes place over a time
interval, modeling the dimension of time would complicate the analysis with little
additional insight. For simplicity, we model the batch system as a static assign-
ment. The assignment by the batch system is determined in one of the following
two cases:
(i) The total number of applications does not exceed the number of slots, i.e.,
n
d
+ n
s
≤ m . The scalper obtains a slot for each of his applications, n
s
= s ≤ m .
Also, each direct applicant gets a slot. If n
b
≤ n
s
, n
b
slots go to the buyers, and
the remaining slots of the scalper ( n
s
− n
b
) are assigned to fake IDs and lead to
no-shows. If n
b
> n
s
, the s slots are assigned to the buyers whose applications were
submitted by the scalper. Thus, each buyer gets a slot with probability n
s
/ n
b
.
(ii) The total number of applications exceeds the number of slots, i.e., n
d
+ n
s
> m .
The m slots are randomly allocated to applicants with real or fake IDs. Each buyer,
fake ID, and direct applicant get a slot with probability m/( n
d
+ n
s
) .
In the immediate system, the scalper can secure up to m slots for the buyers,
which allows him to preempt the direct applicants completely. By contrast, in the
batch system the scalper cannot secure slots for the buyers with certainty. While
he is almost certain to get the full supply of slots by submitting a large number
of applications with both fake and real IDs, he cannot transfer slots with fake IDs
to the buyers because canceled slots are reallocated only in the next period where
the scalper would again face competition from seekers who apply directly. Thus,
submitting more applications than n
b
reduces the likelihood that he can get slots
for his clients, while submitting fewer applications than n
b
reduces his prot.
We conclude that the scalper makes n
b
applications when observing n
b
(
≥ 0
)
buyers.
Another characteristic of the batch system is that given such optimal behavior of
the scalper, a seeker has the same probability of getting a slot from buying as from
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applying directly.
16
Thus, since buying a slot is costly for the seeker, she always
prefers to apply directly. The main properties of the batch system are summarized
in Proposition 2.
PROPOSITION 2 (Equilibrium in the Batch System): In the batch booking system,
there exists a symmetric equilibrium where the scalper does not enter the market on
the equilibrium path .
In particular, the scalper not being active is a unique equilibrium outcome
if R < c , where R is an upper bound of the expected revenue, dened as follows:
R =
∑
k=1
n
(
n
k
)
(
2n − k − 1
_
2n − 1
)
2n−k−1
(
k
_
2n − 1
)
k
max
{
n − 1, m
}
_
n
k v
–
.
Just as in the immediate system, the order of moves is not crucial for this result.
In the batch system, the seekers and the scalper essentially move simultaneously.
The condition of uniqueness of the equilibrium outcome is rather mild and likely
to be satised in many settings. Online Appendix Figure A.1 presents the graph of
the function R depending on n for v
–
= 1 . The revenues of the scalper never exceed
0.55. Thus, whenever the entry cost of the scalper is higher than 55 percent of the
highest valuation, not entering the market is the unique equilibrium outcome.
When R > c , there may exist another equilibrium under the batch system in
which the scalper enters the market by threatening to ood the market with appli-
cations in the case of zero buyers. We describe it in Proposition 3 in the online
Appendix. The risk posed by this equilibrium to the authority ghting scalping is
limited, since only a few seekers with high valuations buy from the scalper while
most seekers receive a slot through direct applications. This is in contrast to the
equilibrium under the immediate system where seekers can only get a slot through
the scalper if he is active. Moreover, we believe that it is difcult for the scalper’s
threat to ood the market to be effective. Since all applications are accepted in the
batch system, the seekers can always apply for slots, and even if they do not get a
slot in one batch, they can try again in the next. Thus, they cannot observe the scalp-
er’s activity. This is in contrast with the immediate system where the seekers observe
that no slots can be booked, and therefore seek the scalper’s service.
Example.—Consider again a market with 20 seekers competing for 15 slots, the
valuations of the seekers uniformly distributed on the interval
[
10,100
]
, and the entry
cost of 100. The unique equilibrium outcome prescribes that the scalper does not
enter the market. To see this, note that the condition for a unique equilibrium is sat-
ised with c = 100 > 0.55 ⋅ 100 = 0.55 v
–
.
16
See Lemma 4 in the online Appendix for the scalper’s behavior. To see the equal probabilities of a seeker,
say, for the excess demand case ( m < n ), let n
ˆ
b
and n
ˆ
d
be the number of buyers among the other seekers. If she
applies directly, the probability is m/
(
(
n
ˆ
d
+ 1
)
+ n
ˆ
b
)
; if she buys, it is m/
(
n
ˆ
d
+
(
n
ˆ
b
+ 1
)
)
. See Lemma 5 in the online
Appendix for a complete analysis.
