Trading kidneys, repugnant markets and stable marriages win the Nobel Prize in Economics

Roth and Shapley charted a course for economists to go beyond simply arguing for markets in everything.

The 2012 Nobel Prize in Economics - technically the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, but nobody cares - has been awarded to two American Economists, Alvin Roth and Lloyd Shapley "for the theory of stable allocations and the practice of market design". The Nobel Committee explains what that means:

This year's Prize concerns a central economic problem: how to match different agents as well as possible. For example, students have to be matched with schools, and donors of human organs with patients in need of a transplant. How can such matching be accomplished as efficiently as possible? What methods are beneficial to what groups? The prize rewards two scholars who have answered these questions on a journey from abstract theory on stable allocations to practical design of market institutions.

Lloyd Shapley used so-called cooperative game theory to study and compare different matching methods. A key issue is to ensure that a matching is stable in the sense that two agents cannot be found who would prefer each other over their current counterparts. Shapley and his colleagues derived specific methods – in particular, the so-called Gale-Shapley algorithm – that always ensure a stable matching. These methods also limit agents' motives for manipulating the matching process. Shapley was able to show how the specific design of a method may systematically benefit one or the other side of the market.

Alvin Roth recognized that Shapley's theoretical results could clarify the functioning of important markets in practice. In a series of empirical studies, Roth and his colleagues demonstrated that stability is the key to understanding the success of particular market institutions. Roth was later able to substantiate this conclusion in systematic laboratory experiments. He also helped redesign existing institutions for matching new doctors with hospitals, students with schools, and organ donors with patients. These reforms are all based on the Gale-Shapley algorithm, along with modifications that take into account specific circumstances and ethical restrictions, such as the preclusion of side payments.

Even though these two researchers worked independently of one another, the combination of Shapley's basic theory and Roth's empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets. This year's prize is awarded for an outstanding example of economic engineering.

The committee have yet again reaffirmed the old adage that the most important thing to do when trying for a nobel prize is to live long enough that your achievements are recognised. The Gale-Shapley algorithm, for instance, was devised in 1962, when Lloyd Shapley was 34. It concerns a maths problem known as the stable marriage problem: if you have an even number of men and women, can you always come up with a set of marriages where there are no two people of opposite sex who would both rather have each other than their current partners? (1960s maths problems: usually heteronormative.) If you can, then the marriage is "stable".

The Gale-Shapley algorithm is a way of always ensuring stable matches; and much of Shapley's work covers the same areas, straddling the boundaries between economics, mathematics, and computer science.

Roth is the younger of the two winners, and works in a far more empirical sphere. As the committee points out, although the two men never actually collaberated, Roth took Shapley's theoretical work and applied it to actually existing markets. For instance, Roth used the Gale-Shapley agorithm to ease the kidney shortage in the US. David Wessel explains (£):

As of noon yesterday, 58,470 people in the U.S. were waiting for a kidney transplant. Most won't get one this year. There aren't enough donated kidneys to go around. Surgeons transplanted just 15,129 kidneys last year. Now a band of transplant surgeons and economists are trying to fix that by creating a moneyless market for exchanging kidneys. Most transplanted kidneys come from a person who has died, a supply that grows slowly because of ignorance about the need for donations or grieving relatives' reluctance. But a kidney taken from a live donor works better, and almost everyone has a spare. As techniques improve for removing healthy kidneys and for suppressing the body's tendency to reject a transplant, doctors increasingly turn to kidneys from living donors, usually relatives. Last year, 43% of kidneys transplanted in the U.S. came from living donors, up from 28% a decade ago. But a biological barrier often blocks a transplant from a relative. In about a third of all would-be pairs, blood types are incompatible. In others, the sick person has antibodies that can initiate a rejection of the donated organ. It's heartbreaking "to have the treasure of the live donor and then have that not go forward because of a biological obstacle," says Massachusetts General Hospital transplant surgeon Francis DelMonico.

Occasionally, transplant centers spot a way out: One New England father with blood type A couldn't donate a kidney to his daughter with blood type B. So he gave a kidney to a teenager with blood type A, and the teenager's sister gave a kidney for the man's daughter. New England's transplant centers have done six such exchanges. Baltimore's Johns Hopkins University has done seven.

The crucial thing about Roth's work, from an economic point of view, is that it involves finding stable allocations using market-like situations without involving money. The kidney swaps in the New England situation are market-like, trading kidneys for kidneys in a way that makes all parties better-off, but they don't actually require kidneys to be bought and sold.

We can see the importance of this by looking at another paper of Roth's, not cited by the committee, on repugnance in markets (pdf). Roth demonstrates that some markets are limited because the very existance of a market in some goods is considered repugnant. He argues, for instance, that the trade in horse meat being banned in California is not done through fears that eating horse meat is unsafe; nor is it done for animal welfare reasons, since it is still legal to farm and kill horses. But banned it is, and Roth argues that the natural response of economists to situations of this type - to argue for freer markets - is wrong, since it ignores the very strong feelings involved in the situation. Instead:

Being aware of the sources of repugnance can only help make such discussions more productive, not least because it can help separate the issues that are fundamentally empirical—like the degree of crowding out of altruistic donations that might result from different incentive schemes compared to how much new supply might be produced—from areas of disagreement that are not primarily empirical.

