Economics that adds up

19 October 2012

Alvin Roth, who with Lloyd Shapley won the 2012 Nobel prize for economics.
Alvin Roth, who with Lloyd Shapley won the 2012 Nobel prize for economics.

This year's Nobel prize in economic sciences was awarded to Alvin Roth and Lloyd Shapley for their market design research and specifically for matching theory and its applications.

Their work has implications for organising markets to improve welfare in many situations including matching students to schools, workers to jobs and organ donors to organ recipients, all areas Roth has been instrumental in reorganising the past two decades.

An underlying principle in economics is mutually beneficial exchange. In most markets this is determined by buyers who choose what they want assuming that all that buyers have to do is pay market prices, and similarly sellers producing whatever they want to produce, assuming they can sell as much as they want at market prices.

However, in matching markets things are not so straightforward. In matching markets there is an application process (for example, university admissions, jobs) and both sides must agree to be matched; person A may want to match with person (or school or firm) B, but the match only occurs if B also wants to match with A.

Mathematicians David Gale and Lloyd Shapley (1962) originally discussed matching markets in the context of marriage; a man could not simply choose a woman, nor could a woman simply choose a man, they had to choose each other. Roth recognised that there are many environments where each side had to choose each other, including (as Roth remarked at his Nobel press conference) some of the most important crossroads in people's lives including school, career and partner choices.

Gale and Shapley's original work focused on one-to-one matches like marriage, and researchers have extended matching theory to many-to-one matches, many-to-many matches and many-to-few matches like school choice with many students matching to a few schools.

To organise these markets, algorithms (essentially a set of rules) are often used in which everyone on each side of the market lists their preferences for whom they want to get matched with. Matching theory examines two central issues regarding a matching algorithm's success: stability and strategy proofness. A match is stable if there is no pair who mutually would want to switch from the outcome generated by the algorithm in order to get matched with each other. An algorithm is strategy-proof if it induces everyone to feel safe to indicate their true preferences.

Shapley and Roth's research showed that some algorithms create stable, strategy-proof matches while others do not. When an algorithm fails to be stable or strategy-proof, the consequences can be severe students possibly not getting into preferred schools (or any school), or people making arrangements privately and well in advance of the algorithm that would have been made differently (and better) if they could have chosen later.

Roth's research showed that in the US the allocation of medical school graduate students to hospitals for internships actually used Gale and Shapley's (1962) stable match, while several regions in England used algorithms that were not stable. Roth showed that in the US the algorithm worked; students entered the match in their last year of medical school when they knew what hospitals would be best for them, and hospitals had the best information to know which students fitted their needs.

However, essentially all the algorithms in England, without stability, failed to work, resulting in students having to commit to hospitals very early in their medical school education and hospitals having to commit to students before getting good signals on students' abilities or fit.

Roth explained that the US matching algorithm also started unravelling in the 1980s. This was when there were more female students in medical school, and importantly more couples, whose preferences were no longer just a list of the hospitals they liked most but also included wanting to get matched to a hospital near to where their partners got matched. The original algorithm could not accommodate these more complex preferences and so it was no longer stable and gave students and hospitals increasing incentives to make arrangements much earlier.

Roth solved the problem theoretically for these more complex preferences and implemented the new algorithm used today, creating stability without more unravelling.

Roth's more recent and closely related research has been instrumental in developing kidney exchanges. One problem to overcome with kidney donations is that people often wish to donate a kidney to loved ones only, but there is an extremely high chance of biological incompatibility making one's donation not useful to the loved one.

In a kidney exchange, however, Roth formally developed the idea to take advantage of the fact that there could be many interested donors with these biological mismatches, and a series of exchanges could be beneficial to everyone: for instance, suppose the Smiths, Joneses and Williamses cannot donate to their own spouses due to biological mismatches, but Mr Smith can donate to Mr Jones, Mrs Jones can donate to Mrs Williams and Mr Williams can donate to Mrs Smith, creating a three-way kidney exchange.

Extending this idea, kidney exchanges have recently had dozens more participants. Given that tens of thousands of people wait for a kidney each year, and many die waiting, improving the efficiency of kidney donations through these exchanges is literally saving lives.

In sum, matching markets are at the crossroads of many of life's most important decisions. These decisions are often complex with many important considerations. Roth has shown that the algorithms in which matches are actually made can be designed to reduce some of the complexity and directly improve the outcomes of people's lives.

Roth is at the vanguard of economists who relate the arcane, often abstract and esoteric art of economic science to the real world.

Many economists who today see shortcomings (poor school choice systems and missed opportunities for kidney transplants) are no longer just writing about them to other economists, but are now doing something about them.

The author of this article, having worked closely with Roth, believes the broader message is that economists' work can improve institutions well beyond matching markets and kidney exchange. For instance, my colleagues and I are working closely with the Australian Red Cross Blood Service to improve the nation's blood supply, applying economic theory to real world issues. Many other economists are using similar approaches to work with governments on better designed auction mechanisms and improving institutions dealing with environmental policy. The change in how many academic economists are now directly addressing real world issues is why Roth is deserving of a Nobel prize and why this year's Nobel prize is important.

Robert Slonim is a professor in the School of Economics at the University of Sydney. He specialises in game theory, incentives, trust, learning and most recently public policy applied to education and blood donations.

Alvin Roth gave a Sydney Ideas lecture on matching markets at the University of Sydney in July 2012. Read more about his lecture.

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