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II. Experiment
We conducted an experiment that serves as a testbed of the proposed batch sys-
tem. We also study the immediate system to understand the conditions under which
scalpers can protably enter the market. The experiment allows us to compare the
observed strategies and outcomes to the equilibrium predictions in a tightly con-
trolled environment.
A. Treatments and Procedures
There are four slots to be allocated in every round, m = 4 . Of the ve seekers
in each market, three are active in every round, while the other two are active in
only half of the rounds, thus n = 3 or n = 5 depending on the round. This design
allows us to vary the demand for slots between rounds.
At the beginning of each round, every participant is informed about her valu-
ation v for a slot, drawn from the uniform distribution over the interval between
50 and 100. Each participant has an ID, which is assigned anew in every round
to ensure anonymity of the feedback across rounds. The ID allows us to iden-
tify seekers and assign slots to them. Every seeker can receive at most one slot
per round. There is one scalper in every round who can enter the market. The
scalper has a value of zero for the slots, but he can book slots and sell them to the
seekers.
The slots are allocated through either the immediate or the batch system. Each
round consists of two steps. Step 1 is the same for both booking systems while step
2 differs between them.
In Step 1.—At the beginning of each round the participants are informed of the
booking system that is in place as well as of the number of active seekers in the
round (three or ve). Each seeker’s valuation for a slot is drawn randomly from the
interval [50, 100]. Each seeker is informed of her own valuation, but the scalper does
not know the valuations. The scalper decides whether to enter the market. Entering
the market entails a xed cost of 150 points for the scalper, c = 150 . If the scalper
enters, he sets the price p that is paid by the seeker if the scalper provides a slot.
The scalper has a choice between the following prices: 15, 20, 25, …, 75, 80, or 85.
Each seeker decides whether she wants to pay for the scalper’s service at the price
or whether she wants to apply directly, i.e., without the scalper.
Step 2.—Differs between the two booking systems.
Immediate System: In step 2, when the scalper enters the market, he learns how
many seekers have bought his service. He can book as many slots as he wants for
free. If the scalper sold a slot to a seeker in step 1, the system assigns him a slot for
the ID of this seeker.
Batch System: In step 2, if the scalper is active in the market (that is, he entered
the market in step 1 at a cost of 150 points), the scalper learns how many seekers
bought his service. He can then submit as many applications for slots as he wants
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VOL. 111 NO. 7
for free. The scalper enters the IDs of the seekers who decided to apply through him
in step 1.
17
We implemented a 2×2 within-subjects design by varying the demand and the
booking system. Before each block of ve rounds, the booking system (immediate
or batch) and the demand for appointments (three or ve seekers) are announced.
Both dimensions remain constant for ve rounds. We refer to the treatments with
the immediate booking system with ve and three seekers as Im5 and Im3, and the
treatments with the batch booking system with ve and three seekers as Batch5
and Batch3. The ve-round block design allows the scalper to develop a reputation,
and the seekers to adjust to the behavior of the scalper and of the other seekers. By
changing the ID of the seekers in every round, we attempt to capture the situation
where new seekers enter the market in every round while the scalper remains active
in multiple periods. Overall, each session of the experiment consisted of 40 indepen-
dent decisions, i.e., 40 rounds.
Online Appendix Table C.1 presents the order of treatments by rounds. Each
treatment was implemented twice, such that we can look at mature behavior in the
second block of ve rounds after subjects have already experienced all four treat-
ments. The order of the treatments was chosen so as to rst allow scalpers to make
a prot in the immediate system with ve seekers (see the equilibrium predictions
below). Then, the treatments follow where the scalper should make no prot by
entering the market. This allows us to study our main research question, namely
whether a change in the booking system from immediate to batch will reduce the
amount of scalping.
Payoffs.—Each seeker has an endowment of 220 points at the beginning of each
ve-round block. Within the course of the ve rounds of a block, points are added to
and deducted from this endowment. If active, a seeker earns her valuation minus the
price if she receives a slot through the scalper. If the seeker receives a slot without
the scalper, she simply earns her valuation without paying anything. If the seeker
does not receive a slot, either with or without the scalper, her payoff is zero in this
round, and her endowment is unchanged. Every seeker who is not active in a block
of ve rounds with low demand receives the equilibrium payoff of the active seek-
ers in this round. This limits potential differences between subjects that are due to
income effects.
The scalper has an endowment of 750 points at the beginning of each ve-round
block, and points are added and deducted to this endowment over the course of the
ve rounds. If the scalper enters the market, he pays 150 points, and he receives
the price times the number of slots sold. Note that the 750-point endowment allows
the scalper to enter the market in every round, even if he does not sell any slots.
