Alvin Roth is the Craig and Susan McCaw Professor of Economics at Stanford University and co-winner of the 2012 Nobel Prize in Economics. In January of this year, at the close of his term as president of the American Economic Association, he offered his presidential address, “Marketplaces, Markets, and Market Design,” which followed up on his 2016 book, Who Gets What—And Why. His address interested me enough to pick up the book and write this review.

In it, he proclaims, “The new economics of market design brings science to matchmaking, and to markets generally. That’s what this book is about” (Roth’s emphasis). “My hope,” he tells readers, “is that this book will help you see markets in new ways.”

If there is a shortage in the market for a commodity, economists predict that buyers will bid higher prices and sellers will accept the higher prices in return for increasing the quantity supplied. In this case, it doesn’t matter what commodity is being traded. “The price does all the work,” he explains, “bringing [buyer and seller] together at the price at which supply equals demand.”

However, in some cases, what is being traded does matter. For instance, consider a “matching market” such as a market for donor organs. In such a market, buyers must choose sellers and sellers must choose buyers in order for the exchange to be mutually beneficial. Roth puts it this way: “A market involves matching whenever price isn’t the only determinant of who gets what.” Or who gets whom, for that matter.

Market necessities / Some economists try to make the world a better place by recommending better public policy. Roth makes the world better by designing markets so that they work better. “Market design” is the set of rules according to which buyers and sellers interact; it is also the making of those rules.

A market works well, in the jargon of market design, when it is “thick,” “uncongested,” and “safe.” A market is thick if there are many buyers and sellers. It is uncongested if buyers and sellers have enough time to evaluate offers. In general, if buyers and sellers feel comfortable participating, a market is safe. A matching market in particular is safe if buyers and sellers honestly share who they want to deal with. For example, school choice requires that parents “list their true preferences” for schools, which may differ from what they think they might get based on the school board’s assignment criteria.

A market “fails” or “unravels” when it becomes thin, congested, or unsafe. Roth strives to repair those problems.

Thickening markets / Kidney exchange illustrates the features of a matching market as well as the benefits of market design. Roth first pondered kidney exchange in the early 1980s. He reports that in 2014, the shortage of kidneys exceeded 100,000. Given that shortage and the National Organ Transplant Act of 1984, which bans the sale of kidneys, market designers aimed to thicken the market by increasing the number of donors. After that, the author says, “making the market thick involved assembling databases of patient–donor pairs.” These pairs must match based on blood type and immune system. Roth and his colleagues devised an algorithm to determine matches.

To shed light on the possibilities, consider how a database enables “trading cycles.” Suppose Mr. Jones needs a kidney and Mrs. Jones is willing to donate one of hers, but they are incompatible. Likewise, Mrs. Smith needs a kidney and Mr. Smith is willing to donate one of his, but they too are incompatible. Roth’s algorithm determines that Mr. Jones and Mr. Smith are compatible, and Mrs. Jones and Mrs. Smith are compatible. Doctors perform one transplant from Mr. Smith to Mr. Jones and another from Mrs. Jones to Mrs. Smith. This “two-way cycle” saves two lives. Likewise, a “three-way cycle” saves three lives. Last year, doctors at Yale–New Haven Hospital performed a nine-way cycle.

Trading “chains” make the market thicker yet. In contrast to a trading cycle in which a donor expects a loved one to receive a kidney, a “non-directed donor” initiates a chain that will include “some patient–donor pairs, and end with a donation to someone on the waiting list.” Another significant benefit of a chain is that transplants may occur non-simultaneously. Note that Mr. Smith would hesitate to donate his kidney to Mr. Jones if he could not expect Mrs. Jones to give up hers at the same time and place to Mrs. Smith. Doctors perform the transplants in a kidney trading cycle simultaneously in order to prevent the possibility that a directed donor cannot or will not give up a kidney after his or her loved one has already received one.

The problem with simultaneous operations is that they bump into resource constraints because of the limited availability of doctors, nurses, and facilities. A non-directed donor relaxes those constraints; he or she donates to Mr. Jones, and even if Mrs. Jones fails for some reason to reciprocate, no one has donated without a loved one receiving a kidney. To paraphrase Roth, Mr. Smith may remain in the kidney exchange as a donor to benefit his wife at some point in time. The author shares the story of a non-directed donor who initiated a chain that involved 16 operations over a period of years. More recently, since publication of this book, Roth described a chain involving 60 donors and recipients.

The aforementioned resource constraints that hindered simultaneous transplant operations congested the market for kidneys. Trading chains not only thicken the market; the non-simultaneous operations they make possible also decongest the market by relieving those resource constraints.