Hopefully his new Nobel Prize should give that argument greater weight in the years ahead.

A patient receives a kidney in Johns Hopkins university in Baltimore. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Arsène Wenger: how can an intelligent manager preside over such a hollowed-out team?

The Arsenal manager faces a frustrating legacy.

Sport is obviously not all about winning, but it is about justified hope. That ­distinction has provided, until recently, a serious defence of Arsène Wenger’s Act II – the losing part. Arsenal haven’t won anything big for 13 years. But they have been close enough (and this is a personal view) to sustain the experience of investing emotionally in the story. Hope turning to disappointment is fine. It’s when the hope goes, that’s the problem.

Defeat takes many forms. In both 2010 and 2011, Arsenal lost over two legs to Barcelona in the Champions League. Yet these were rich and rewarding sporting experiences. In the two London fixtures of those ties, Arsenal drew 2-2 and won 2-1 against the most dazzling team in the world. Those nights reinvigorated my pride in sport. The Emirates Stadium had the best show in town. Defeat, when it arrived in Barcelona, was softened by gratitude. We’d been entertained, more than entertained.

Arsenal’s 5-1 surrender to Bayern Munich on 15 February was very different. In this capitulation by instalments, the fascination was macabre rather than dramatic. Having long given up on discerning signs of life, we began the post-mortem mid-match. As we pored over the entrails, the curiosity lay in the extent of the malady that had brought down the body. The same question, over and over: how could such an intelligent, deep-thinking manager preside over a hollowed-out team? How could failings so obvious to outsiders, the absence of steel and resilience, evade the judgement of the boss?

There is a saying in rugby union that forwards (the hard men) determine who wins, and the backs (the glamour boys) decide by how much. Here is a footballing equivalent: midfielders define matches, attacking players adorn them and defenders get the blame. Yet Arsenal’s players as good as vacated the midfield. It is hard to judge how well Bayern’s playmakers performed because they were operating in a vacuum; it looked like a morale-boosting training-ground drill, free from the annoying presence of opponents.

I have always been suspicious of the ­default English critique which posits that mentally fragile teams can be turned around by licensed on-field violence – a good kicking, basically. Sporting “character” takes many forms; physical assertiveness is only one dimension.

Still, it remains baffling, Wenger’s blind spot. He indulges artistry, especially the mercurial Mesut Özil, beyond the point where it serves the player. Yet he won’t protect the magicians by surrounding them with effective but down-to-earth talents. It has become a diet of collapsing soufflés.

What held back Wenger from buying the linchpin midfielder he has lacked for many years? Money is only part of the explanation. All added up, Arsenal do spend: their collective wage bill is the fourth-highest in the League. But Wenger has always been reluctant to lavish cash on a single star player, let alone a steely one. Rather two nice players than one great one.

The power of habit has become debilitating. Like a wealthy but conservative shopper who keeps going back to the same clothes shop, Wenger habituates the same strata of the transfer market. When he can’t get what he needs, he’s happy to come back home with something he’s already got, ­usually an elegant midfielder, tidy passer, gets bounced in big games, prone to going missing. Another button-down blue shirt for a drawer that is well stuffed.

It is almost universally accepted that, as a business, Arsenal are England’s leading club. Where their rivals rely on bailouts from oligarchs or highly leveraged debt, Arsenal took tough choices early and now appear financially secure – helped by their manager’s ability to engineer qualification for the Champions League every season while avoiding excessive transfer costs. Does that count for anything?

After the financial crisis, I had a revealing conversation with the owner of a private bank that had sailed through the turmoil. Being cautious and Swiss, he explained, he had always kept more capital reserves than the norm. As a result, the bank had made less money in boom years. “If I’d been a normal chief executive, I’d have been fired by the board,” he said. Instead, when the economic winds turned, he was much better placed than more bullish rivals. As a competitive strategy, his winning hand was only laid bare by the arrival of harder times.

In football, however, the crash never came. We all wrote that football’s insane spending couldn’t go on but the pace has only quickened. Even the Premier League’s bosses confessed to being surprised by the last extravagant round of television deals – the cash that eventually flows into the hands of managers and then the pockets of players and their agents.

By refusing to splash out on the players he needed, whatever the cost, Wenger was hedged for a downturn that never arrived.

What an irony it would be if football’s bust comes after he has departed. Imagine the scenario. The oligarchs move on, finding fresh ways of achieving fame, respectability and the protection achieved by entering the English establishment. The clubs loaded with debt are forced to cut their spending. Arsenal, benefiting from their solid business model, sail into an outright lead, mopping up star talent and trophies all round.

It’s often said that Wenger – early to invest in data analytics and worldwide scouts; a pioneer of player fitness and lifestyle – was overtaken by imitators. There is a second dimension to the question of time and circumstance. He helped to create and build Arsenal’s off-field robustness, even though football’s crazy economics haven’t yet proved its underlying value.

If the wind turns, Arsène Wenger may face a frustrating legacy: yesterday’s man and yet twice ahead of his time. 

Ed Smith is a journalist and author, most recently of Luck. He is a former professional cricketer and played for both Middlesex and England.

This article first appeared in the 24 February 2017 issue of the New Statesman, The world after Brexit