Thus, we chose a budget that does not constrain the scalper’s choices. If the scalper
decides not to enter the market in one of the rounds, his endowment is unchanged
in this round.
17
The details of the immediate and batch system implemented in the experiments can be found in online
Appendix Section C.2.
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After every round, all participants received feedback about the allocation of slots:
a slot can be vacant, allocated to a seeker directly, allocated to a seeker through the
scalper, or allocated to a fake ID.
At the end of the experiment, one block was randomly drawn and the nal earn-
ings of this block were paid out in euros. The exchange rate was 1 point = 2 cents.
The experiment lasted, on average, around 100 minutes, and the average payoff was
EUR 14.73, including a show-up fee of EUR 5.
The experimental sessions were run at the WZB TU lab at the Technical University
Berlin. We recruited subjects from our pool with the help of ORSEE by Greiner
(2015). The experiments were programmed in z-Tree (Fischbacher 2007). We con-
ducted 10 sessions, with 24 subjects each. Thus, we end up with 40 independent
matching groups. The data from the experiment and the replication code are avail-
able in Hakimov etal. (2021).
At the beginning of the experiment, printed instructions were given to the sub-
jects (see online Appendix Section C). Participants were informed that the exper-
iment was about the study of decision-making, and their payoff depended on their
decisions and the decisions of other participants. The instructions explained the
details of the experiment and were identical for all subjects. Questions were asked
and answered in private. After reading the instructions, all subjects participated in a
quiz to make sure they understood the main features of the experiment.
B. Predictions
The four treatments differ with respect to the predicted entry of the scalper, the
predicted price of a slot, and the number of slots sold. This results in different prots
for the scalper and payoffs for the seekers.
18
The only treatment where the equi-
librium predicts positive expected prots for the scalper is Im5, where the scalper
chooses the prot-maximizing price of 60, leading to less than four slots being allo-
cated in equilibrium. In Im3, the scalper can at most break even in equilibrium due
to the lower demand. He charges a price of 50 to guarantee that all three seekers are
willing to buy a slot which just covers the entry cost of 150. In Batch3 and Batch5,
the scalper does not enter the market in equilibrium.
We use the stage-game predictions, although subjects play the game for ve
rounds changing the ID numbers of the seekers between rounds to capture that
scalpers are longer-lived than seekers. The repetition can generate multiple equilib-
ria, but playing the stage game Nash equilibrium in every round is a Nash equilib-
rium of the repeated game.
C. Experimental Results
The main questions addressed by the experiment are whether scalping is prot-
able and scalpers enter the market. We also summarize the main ndings regarding
the seekers’ choices. All results reported are signicant at the 5 percent level if not
18
Online Appendix TableC.2 presents a summary of the equilibrium predictions of the stage game by treatments.
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VOL. 111 NO. 7
stated otherwise. For all results, we focus on the second block (i.e., the last ve
rounds) of each treatment .
The batch system was designed to remove the incentives of scalpers to enter the
market, book slots, and sell them to the seekers. We therefore begin by investigating
the entry decisions of scalpers across treatments. The left panel of Figure 2 shows the
average proportions of scalpers entering the market in the second block of each treat-
ment. The highest proportion of scalpers in the market is observed in Im5, amounting
to 79 percent, on average, for the last ve rounds of the treatment. This is qualitatively
in line with the equilibrium prediction, according to which scalpers enter the mar-
ket. In the equilibrium with low demand (Im3), the scalpers are indifferent between
entering and not entering the market as the expected prot is zero. We observe, on
average, 47 percent of market entry by scalpers. This proportion is signicantly lower
than in Im5. For the treatments with the batch system, the equilibrium predicts that
scalpers do not enter the market, independent of whether demand is high or low. We
nd 20.5 percent of market entry by scalpers in Batch5 and 7.5 percent in Batch3 in
the last ve rounds of the treatment. This is signicantly lower than in Im5 and Im3.
19
We sum up the ndings as follows.
RESULT 1 (Market Entry): The proportion of market entry by scalpers is highest in
Im5, followed by Im3, while entry is lowest in Batch5 and Batch3.
Are the scalpers’ entry decisions optimal? To answer this question, we turn to
the analysis of the scalpers’ prots. The right panel of Figure2 shows the average
prots conditional on entering the market for each treatment. Only treatment Im5
leads to positive average prots for the active scalpers both in theory and in the
data. However, the realized prots are lower than predicted: equilibrium prots are
19
All pairwise comparisons of the proportion of market entry by scalpers in the last ve rounds of each treat-
ment show signicant differences ( p < 0.01). For the tests, we use the p-values for the coefcient of the dummy of
interest in the probit regression on the dummy for entering the market. Standard errors are clustered at the level of
matching groups and the sample is restricted to the treatments that are relevant to the test.
