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Photo credit: M. Sander/D. Ausserhofer/ WZB
Vaccinations are an important part of countries’ strategies to deal with the global coronavirus pandemic. As a result of new technologies, especially mRNA-based vaccines, there are now several vaccines available, although the production of vaccines is not yet sufficient to allow for most of the global population to be vaccinated. Given the limited supply of vaccines, it is imperative to ensure that the vaccine supplies that are available are used most efficiently.
Often, quite small changes in how the vaccination program proceeds can make a large difference. For example, it was discovered early on that the vials containing the BioNTech/Pfizer vaccine could be used for extracting six doses, rather than the presumed five doses, when making use of a special type of syringe that is less wasteful. Just by using a different instrument to administer the vaccine, the overall supply of the vaccine could thus be increased by 20% - without having to invest in additional manufacturing capacity. At the same time, not using these syringes can mean wasting millions of doses.
Additional efficiency gains can be obtained by scheduling the vaccinations themselves. Scheduling appointments for vaccinations may appear to be trivial compared with the scientific breakthroughs necessary to produce the vaccines. Ensuring that the vaccine is administered and administered quickly is, however, of vital importance for the overall success of the vaccination campaign. For example, when the freezer storage of the vaccine in Seattle failed, the responsible hospital staff quickly decided to vaccinate as many people as possible – eligible as part of a risk group or not – to ensure the vaccine is not wasted.
Booking an appointment for a Covid vaccination is tedious. It can mean being on hold for hours when calling up hotlines, trying to access a website that breaks down regularly, or getting up early to make sure to be among the first. It is like getting a ticket for Wimbledon, the Olympic Games, a Lady Gaga concert, or the Berlin Philharmonic Orchestra. But those who currently hunt for appointments are 80 years and older.
The first-come-first-served system can be convenient when many appointment slots are available, as people can simply visit a website or make a phone call and choose their preferred appointment slot from the available ones. However, the first-come-first-served system becomes much less effective when demand is high relative to the supply of slots. Under excess demand, booking websites or call centers will simply not have any free appointment slots for people to choose from. People are thus forced to go back to the website frequently or make phone calls to check for whether any new appointment slots have become available. This is not only frustrating, as people waste their time by checking the website or calling, but also burdens the websites and call centers with additional traffic that can lead the systems to crash. As additional segments of the population become eligible to get vaccinated, many more appointments will have to be scheduled. Importantly, the excess demand for appointment slots is more likely to become higher than now, as the new target groups are going to be larger groups of citizens, while the increase in the supply of vaccine will probably not increase as dramatically over the next few months.
Bookings via the phone or a website that depend on speed also raise fairness concerns. Some elderly get assistance, e.g., from their children or grandchildren--who can dial the phone number multiple times per minute or click repeatedly on the right buttons for online bookings. These persons have a much higher chance of receiving an appointment than others who do not get help.
Even more problematic is that the first-come-first-served system creates opportunities for scalpers. By using computer programs to book appointment slots, the scalping firms can obtain slots faster than any human. The scalpers then turn around to sell the appointments slot to whoever values them most. Such black markets for appointments are observed worldwide, e.g., for visa appointments at German and US consulates, at public agencies that give out residence permits in France and Ireland, and many more. In the black markets that we have observed, there are many no-shows such that appointment slots are wasted. This is due to the scalper not selling all booked slots to keep the prices up. In the case of slots for vaccinations, this would be very costly since no-shows can lead to the vaccine-an expensive and highly over-demanded resource-being wasted.
Before discussing ways in which the system for scheduling vaccination appointments can be improved, it is important to clarify what objectives such a system should accomplish. While economists often suggest maximizing overall welfare by using prices, such a procedure seems unacceptable, or repugnant, for vaccinations. The reason is that wealthier people with a higher willingness to pay may get vaccinated before elderly patients who are most at risk. Indeed, there have been many reports of people who potentially abused their positions of power to get vaccinated before those most in need.
