Matchmaker, Matchmaker, Make Me a Match

How do economists tackle real-world markets? Alvin Roth reveals all in his wonderful book on matching markets.

It’s that time of the year when students wait anxiously to hear back from universities on their applications for further studies. The process of college admissions, especially in American colleges, can be understood as a matching market. The actors in this market are the students and college admission committees. A student’s capital is her credentials, the number of letters of recommendation her professors are willing to provide, and the money she can afford to pay in application fees. On the other hand, an admission committee has only a limited number of offers it can extend. While students prefer Ivy League colleges and the admission committees want the best students, in reality both these parties must acknowledge the reality of the marketplace – an incomplete knowledge of how their competitors are interacting with their preferred choices.

In economic terms, a matching market like the one above is characterized as one where price is not the only determinant for a trade. Unlike in commodity markets, in matching markets buyers and sellers care about whom they are dealing with and sometimes even make an effort to woo each other. Taxi aggregator apps like Uber, short-term lodging services like Airbnb, dating apps like Tinder, and corporate hiring are all examples of matching markets where price is just one of the many factors that seals the deal between two parties.

However, like commodity markets, matching markets can be prone to failures and inefficiencies. If not carefully designed, a matching market runs the risk of remaining underdeveloped or even facilitating sub-optimal allocations. It is the design of matching markets that Nobel laureate Alvin Roth studies in his book Who Gets What and Why. In fact, Roth won the Nobel prize (with Lloyd Shapley) “for the theory of stable allocations and the practice of market design.” In Roth’s words, “What often makes matching markets especially challenging is that everyone has to puzzle through not only their own desires but also those of everyone else and how all those other market participants might act to achieve their preferences.”

In this accessible book, Roth delves in great detail into the four pillars of an efficient matching market, emphasizing that one must be careful while designing a marketplace. These pillars are thickness, ease of congestion, safety of participants, and simplicity of use. While thickness of a marketplace refers to its ability to bring many participants (both buyers and sellers) together, ease of congestion signifies the comfort with which participants can evaluate their options and then close the deal. Each of the case studies in the book, which illuminate these four factors, draws from a variety of markets — college and school admissions, hiring of lawyers, kidney donations, assignment of American medical students to residency programmes in hospitals, etc.

In the case of university admissions, the risk aversion of students and universities creates inefficiencies. Students might not apply to the universities they actually prefer, while universities might not make offers to really motivated students.

To solve for this problem, Roth suggests having a central clearinghouse that works on the principle of deferred-acceptance, an algorithm that allows participants to reveal their true preferences and results in a stable final matching for both students and universities.

One of Roth’s outstanding contributions is his work on designing a marketplace for kidney exchanges in the New England region of USA. Since kidneys cannot be legally sold anywhere in the world (except in Iran), a shortage of kidneys for transplants leads to long waiting lists and results in avoidable suffering and death. Al Roth and his colleagues have designed a market that matches incompatible kidney donor pairs and lone altruistic donors with other recipients and donors. The matching system also tries to minimize the wait time and find the best match for the recipients. To read how Roth went from designing efficient three-way transplants (three pairs of donors and recipients) to complex but elegant long chains of exchanges is nothing short of fascinating.

Another interesting concept that Roth explains in great detail is that of Unravelling, a failure specific to matching markets. When trades in a matching market start to happen too soon — before all alternatives are available for the participants to explore — a market is said to have unravelled. As I have explained here, this leads to problems and inefficiencies in allocation, and ruins a matching market’s ability to make good matches.

Given that this is a popular book on economics, Roth does a good job of walking the tightrope between keeping his writing simple and intelligible to the general reader, and yet thorough enough to satisfy those interested in details. However, most of the examples that Roth provides to explain the four factors of market design are America-centric. Culture cannot be completely separated from how people make choices to allocate scarce resources. The reader is left wanting for more diverse examples that would add this cultural nuance. For instance, it is not clear if the USA’s kidney exchange system can be imported to India and what, if any, modifications would be required.

Al Roth’s work is highly recommended for anyone who wants to see how economists go about solving real-world challenges.  Markets are after all human artifacts, and Roth urges economists to be more like engineers and not just understand markets but “intervene in them, redesign them, fix them when they’re broken, and start new ones where they will be useful.”

About the author

Nidhi Gupta

Nidhi Gupta is Head, Post-Graduate Programmes at the Takshashila Institution. She is a graduate of the London School of Economics and Political Science. Her research interests lie in behavioural economics and in origins of public opinion.