F2. P M E S () A P ()
Notes: Gray bars represent 95 percent condence intervals. High demand stands for ve seekers (Im5 and Batch5)
while low demand for three seekers (Im3 and Batch3). The gure is based on all decisions in the second block.
−140
−120
−100
−80
−60
−40
−20
0
20
40
Average prot
High demand Low demand
Immediate system Batch system
0
0.2
0.4
0.6
0.8
Proportion of market entry
High demand Low demand
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70.34 while average prots are 22.8, with 36.5 in the last round of the treatment.
Similarly, in Im3 prots are lower than the predicted equilibrium prots of zero.
Turning to the prots of the scalpers in the batch system, the scalpers do not enter the
market in equilibrium, and thus equilibrium prots are zero. As shown by Figure2,
we observe negative prots, conditional on entering the market.
Regarding the booking decisions of scalpers, in Im5 and Im3 scalpers booked the
entire supply of four slots in 91 percent and 87 percent of cases, respectively, after
entering the market. This behavior is close to the equilibrium prediction of 100 per-
cent. In Batch5 and Batch3, the scalpers do not enter the market in 89 percent and
66 percent of all cases, respectively, as predicted in equilibrium, and therefore do
not make any booking decisions. Conditional on out-of-equilibrium entry in the
batch system, scalpers try to block the system by submitting 10 or more applica-
tions in 33 percent and 30 percent of cases in Batch5 and Batch3, respectively. This
points to the attempts of scalpers to block the market, but it is not protable.
The main ndings can be summarized as follows.
RESULT 2 (Prots and Booking Decisions of Scalpers): Scalpers earn positive
prots only in Im5. In the immediate system, in almost 90 percent of cases after
equilibrium entry, the scalpers book all four slots, which is the equilibrium booking
strategy. In the batch system, the majority of scalpers do not enter the market, as
predicted in equilibrium, and therefore do not take any booking decisions.
Appointment Seekers.—We next study the welfare of seekers and the total num-
ber of slots allocated to them. For detailed analyses of the seekers’ behavior, we
refer the reader to online Appendix Section C.5. First, we consider the seekers’ deci-
sions to buy the service from the scalper. Then, we study the welfare of appointment
seekers and the total number of slots allocated.
Figure 3 shows the average payoffs of seekers by treatments. As predicted, the
batch system leads to signicantly higher payoffs for seekers than the immediate sys-
tem, and seekers fare worst in Im5. All pairwise comparisons of treatments with differ-
ent booking systems with the same demand yield signicant differences ( p < 0.01).
20
Regarding absolute levels, the observed average payoffs of seekers are 55 and
73 in Batch3 and Batch5, compared to the prediction of 60 and 75 respectively.
Thus, in the batch system the payoffs of the seekers are slightly below the equilib-
rium payoffs. In Im3 and Im5, the observed payoffs of the seekers are higher than
in equilibrium, namely 30 instead of 15 in Im5 and 51 instead of 25 in Im3. These
deviations from the equilibrium are due to excessive entry of scalpers in treatments
with the batch system, and too little entry in the immediate system.
Summing up, Result 3 states that in line with the equilibrium predictions, a
designer who cares about the utility of seekers should implement the batch system.
RESULT 3 (Payoffs of Appointment Seekers): The average payoffs of appointment
seekers are higher in the batch than in the immediate system for a given demand.
20
The p-values are computed for the coefcients of the dummies of interest in an OLS regression of the seekers’
payoffs; standard errors are clustered at the level of matching groups, and the sample is restricted to treatments of
interest for the test.
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A potential source of welfare loss are slots that are wasted due to scalping. We
compare the number of slots allocated to seekers by treatments. With high demand,
the proportion of slots allocated to seekers is almost identical in both booking sys-
tems at around 90 percent. With low demand, it is signicantly higher in the batch
system than in the immediate system. For further details on the allocation of slots,
see online Appendix Section C.7.1, and for details on the valuations of the seekers
who receive a slot, see Section C.7.2.
III. Practical Challenges, Alternative Solutions, and Other Markets with Scalping
In this section, we discuss design features of the batch system that are not part of
the model but are important for its implementation. Moreover, we discuss alternative
solutions for the problem of scalping under rst-come-rst-served booking systems
and the applicability of the batch system to other markets with scalping.