Decongesting markets / Another factor impedes trading. “Keep in mind,” Roth writes, “that hospitals earn revenue on their transplants; they’re commercial enterprises as well as caregivers.” Thus hospitals have an incentive to keep their “easy-to-match” pairs off the market and refer the “hard-to-match” pairs to the market. The problem is that “when transplant centers withhold easy-to-match pairs and transplant them internally, it reduces the number of people who can be matched nationwide, because it’s easier to find matches for hard-to-match pairs if they don’t always have to be matched with other hard-to-match pairs.”

Roth and a colleague imagine that the problem can be fixed by rewarding hospitals with more matches based on the number of easy matches they refer to the market. Their idea is unlikely to be implemented, Roth laments, because health care providers refuse to admit that “hospitals are strategic players in competition with one another.” More lives are likely to be saved by integrating regional markets for kidneys into a national market and relying on trading chains.

At the time he was writing, Roth anticipated kidney exchange would go global. Since publication, that has become a reality. Transplants cost less than dialysis; the cost savings finance travel, transplant operations, and other health care for patients and donors from poor countries to rich countries in what one of Roth’s medical colleagues calls “reverse-transplant tourism.”

Recall that the National Organ Transplant Act prohibits the buying and selling of organs. Why? Roth’s term for it is repugnance. “Let’s call a transaction repugnant,” he suggests, “if some people want to engage in it and other people don’t want them to.”

He begins his chapter on repugnance by noting that even though there would be willing producers and consumers of horsemeat, a majority of voters in California banned the market. What offends third parties, as they observe other people buying and selling, varies over time and from place to place. Roth gives several examples. Money lending used to be repugnant in the West; it remains so in Islamic society. On the other hand, indentured servitude was not repugnant in early America, but eventually became so. The French and the Germans continue to dine on horsemeat.

If anyone can think of a way to enable the buying and selling of kidneys without arousing repugnance, the gains from trade—in terms of lives saved—would be large. Roth presents a few ideas. Some people object to buyers compensating sellers because they expect the former to have high incomes and the latter to have low incomes. The objection fails to see that by allowing donors to be paid, the increase in the quantity supplied of kidneys will benefit low-income patients by reducing the time they spend on waiting lists. There is nevertheless a way to avoid this objection based on income inequality. Roth points out that the government could raise taxes and buy kidneys, which would then be assigned to patients on waiting lists based on criteria other than income.

Another objection is that allowing donor compensation could lead to undue influence. For example, creditors might pressure debtors into paying off their obligations by selling a kidney. To counter this objection, the author recommends donors undergo a “cooling-off period” so that they are sure they are making the right decision.

At the time he was writing, Roth admitted that he was pessimistic about overturning repugnance in the buying and selling of kidneys. He refuses to give up, however. His latest tack advances a question put forth by Philip Cook and Kimberly Krawiec of Duke University: If society finds it acceptable for professional football players to put their health at risk for compensation, why not kidney donors? (“If We Pay Football Players, Why Not Kidney Donors?” Spring 2018.)

Although kidney exchange teaches many lessons about a matching market and market design, the book offers much more. Roth explains the intricacies of matching law students with judges, medical students with residencies, and students with schools. He describes the latest ideas of market designers who are trying to solve problems that arise when stock traders compete down to a fraction of a millisecond, or Federal Communication Commission officials auction “a package of licenses” to businesses that use a portion of the radio spectrum.

The book has an offbeat element reminiscent of Freakonomics, the 2005 bestseller from economist Steven Levitt and journalist Stephen Dubner. For example, Roth writes of his and colleague Xiaolin Xing’s discussion of an amazing case of early trading in which a polygynous Aboriginal Australian tribe matched newborn boys with the future daughters of newborn girls. Other colleagues discovered that delivering “virtual ‘roses’ ” on a dating website was as effective in generating mutual interest as good looks and a good job. The reader will encounter market maladies such as “sniping” (offering to buy just before the market closes) and “exploding offers” (those that expire rapidly). Sometimes market designers solve or attenuate these problems, sometimes not.

Readers of Regulation may be interested in how Roth handles this question: “How do we square market design with the notion of the ‘free market’ that so many people hold dear?” To him, a free market is “a market with well-designed rules that make it work well.” Those who design the rules may be buyers and sellers in the market as well as government officials imposing mandatory regulations. Both the private actors and the government regulators, he lets us know, are capable of making mistakes.

He thinks of “economists as engineers.” Readers might balk at that because it sounds like dreaded social engineering. But Roth points out that markets are “human artifacts” just like agriculture and the medical profession. Just as farmers tweak seeds and doctors prescribe medicine, economists may recommend modifications that help markets work better. Let’s hope that economists who think of themselves as engineers use persuasion in the marketplace of ideas and refrain from advocating coercive government intervention.