Several countries have adopted strict guidelines on the priority with which people should be vaccinated. In Germany, for example, the relevant regulation defines three categories of at-risk-populations. The highest priority are people at age 80 or above and medical staff with a high exposure to risk. People at age 70 and above as well as those with severe pre-existing medical conditions and additional categories of medical and public security staff are the next-highest priority group. The third group includes people at age 60 and above and those with other pre-existing conditions. All priority groups also contain one or two contact persons of those with a high risk of covid-19 exposure. Those persons who are not in any of the priority groups are to be vaccinated last. These priorities represent a constraint on the choice of scheduling system.
In addition to repugnance, market design is often concerned with ensuring that markets do not suffer from congestion. Congestion means that there is not enough time to organize and complete transactions. It is primarily a concern when the apparent demand for the good to be allocated exceeds the available supply. Indeed, many of the problems associated with current systems to schedule vaccination appointments can be said to suffer from congestion, often quite literally when the websites for appointment scheduling break down due to heavy traffic. Managing this congestion is thus one of the crucial components of a successful market design. This is particularly the case as the congestion may create incentives for scalpers to exploit and worsen the congestion to their own benefit.
One could think that a proper verification of the identity when booking a slot can overcome the problems of scalping and congestion, but this is not the case. Despite ID verifications, the firms that book and sell slots can make bookings on fictitious names and passport numbers. Once a customer is found, the firm can cancel a slot and rebook it in the customer's name, including pin numbers etc. required for the booking. There is no risk in this operation: despite competition from many people who continuously try to book a slot, no one can compete with the software regarding speed. Bots can book any available slot within a fraction of a second--too fast for any human.
So even if cancellations are not possible or if the booking system can verify whether PIN number and name of person match, thereby making bookings with fake IDs impossible, people who want to get the vaccination can hire the firm and ask it to book a slot with their credentials. This is not just a purely theoretical concern. It can be observed for example in the context of the sale of exclusive sneakers or train tickets in India.
Suppose for example there are four persons who are currently eligible for a vaccination. Let us call them Anne, Beth, Chris and Dave. Unfortunately, there are only two slots available. In the absence of a scalper, whichever two of the four happen to visit the website or make a phone call first will end up with the vaccine. The other two will be forced to continue visiting the website or making phone calls to see whether new vaccine appointments have become available.
Suppose now that Chris, who has a high willingness to pay for the vaccine, instead of trying to book a slot, makes use of the service of a scalper who promises to book an appointment. If Chris approaches the scalper before the two slots become available, it is guaranteed that Chris will obtain a slot. In return the scalper will get the price that he demanded. Note that even a unique ID or pin number for Chris cannot prevent scalping, since Chris could simply let the scalper know the ID before the appointment slots are put online.
Some countries, for instance, Germany, adopted the system that an appointment can only be booked with a pin code, which is sent to people who have a right to be vaccinated according to the priorities. While the verification of pin codes does not preclude scalping, the authority can eliminate scalping if the pin numbers are sent out such that there is no excess demand for the appointments. However, this is costly and might lead to a waste of vaccine, as some people might not be able to take offered appointments or do not want to be vaccinated. Thus, the authority is interested in creating some degree of overdemand to avoid wasting the vaccine, but this generates the potential for profitable scalping activities.
The system of allocating slots can significantly impact the success or failure of the vaccination campaign. When designing it, we should draw lessons from similar booking systems. If something that is scarce and valuable is allocated for free (or at a low price that leads to excess demand), it creates possibilities for scalping, just like a Lady Gaga concert or tickets to the Champions League final would. One can auction off the slots to the highest bidder to solve the problem, but this lacks fairness in the context of vaccinations. Luckily, unlike with concert tickets, the identity of the person to be vaccinated can be verified easily when she appears for the vaccination. This allows for an elegant solution of the problem. The solution is simple and has been proposed by Hakimov et al. 2021. Instead of relying on speed, the online booking system should collect applications for slots and preferred times over a pre-defined period. Whenever a new batch of appointment slots becomes available, the system randomly determines which applicants get a slot.