A. Practicalities of the Batch System
The theoretical model shows that the batch system makes scalping unprotable,
and the experiments support this prediction. To make the batch system work as
predicted, however, the designer has to carefully choose some additional design
parameters. Our model is static and therefore agnostic about essential details that
can inuence the practical success of the batch system. We have abstracted from the
seekers’ preferences over slots, including the issue of when these preferences arise.
0
20
40
60
80
Average payoff
High demand Low demand
Immediate system Batch system
F3. A P S
Notes: Gray bars represent 95 percent condence intervals. High demand stands for ve seekers (Im5 and Batch5)
while low demand for three seekers (Im3 and Batch3). The gure is based on the second block.
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Length of the Time Interval of Each Batch.—The designer faces a trade-off when
choosing the time interval of a batch.
• Seekers need to have enough time to apply for slots. Sufciently long time
intervals ensure that the scalper cannot book all the slots offered with cer-
tainty, e.g., because seekers do not notice that a new batch is available.
Thus, sufciently long time intervals ensure that the scalper faces competi-
tion from seekers’ direct applications for every batch. For instance, long
time intervals prevent the scalper from ooding the market with applica-
tions for fake IDs for one batch and using a later batch with no competition
from seekers to cancel these slots booked for fake IDs and transfer them to
their clients’ IDs. Note that in the extreme case when the length of the inter-
val is very short, the batch system is essentially equivalent to the immediate
system.
• Seekers want to learn as soon as possible whether they received a slot, and
when the appointment will take place. Short time intervals during which
applications are collected guarantee this while long time intervals mean
that uncertainty regarding the allocation of slots is resolved only after a
considerable period of time. Moreover, long time intervals can make it
impossible to reallocate canceled slots when the appointments take place
before the end of the next allocation procedure. This can lead to welfare
losses.
What is the right length of the time interval for a batch? The answer will depend on
the context. In many cases, it seems reasonable to start with a one-day time interval.
It is long enough to make regular monitoring of the system by the seekers not too
costly and short enough for seekers to learn about the outcome relatively quickly
and make plans.
We suggest monitoring the system of one-day time intervals and looking for signs
of scalping. If the designer observes a high volatility of the probability to obtain a
slot, the time interval should be extended to give seekers a better chance of apply-
ing. However, if the probability of receiving a slot is constant between batches, the
designer may shorten the interval to increase the convenience of the system for the
seekers.
As a complementary measure, to make the batch system more convenient for
seekers and less likely to be protable for scalpers, the designer can provide the
seekers with the option of automatic reapplications for the next batch if their pre-
vious application was unsuccessful. If a seeker opts for this, her application will
remain in the system until she receives a slot. This can help to ensure that there are
direct applications for every batch, thereby decreasing the opportunity for scalpers
to book slots. Depending on the exact context, this could also be the default choice
for all seekers. In this case, the length of the time period of each batch is not essen-
tial, since there is one set of seekers for all batches. This set would change over time
with arrivals of new applicants and departures of those who received a slot. The only
design choice would then be the frequency in which batches are allocated to best
accommodate the seekers’ needs, but this choice would not affect the protability
of scalping.
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Time at Which Canceled Slots Become Available for Rebooking.—The model
does not specify the exact timing of when canceled slots should reappear in the sys-
tem. To avoid the potential welfare loss of slots that are not used, the designer should
make the canceled slots available immediately after their cancellation in the next
batch. Slots that are canceled late, namely after the last batch was allocated before
the appointment, will be wasted, however. It is crucial to commit to not allocating
them in the last moment, since this would reintroduce an advantage of speed and
incentives for scalping.
Accommodation of Preferences over Slots.—In our theoretical analysis, we
abstract from the fact that seekers might have preferences over specic slots. The
immediate booking system makes it convenient to choose among slots. The batch
system can also accommodate preferences if seekers submit rank-order lists of the
different slots with their application. Instead of a random lottery assigning the slots,
the random serial dictatorship mechanism can be employed. A lottery then deter-
mines the priority of applicants, such that the rst person in the order receives her
highest-ranked slot, the second in the order receives the highest-ranked slots among
those that are still available, and so on.
Time Interval between the Date of the Slot and the First Possibility to Book the
Slot.—One important feature of every booking system is how long in advance the
slots can be booked. A short time interval between the batch being offered and the
date of the slots helps those seekers who realize their demand for appointments
on short notice. The benet of a long time interval is that there are many batches
in which slots can be reallocated in the case of cancellations. In our model, we
assume that seekers know their demand for slots when booking becomes possible,
but this is unrealistic when slots are offered very far in the future. For example, if
there is excess demand for slots and slots are allocated three months in advance,
this would require seekers to make long-term plans, and short-term needs could not
be accommodated. Also, seekers might have an incentive to apply for a slot despite
being uncertain whether they will need it. This can lead to welfare losses when such
seekers frequently cancel a slot or do not show up. For these reasons, it can be useful
to bundle slots arriving soon and slots arriving in the future in the batches to accom-
modate the different needs. Note that the choice of the time interval does not affect
the potential vulnerability of the batch system for scalping but should be chosen
to best accommodate the needs of the seekers in the relevant context. For instance,
slots at consulates can often be booked three months in advance, since the trips for
which the visa are required are usually planned in advance. On the other hand, table
reservations in restaurants are often made available on short notice.
