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LLOYD Shapley, who won the Nobel prize for economics in 2012, died on March 12th at the grand old age of 92. He might not have been too pleased about being memorialised on this economics blog; after winning the prize he said "I consider myself a mathematician and the award is for economics. I never, never in my life took a course in economics." If his co-winner, Alvin Roth, was a practical economist, then Mr Shapley was the theoretical mathematician.
He was drafted into the American army in the middle of his third year at Harvard University. Recognising that his mathematical prowess would be much more useful than his skills with weaponry, they set him to help with making accurate weather forecasts, to know when exactly to bomb the Japanese. His biggest achievement was cracking the Soviet weather code (weather fronts drifted from Siberia across to Japan, so they knew about the weather first). His son remembers that “for this he received a Bronze Star, promotion to corporal, and a raise of $4 a month. I remember him mentioning that the pay increase seemed to him at the time to be the most important part.”
One of Mr Shapley’s better-known achievements is the Gale-Shapley matching algorithm, which he devised after an old university friend (David Gale) asked for help to solve a problem. Given two groups of people, each with slightly different preferences, is there a way to match them in such a way that people aren’t constantly ditching their partner? After much head-scratching, Mr Gale suspected there was no solution, but could not prove it. As Mr Shapley told it, the solution took him the best part of an afternoon.
he solution is as follows: imagine a hall full of heterosexual singletons, with equal numbers of men and women. They have done enough idle chitchat to know who prefers whom—everyone has their own ranking of people in the other group. In round one, a starting gun is fired, and each man approaches his favourite women. The women reject everyone apart from their favourite, and then the process is repeated in a second round. No man should look too smug having not been rejected; if a woman is made a better offer, she should ditch an earlier one. The rounds continue until everyone is matched. The outcome is ‘stable’; no two people would prefer to partner with each other than their current match, otherwise the algorithm would already have paired them.
Mr Shapley wrote up the paper with Mr Gale, proving without equations that this method would always yield a stable solution. After two initial rejections (for being too simple) it was published, and fifty years later in 2012 he won the Nobel Memorial Prize in Economic Sciences “for the theory of stable allocations and the practice of market design” (see Free Exchange column here).
This algorithm became the workhorse of matching theory. It might have taken Alvin Roth to infuse the theory into practical policy, from matching organ donors to recipients and medical students to hospitals, but Mr Shapley’s ideas formed the theoretical underpinnings.
As we wrote here, economics is about much more than the invisible hand; sometimes we cannot rely on prices to allocate things to those who value them most. In such situations, we need people like Mr Shapley (and Mr Roth) to think about alternatives. Mr Shapley may have thought of himself as a mathematician, but he cannot avoid being remembered for his huge contributions to economics.
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