To see how this works, let us reconsider Anne, Beth, Chris and Dave looking for vaccination appointments. Under the first-come-first-served system, whoever of them was first to visit the website got the appointment, or, alternatively, whoever was willing to pay the price demanded by the scalper got the appointment. With a batch system, all four of them would register their demand for a vaccine slot on the website or on the phone. Once the time interval for the batch has expired, the two slots would then be given randomly to two of the four. Notably, the time at which the demand was registered would not be a relevant factor for determining who gets the appointment. Registering additional demand would not be feasible, since each ID can only be used once.
Under the new system, the scalper could no longer be active. If Chris were again willing to pay to obtain a slot, the scalper can no longer ensure Chris to get one. The scalper would be forced, like Anne, Beth and Dave, to submit the demand for Chris and then hope that the random allocation of slots picks Chris. Since speed no longer matters for the appointment slot allocation, the scalper can no longer book a slot before everyone else. Knowing this, Chris would no longer be willing to pay for the scalper’s service. As a result, a batch system would be immune to the sort of scalping that has been observed in many markets and could also appear for vaccination appointments.
We conducted a series of lab experiments to test our proposed batch system. These results confirm that first-come-first-served scheduling systems are vulnerable to scalpers, particularly when the demand for appointments is high. On the other hand, batch systems that remove the scalper’s speed advantage are robust to scalping irrespective of whether there is excess demand or not.
Another advantage of the batch system is that it saves the time of those who did not initially get a slot. By having registered their demand, the authorities know of their demand for a vaccination which they can then try to satisfy at the next opportunity. There would therefore be no need for unsuccessful appointment seekers to revisit the website or make a phone call again and again. Not only does this save their time (and nerves) but it also reduces the traffic load on the websites and the time demands on the call center workers. An additional benefit is that the authorities also obtain a much clearer picture of the number of people who are willing to get vaccinated, so that they can better decide when to open vaccinations to lower priority groups.
Under a batch system, there is no time pressure when applying for a slot, websites will not break down anymore, and fairness can be restored by making sure that the desired priorities are followed. Importantly, this system is immune to black market activities.
Instead of a completely random allocation, the system can also use priorities based on the applicants' attributes. Suppose for example that Anne and Beth are both 95 years of age while Chris and Dave are both only 91 years of age. In a first-come-first-served system, whichever of them was first to use the website would get the slot. In the batch system, once the demand of all four has been registered, it could be decided that rather than allocating the two available slots randomly among them, Anne and Beth should be given the slot due to their more advanced age.
Additionally, a batch system can easily be modified to accommodate different choices regarding vaccination strategies. For example, many countries insist on giving people their second vaccination before giving the first vaccination to people with a lower priority. When scheduling appointments in a batch system, the allocation of appointment slots could give a higher priority to those who either have or have not yet received the first dose of the vaccine.
The batch system can also accommodate different preferences over the timing of the vaccination slots. When registering their demand, people could be asked about their preferred day of the week and time of the day to receive the vaccine. This information could then be used by the authorities to schedule the appointments to accommodate these preferences as good as possible.
What are the disadvantages of the proposed system? The only disadvantage is that applicants will need to wait for some time until they learn whether they received a slot. The allocation of a batch can, for instance, be determined every other day, offering new slots a week later. In this case, a person will receive the result of the allocation every two days, without any time-consuming activity in between. Waiting for feedback seems like a small price to pay for a fair and stress-free system lacking a black market. Another potential disadvantage of the batch system when there are multiple concurrent allocation schemes is that double (or triple or quadruple) booking may occur. People who have entered their name on one waitlist may decide to enter additional waitlists at another hospital to increase the chance of getting an appointment. If such people are then successful in obtaining a slot in more than one hospital, there is a risk of vaccines being wasted as people only show up for one of the appointments. When the allocation of appointments is not centralized, the batch system may therefore inadvertently create artificial congestion. Hence, when designing batch systems care should be taken to coordinate appointments centrally to ensure that no double booking can take place.
This Insight is based on "How to Avoid Black Markets for Appointments with Online Booking Systems" which can be accessed through https://rationality-and-competition.de/wp-content/uploads/discussion_paper/179.pdf
The original study has been conditionally accepted at American Economic Review.