B. Alternative Solutions
One possible alternative to ght scalping is to require a booking deposit, i.e., a
small payment which is refunded when an applicant shows up at her appointment.
We have modeled this policy and characterize the equilibria under the two booking
systems with a deposit in online Appendix Section B in Propositions 4 and 5. While
this policy restricts the set of parameters where scalping is protable in equilibrium
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in the immediate system, it does not preclude scalping with an excess demand for
slots. In the batch system, the scalper’s non-entry is the unique equilibrium outcome
for all parameter values. Thus, the introduction of a deposit does not solve the prob-
lem of scalping in the rst-come-rst-served system, but makes scalping even less
protable in the batch system.
A second possible remedy is the introduction of a cancellation fee. In the imme-
diate system, when the slots are rst booked under fake names and then rebooked
under clients’ names, the cancellation fee is incurred at the moment of rebooking.
Thus, from a modeling perspective, the cancellation fee is equivalent to a deposit,
and Propositions 4 and 5 hold (see online Appendix Section B). Moreover, the
scalper can operate in the immediate system without making use of cancella-
tions, as demonstrated by our experiment and the case of train tickets in India (see
SectionIIIC). Under the batch system, a cancellation fee does not affect the equi-
librium, since there are no cancellations. This is due to the inability of the scalper to
transfer canceled slots to other applicants.
A third possible solution is to provide canceled slots to seekers forming a
physical line instead of making the slots available online. This can prevent the
immediate rebooking of canceled slots by the scalper under the names of his cus-
tomers. But note again that scalping in the immediate system does not require
cancellations and rebookings, as in the Indian Taktal train ticketing scheme.
Even when rebookings are necessary for protable scalping, allowing for lines
at the public ofce defeats the purpose of using an online booking system.
Lines in front of public ofces essentially create another rst-come-rst-served
system.
Another potential solution is tighter control of the booking process itself, e.g., by
introducing ex post verication of the allocation to cancel suspicious applications
such as multiple applications made within a second, or by requiring pre-registration
as a “veried user.” These measures are often observed on sport ticket platforms.
While the measures may render scalping slightly more complicated, the scalper still
has the advantage of speed relative to the seekers. Thus, some seekers with a high
valuation may prefer to pay the scalper and provide him with the registration infor-
mation for a higher chance of getting a slot relative to applying directly (see again
the example of train tickets in SectionIIIC).
Finally, a simple wait list could be employed instead of the rst-come-rst-served
system. Seekers put their name on a wait list or in a virtual queue and are assigned a
slot once it is their turn. Applicants will be on the wait list for some time and will only
be assigned a slot once they have moved up on the list. Typically, the slot assignment
happens shortly before the actual appointment, and not far in advance. This is due
to the possibility of cancellations that need to be accommodated. If a seeker cancels
her slot, all seekers on the wait list are moved upwards. This uncertainty regarding
the exact date and time of obtaining a slot can be a disadvantage when seekers have
to travel a considerable distance for their appointments. Moreover, a waitlist system
can suffer from appointment seekers hoarding slots where people put their names
on the wait list even if they do not need an appointment but expect that this need
may arise in the future. Finally, it is not clear whether the scalper can make prots in
equilibrium. While the speed of bookings does not matter since the waitlist is always
open, the scalper could offer to shorten the waiting time for seekers by canceling
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appointments with fake IDs that he put on the wait list before. We leave a rigorous
analysis of waitlists for future research.
21
Increasing the supply of slots has been suggested as another remedy for scalping.
However, our model shows that scalping can be protable without excess demand.
It is enough that the number of seekers and their valuations are sufcient to cover
the scalper’s costs. Another problem is that the true demand is not easy to gauge in
the immediate system, since applicants who do not receive a slot are not observed. It
is an advantage of the batch system that the market designer can observe the entire
demand for slots, and can adjust the supply if possible.
We believe that our proposed solution is simple and straightforward to imple-
ment. While the small delay (e.g., one day) before nding out the result of an appli-
cation can carry a cost, the costs of alternative systems seem much higher. Most
importantly, unlike all alternative solutions discussed above, the batch system, just
as the immediate system, features online bookings, appointments scheduled at a
predetermined time with no physical lines, and no payments.
