Profile: Lloyd Shapley and Alvin Roth

Rolf Hellgardt (left) former Kabel Eins head of programming accepts the proposal of marriage from his girlfriend former German TV presenter Monika Lierhaus Prof Shapley framed his theory as one of matching husbands and wives, noting that there was a distinct advantage for the side doing the proposing

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Although it is common practice for Nobel Prizes to be awarded to pairs of academics, on this occasion it was particularly apt.

The two American economists Lloyd Shapley and Alvin Roth, who have jointly won the 2012 prize for economics, both made their names by developing theories of match-making.

It is a common problem in market-places: How do students find university places, tenants find flats, workers find employers or indeed husbands find wives?

In each case, you have a large group of people on either side of the market, who need to be married up with one another one-for-one.

The problem - as anyone who has applied to university or put their child into primary school will know - is that people's preferences do not necessarily marry up quite so neatly.

The theoretical challenge taken on by each of these economists was to develop a set of rules that will match up as many people in a market as possible, and that - whilst not pleasing everyone - will at least avoid an unstable outcome.

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Mr Roth helped New York City redesign its system for allocating children to public school places”

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If you are wondering what an "unstable outcome" means, then imagine a situation where a husband and wife both wish they had married each other instead of their current spouse.

Unhappy parents

Somewhat ironically, considering their area of expertise, the two economists are separated by a generation and have never actually worked together.

The senior of the two, Lloyd Shapley was born in 1923 in Cambridge, Massachusetts - the home town of Harvard University, where he studied mathematics.

He went on in 1953 to become a professor at another Ivy League college - Princeton in New Jersey.

Professor Shapley was drawn into game theory, a novel branch of mathematics being pioneered by his Princeton contemporary and the 1994 Nobel laureate, John Nash, who was famously depicted in the 2001 film "A Beautiful Mind".

Gale-Shapley rules

In the case of parents applying for primary school places for their children:

  1. Parents express their first preference school place
  2. Schools that receive too many applicants send out rejection letters based on their own preference criterion (for example, to those who live the furthest walking distance from the school); however acceptance letters are not sent out yet
  3. Rejected parents then get to express their next preference
  4. If an oversubscribed school now receives even more second-preference applicants, it sends out further rejection letters
  5. Repeat the process until every parent has been allocated a place, at which point the acceptance letters can be sent out

Professor Nash would make his name by considering non-co-operative games such as the notorious "Prisoner's Dilemma" in which two suspects being interrogated in separate cells must decide whether to inform on each other.

Lloyd Shapley by contrast earned his Nobel for his work with the late David Gale to develop theories of cooperative games - in other words, situations where individuals are not locked up in separate cells and can actually work together to achieve better outcomes (think of those unhappy couples agreeing to swap spouses).

In 1962, the two came up with the rather less catchily titled "deferred acceptance algorithm", or "Gale-Shapley" as it is better known in the trade.

Essentially it was a set of rules that could be applied in any market, such as schools places or indeed Professor Shapley's preferred analogy of a mass wedding, where individuals on each side of the market needed to be paired up.

The rules not only ensured a "stable" outcome every time, but they avoided creating an incentive for parents applying for primary school places, for example, to lie about their preferences in order to gain a strategic advantage - as might occur if second or third preferences were given some kind of special priority.

Matches and couples

If Professor Shapley was the theorist, then Alvin Roth was the practitioner.

Born in 1951 to two school teachers, in the late 1960s the young Mr Roth dropped out of high school in New York because, according to an interview in 2010 with Forbes magazine, he felt "under-stimulated".

Despite this setback, he went on to study engineering at Columbia University, before completing his doctorate in the subject at Stanford, and eventually landing a post at Harvard.

He too was drawn into game theory, but he was particularly concerned to find a more useful purpose for what could often seem arcane mathematical riddles.

In the mid-90s he was given his opportunity.

Every year, some 25,000 medical students had to be offered places at hospitals across the entire US. The system, which had been designed by doctors in the 1950s, had lately run into trouble.

The presentation of the 2012 Nobel Memorial Prize in Economic Sciences, with the winners Alvin Roth (left) and Lloyd Shapley pictured above The two economists have never actually worked together

It didn't cater well for couples, who understandably had a strong preference to be accepted at the same hospital (or at least ones in the same town) over-and-above whatever individual preferences they might have.

The system did not take account of couple preferences, with the result that many started trying to negotiate places outside the formal applications system.

In other words, the system was "unstable", and Professor Roth was invited in to revamp it.

The professor already knew the system well, having studied it in the 1980s and intriguingly discovered that it actually conformed to the Gale-Shapley rules - apart from the small matter of accommodating couples.

He successfully redesigned the system based on the same principles developed by his theorist predecessors.

Having cut his teeth on medicine, he was later asked to sort out the somewhat chaotic New York City high school applications system in 2003.

And more recently he has been devising a system for allocating donated kidneys - a set of decisions that is complicated, often with fatal delays, by issues of donor preferences and blood incompatibility.

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