A Nobel Prize for beauty – and truth

Hospitals featured during the Olympic opening Image copyright Getty Images
Image caption The award-winning theories have been applied to the allocation of patient care

In the wake of the financial crisis it's become fashionable to beat up on mainstream economics for becoming too mathematical - for "mistaking beauty for truth", as Paul Krugman memorably put it.

Looking at the potential benefits of increasingly complicated financial contracts, it is said that too many economists fell in love with the theory - without thinking hard enough about what it would all mean in practice.

Maybe. But it's not the whole story of modern economic theory - as the recipients of this year's Nobel Prize for economics well demonstrate.

The work of Lloyd Shapley and Alvin Roth reminds us that economics can be both deeply mathematical and abstract, and deeply practical - not to say hugely useful to public and private organisations all over the world.

The older winner, Lloyd Shapley, has long been a key figure in the history of game theory. That's the part of economics that deals with strategic decision making, which emerged only after World War II and was made famous by the book and film about John Nash, A Beautiful Mind.

In the late 1950s and 1960s, Mr Shapley came up with a number of "beautiful" solutions to various problems in game theory, including an algorithm - or arithmetical rule - for "pair-wise matching". That sounds complicated but it actually deals with a basic problem , for economists and admissions departments alike.

Imagine you've got a long list of different people, with different preferences looking for an X, and a long list of different X's - what's the best way to match them up?

The example used in the original, seminal paper, co-written with David Gale, was marriage: you have 10 women and 10 men, how do you reach a set of "stable" matches, where the couples wouldn't always be breaking up and going off to find something better? There were two possible solutions, depending on whether the women or the men got to propose first.

It was interesting to consider how the results would depend on which sex got their bid in first, but you can see why people didn't think it was necessarily very practical to the real world. The model assumed, for example, that pairs could swap with one another as much as they wanted before settling down. When there were no more mutually beneficial swaps to be done, the resulting matches were said to be efficient and "stable".

But, 20 years later, Alvin Roth discovered that something very close to the Gale-Shapley algorithm was in fact being used in the real world, by the clearing house involved in matching junior doctors to residency positions at hospitals in the US. And, he realised, the same ideas could be very usefully applied to other real-world matching situations, like matching students to high schools - or kidneys to transplant patients. Not to mention speed-dating.

The reason the theories are so useful is they apply to the many cases where either money cannot be a factor in the original allocation - or we don't want it to be. You don't need a Hale-Shipley algorithm to help you allocate different kinds of television sets to different households. Soviet planners had a crack at it, but we know that price signals in the market do it much better. We buy the television that best fits our needs, subject to our ability to pay.

But doctors will be thinking about a lot of different factors in choosing a hospital - and vice versa. Money is only one consideration. And, though you can debate whether people should be able to buy or sell their kidneys, in most health systems around the world, the authorities will want the scarce number of kidneys to be allocated on medical grounds, not financial ones. That is where matching theory comes in: it can help fill the gap, and create a kind of market, where you might have thought none could exist.

Mr Roth helped New York City redesign its system for allocating children to public school places. Using his algorithm led to a 90% fall in the number of students who ended up in schools that they had not even included among their five listed preferences. Now cities all over the US use some form of Mr Roth's algorithm for allocating students to schools.

By my count, nearly a dozen game theorists have now been awarded the Nobel Prize for economics. That's a reflection of what game theory has achieved in a remarkably short period of time. In the past 50 years, game theorists - and micro-economics in general - have genuinely made the world a better place. Either they have helped to solve practical real-world problems or, where there is no solution, they have helped us to understand the issues more clearly.

Unfortunately for all of us, the part of economics that we hear about every day - macroeconomics - can boast of no similar achievement, as you could see, perhaps, in my recent programmes on John Maynard Keynes and Friedrich Hayek.

In the years before the crunch, many economists and policy makers thought they had finally gotten a handle on how to control inflation and growth in the real world.

They were wrong. The central economic debates we hear now over how best to handle the aftermath of a financial crisis are not much different from when Hayek and Keynes did battle more than 80 years ago. You can see why the awards committee might want to look elsewhere.