C. Other Markets with Scalping
In this subsection, we discuss other markets that are prone to scalping. We also
consider whether our solution is suitable for these markets.
Tickets for Major Sporting Events (Olympic Games, FIFA World Cup, etc.).—
Sporting events and concerts have been the object of scalpers for a long time. Tickets
for such events are often sold out within the rst minutes of being on sale, and are
offered on the black market for a higher price shortly after. Using bots to buy large
numbers of tickets is protable because prices are set below the market-clearing
price.
22
Artists and ticket platforms make attempts to ght scalping, e.g., by offering
tickets to ofcial fans only, but the estimated prot of the resale business is eight
billion dollars per year in the United States alone.
23
Governments have even intro-
duced anti-scalping legislation: the Better Online Tickets Sales Act, also known as
the BOTS Act, was passed by the US Congress in 2016. It outlaws using bots or
other technology for obtaining tickets via online systems to resell them on the sec-
ondary market. However, for the allocation of tickets for the 2018 World Cup, FIFA
collected applications for tickets for each match and category, and in the case of
overdemand for a specic match and price category, a lottery decided who received
the tickets. Scalping was still observed, since people without a matching ticket and
fan ID were allowed to enter the stadium. Without ID verication, the scalper’s strat-
egy of buying many tickets with fake IDs is successful, since he pays less than the
market price and sells the tickets without any constraints later on.
21
An example is the waitlist for apartments in Stockholm where the waiting time has reached 20 years, and
newborn children are put on the waitlist by their parents well before they need housing. See Maddy Savage, “This
Is One City Where You’ll Never Find a Home,” BBC, https://www.bbc.com/worklife/article/20160517-this-is-one-
city-where-youll-never-nd-a-home, (accessed July 15, 2019).
22
For an analysis of these markets, see Courty (2017) and Leslie andSorensen (2014). Courty (2019) studies
the design of resale platforms with ID verication as a potential solution to scalping.
23
See Adrienne Green, “Adele versus the Scalpers,” The Atlantic, https://www.theatlantic.com/business/
archive/2015/12/adele-scalpers/421362/ (accessed December 1, 2020).
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ID verications are not costly in the case of appointments at public ofces, but
they can be much harder to implement for sporting events and concerts. While orga-
nizers of such events commonly state that ID verication will be used, in reality
they tend to shy away from imposing it. ID checks require additional personnel at
the entrance of stadiums, though this has become easier due to scanners and related
technologies.
24
Another barrier to ID verication is the desire to ll the stadium,
since this is important for the success of the event, and also for broadcast revenues.
One can observe scalpers and people leaving messages on Internet forums trying to
convince buyers that there will be no ID verications required. A potential solution
could be to check the IDs of a small number of people at random and to commit to
refusing entry to those whose ID does not match their ticket. The effectiveness of
such a system depends on many parameters, and we leave its exploration for future
research.
To sum up, the evidence from large-scale sporting events demonstrates that the
batch system is not successful without ID verication, which is in line with our
theory.
Limited Editions of Sneakers and Other Consumer Goods.—Some producers
offer limited editions of certain goods below the market-clearing price to a subset of
customers. Prominent examples are sneakers and streetwear.
25
Some brands man-
aged to build a fan base using these limited releases. This is the business model of
Supreme, which specializes in various kinds of streetwear items and was established
in New York in 1994. Supreme regularly offers new limited-edition items, leading
to long queues and a secondary market that appears almost immediately after the
goods have become available. The goods offered in such “drops” often become col-
lectibles. Some of the limited-edition items are sold online, and scalpers dominate
these sales.
26
Drops in online shops are analogous to the immediate system in that speed
determines who gets the goods. Some companies, however, use preregistration and
random draws for their releases. For instance, one of the most successful limited
editions by Adidas, the Yeezy Boost sneakers collection in collaboration with Kanye
West, used both online shops and lotteries. For some releases, Adidas also uses a
virtual queue to ght scalping. Nike ghts bots by allocating its limited release
sneakers through its own SNKRS App, creating a short time window where cus-
tomers can enter a lottery for a pair of sneakers.
27
These solutions are similar to
the batch system. Our theory, however, casts doubt on the success of these lotteries,
since bots can submit many applications and thereby ensure a high chance of getting
24
At the 2018 World Cup, the tickets had a name and each spectator had to have a fan ID. At the entrance to the
stadium the consistency of the documents was checked, but it was inconsequential.
