The big one in this season of awards

By Tirthankar Mukherjee

As the season for the MMJ awards gets into its own, it seems a good time to talk about another award -- The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, more commonly called the Nobel Prize in economics. This was established in 1968 and is not part of the original group of awards set out in the dynamite tycoon’s 1895 will. There are nit-pickers who do not accept this on par with the other Nobel prizes, and one such Indian went so far as to seek judicial restraint on Amartya Sen being referred to as a Nobel laureate. For the record, the courts did not oblige.

This year’s joint winners are Alvin E. Roth and Lloyd S. Shapleyin recognition of their “theory of stable allocations and the practice of market design” which the award committee deemed “an outstanding example of economic engineering”. No achievement, especially when the prize value is $1.2 million, is universally admired. This time, too, one economist has called this “one of the most boring prizes yet”, and another, a little more peeved, has blogged that the contributions of the two winners “represent grunt work that can easily be provided by computer novices”. Many more, however, think the prize is fully deserved. I shall try to explain the nature of the pioneering work by this economist-mathematician duo on ensuring economic agents find the right match in a market where price is not the deciding factor.

In fact, the award to Shapley rights a wrong committed against him at least once if not twice. The prize in 2005 went to Robert Aumann and Tom Schelling “for having enhanced our understanding of conflict and cooperation through game-theory analysis”. The omission of Shapley was strange, given that he has been the principal architect of modern cooperative game theory, which is, loosely speaking, the study of what outcomes can be expected to emerge when individuals decide to cooperate instead of indulging in cut-throat competition. In fact, admirers of cooperative game theory had been similarly disappointed when John Nash (of Beautiful Minds fame) and two others were jointly awarded the prize in 1994 for their contributions to the other, and certainly more popular, branch of non-cooperative game theory.

Incidentally, the Nobel prize in economics is usually not given to an individual for a single paper or piece of work. In Shapley’s case, too, his prizewinning career goes back to a paper written as early as 1953, where he derived the notion of what has come to be called the Shapley value, an overwhelmingly dominant prescription of what is a fair way of distributing the surplus from cooperation.

The Nobel citation does not mention the Shapley value, mentioning instead that Roth and Shapley have been jointly honoured for their work on matching theory or what has now come to be called market design. This body of economics primarily applies to situations where different agents, institutions or even objects have to be matched or assigned to one another without recourse to prices and through a centralised procedure.

For instance, students are assigned to schools or colleges or medical interns are matched to hospitals through centralised matching procedures in many countries, though not possibly in Mongolia. A more striking example is the procedure to assign donor organs to patients. This area of research was initiated by Shapley in a paper written in 1962 with the late David Gale, a mathematician. They developed what has come to be called the deferred acceptance algorithm. In this algorithm, agents on one side of the market — say hospitals — make offers to prospective interns. Each intern chooses the offer she likes best, and rejects the rest. A crucial part of the algorithm is that offers are not immediately accepted but simply held on to — hence the name deferred acceptance. Any hospital whose offer is rejected can make a new offer to interns who have previously not rejected the hospital. The algorithm terminates when no hospital wants to or can make a new offer and produces a stable outcome — no pair of a hospital and intern wants to form a new match.

Even neoclassical economists do not believe that markets solve all allocation problems. In particular, there are many allocation problems where goods or services should not necessarily go to the highest bidder. Roth has worked on a variety of such allocation problems, including admission to the public school systems in New York City and Boston. Earlier, schools there allocated seats through a complicated process with the objective of assigning students to their top choices as far as possible. The system was very cumbersome and involved repeated student applications, and much heartburn.It also led to strategic behaviour. Parents applied first to less popular schools to make sure they got in, leaving students with none of their top choices.

Roth realised that the matching process could be improved dramatically by applying a version of the Gale-Shapley algorithm. He designed a clearing house system, which continues to be used today.Perhaps, Roth’s most far-reaching contribution — in terms of its effect on human lives — is his work on kidney exchange. A common problem for patients needing organ transplants is that often the donor may be the spouse who has a different blood group. Of course, incompatible donor pairs can often exchange kidneys with other such pairs. Using ideas from matching theory, Roth and co-authors showed how larger scale exchanges of this kind can be conducted in an efficient and incentive compatible manner. Their ideas resulted in a kidney exchange clearing house for patients needing transplants.

I end with an example of the application of their work in an area that stirs the imagination more. How to find a mate is one of the oldest problems in the world and one of many modern answers is to go on a speed dating evening. Shapley became the godfather of modern matchmaking 50 springs ago when he wrote a paper that sought to answer the question of how individuals in a group of people could be paired up when all had different views on who might be their best partner. When matching people up in large groups of, for example, men and women considering marriage, the goal is to ensure that the system is “stable”, that both partners feel that they have got the most attractive possible match; otherwise, they might separate in search of something better.Can algorithms be designed so as to ensure that the outcomes are bilaterally stable in the sense that no two individuals would want to discard their current partners and want to match with each other? Can we ensure that no agent has an incentive to lie about his or her preferences in order to secure a more preferred outcome? These are some of the issues which are central to the burgeoning field of market design.

That work was purely theoretical — no marriages were arranged through its use. Similarly, the Nobel prize does not suggest that the work of the two is terribly relevant to the great macro-economic crises of the day, as many would like an economics award to be. However, any thing that provides a deeper understanding of how markets work acquires importance when that knowledge is put to use by others for the practical benefit of humanity.