Markets are institutions that facilitate the exchange of goods and services. They act as clearing houses. The normal medium of exchange is money in some form. But many markets deal in exchanges that do not involve money and frequently involve matching: Graduating medical students are normally matched with hospitals in order that graduates complete their residency requirement; in many jurisdictions in the US applicants for places in public schools that form a pool within a given school-board must go through an application process that sorts the applicants into the different schools within the board; patients in need of a new kidney must be matched with kidney donors.
These markets are clearinghouses and have characteristics that distinguish them from traditional currency-based markets that we have considered to this point.
- The good or service being traded is generally heterogeneous. For example, patients in search of a kidney donor must be medically compatible with the eventual donor if the organ transplant is not to be rejected. Hospitals may seek residents in particular areas of health, and they must find residents who are, likewise, seeking such placements. Students applying to public schools may be facing a choice between schools that focus upon science or upon the arts. Variety is key.
- Frequently the idea of a market that is mediated by money is repugnant. For example, the only economy in the world that permits the sale of human organs is Iran. Elsewhere the idea of a monetary payment for a kidney is unacceptable. A market in which potential suppliers of kidneys registered their reservation prices and demanders registered their willingness to pay is incompatible with our social mores. Consequently, potential living donors or actual deceased donors must be directly matched with a patient in need. While some individuals believe that a market in kidneys would do more good than harm, because a monetary payment might incentivize the availability of many more organs and therefore save many more lives, virtually every society considers the downside to such a trading system to outweigh the benefits.
- Modern matching markets are more frequently electronically mediated, and the communications revolution has led to an increase in the efficiency of these markets.
The Economics prize in memory of Alfred Nobel was awarded to Alvin Roth and Lloyd Shapley in 2011 in recognition of their contributions to designing markets that function efficiently in the matching of demanders and suppliers of the goods and services. What do we mean by an efficient mechanism? One way is to define it is similar to how we described the market for apartments in Chapter 5: following an equilibrium in the market, is it possible to improve the wellbeing of one participant without reducing the wellbeing of another? We showed in that example that the market performed efficiently: a different set of renters getting the apartments would reduce total surplus in the system.
Consider a system in which medical graduates are matched with hospitals, and the decision process results in the potential for improvement: Christina obtains a residency in the local University Hospital while Ulrich obtains a residency at the Childrens' Hospital. But Christina would have preferred the Childrens' and Ulrich would have preferred the University. The matching algorithm here was not efficient because, at the end of the allocation process, there is scope for gains for each individual. Alvin Roth devised a matching mechanism that surmounts this type of inefficiency. He called it the deferred acceptance algorithm.
Roth also worked on the matching of kidney donors to individuals in need of a kidney. The fundamental challenge in this area is that a patient in need of a kidney may have a family member, say a sibling, who is willing to donate a kidney, but the siblings are not genetically compatible. The patient's immune system may attack the implantation of a 'foreign' organ. One solution to this incompatibility is to find matching pairs of donors that come from a wider choice set. Two families in each of which there is patient and a donor may be able to cross-donate: donor in Family A can donate to patient in Family B, and donor in Family B can donate to patient in Family A, in the sense that the donor organs will not be rejected by recipients' immune systems. Hence if many patient-donor families register in a clearinghouse, a computer algorithm can search for matching pairs. Surgical operations may be performed simultaneously in order to prevent one donor from backing out following his sibling's receipt of a kidney.
A more recent development concerns 'chains'. In this case a good Samaritan ('unaligned donor') offers a kidney while seeking nothing in return. The algorithm then seeks a match for the good Samaritan's kidney among all of the recipient-donor couples registered in the data bank. Having found (at least) one, the algorithm seeks a recipient for the kidney that will come from the first recipient's donor partner. And so on. It turns out that an algorithm which seeks to maximize the potential number of participating pairs is fraught with technical and ethical challenges: should a young patient, who could benefit from the organ for a whole lifetime, get priority over an older patient, who will benefit for fewer years of life, even if the older patient is in greater danger of dying in the absence of a transplant? This is an ethical problem.
Examples where these algorithms have achieved more than a dozen linked transplants are easy to find on an internet search - they are called chains, for the obvious reason.
Consider the following efficiency aspect of the exchange. Suppose a patient has two siblings, each of whom is willing to donate (though only one of the two actually will); should such a patient get priority in the computer algorithm over a patient who has just a single sibling willing to donate? The answer may be yes; the dual donor patient should get priority because if his two siblings have different blood types, this greater variety on the supply side increases the chances for matching in the system as a whole and is therefore beneficial. If a higher priority were not given to the dual-donor patient, there would be an incentive for him to name just one potential donor, and that would impact the efficiency of the whole matching algorithm.
It is not always recognized that the discipline of Economics explores social problems of the nature we have described here, despite the fact that the discipline has developed the analytical tools to address them.