25
Another example is the sale of luxury bags, for instance, the Birkin Bag by Hermès. Despite being released
in 1984, it is still overdemanded with a waiting time of several months. These bags can only be bought through
so-called sales associates that require customers to have a long history of purchases from Hermès: see Lauren
Sherman, “How the Legendary Birkin Bag Remains Dominant,” Bloomberg, https://www.bloomberg.com/news/
articles/2015-06-10/how-the-legendary-birkin-bag-remains-dominant (accessed December 1, 2020).
26
See Damian Fowler, “The Hype Machine: Streetwear and the Business of Scarcity,” BBC, https://www.bbc.
com/worklife/article/20180205-the-hype-machine-streetwear-and-the-business-of-scarcity (accessed December 1,
2020).
27
See Cam Wolf, “The War against Sneaker Bots Peaked at the End of 2018,” GQ, https://www.gq.com/story/
war-against-sneaker-bots (accessed December 1, 2020).
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the underpriced items. Adidas introduced additional barriers against bots, namely
the restriction of one purchase per IP address and credit card, but these measures
can also hurt regular customers.
28
Note that such technical restrictions are not fea-
sible and not necessary for the batch system that we propose for the allocation of
appointments.
Firms that offer limited-release sales could increase the supply to match demand.
However, they benet from the limited availability of their collections since it helps
them to create a fan base and a certain hype around the products. Thus, the rms
may be less opposed to scalping than they claim. Nevertheless, they are concerned
about the perceived fairness of how the limited-release items are allocated. If fair-
ness concerns are sufciently important, the proposed batch system may be useful,
since it is likely to be perceived as fairer than online drops ooded by bots.
Train Tickets in India.—The market for train tickets in India suffers from scalp-
ing despite ID verication. On the day before departure, Indian railways offer tick-
ets for overdemanded trains on short notice, under the so-called Tatkal reservation
scheme. This scheme was introduced to ght scalpers, and to make journeys on
overdemanded routes possible without planning far ahead. The price under the
Tatkal ticket system is 10 percent to 30 percent higher than the normal fare.
29
The
supply of Tatkal tickets is lower than the demand for such tickets, and scalpers use
bots to buy tickets under the names of their clients. Tickets are typically sold out
within four to ve seconds, such that people who want to buy a ticket without the
scalper do not have a chance of obtaining one. The scalpers can book tickets under
the true names of their clients since clients know that they need the help of the scalp-
ers ( so-called travel agencies) to get tickets. The service fee to the agency is often
higher than the price of the ticket.
30
This is an example of a booking system where
even without the possibility to re-book canceled slots or tickets, the advantage of
speed makes scalping protable. Ofcials have tried to prevent scalpers by tracking
suspicious IDs and payments, with limited success. Our proposed batch system is
directly applicable to this market.
Restaurant Reservations.—A related problem concerns scalpers booking tables
in popular restaurants under fake names. Scalpers offer the tables on a website, and
customers who pay for the reservation learn the fake name under which the reser-
vation was made. The restaurants often do not receive any of the fees paid to the
scalpers, and they run the risk of tables not being taken. Note that under the current
rst-come-rst-served system, the checking of IDs by the restaurant would not solve
the problem, since scalpers could still re-book the canceled slots with the real name
of the customers. Under the proposed batch system, scalping would no longer be
possible. However, restaurants are not necessarily concerned about the way their
28
See Edgar Alvarez, “Adidas Tries to Make Buying Yeezys Fair but Misses the Mark,” https://www.engadget.
com/2016-04-07-adidas-yeezy-online-sales-block-ip-addresses.html (accessed December 1, 2020).
29
http://www.indianrailways.gov.in/railwayboard/uploads/directorate/traffic_comm/ CC-2019/Tatkal_
Scheme_02082019.pdf (accessed November 25, 2019).
30
Latitha Sundaram, “Spl Software Helps Touts Book Tatkal Tickets in Secs,” New Indian Express, https://
www.newindianexpress.com/cities/bengaluru/2019/jun/20/spl-software-helps-touts-book-tatkal-tickets-in-
secs-1992638.html (accessed December 1, 2020).
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tables are allocated, and might even have a preference for those clients with the
highest willingness to pay for a table.
IV. Conclusion
This paper considers a novel application for market design, namely the alloca-
tion of appointment slots with online booking systems. With the help of a model
and an experiment, we explain the presence of scalpers in rst-come-rst-served
online booking systems around the world. We also show that the proposed batch
system makes scalping unprotable. Our paper presents a simple solution for an
important problem that has surfaced recently with online booking systems. We do
not claim that it is the unique solution, but it is feasible and technologically simple
to implement. More broadly, we believe that taking into account the incentives of
third parties, such as scalpers, to interfere with matching markets opens up novel
and important research questions.
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