Shapley and Roth inspire us to improve our schools, hospitals and even some marriages
In awarding the Nobel Prize to Alvin Roth and Lloyd Shapley, the Nobel Prize Committee for Economics asserted a truth very often forgotten. In popular parlance in India and elsewhere, markets, especially ?free markets? stand for money and profits and greed . In India, there is a visceral dislike for markets although every kirana store is an example of how the market works.
Economists have a strange attitude to such matters. In pure theory, you can talk about the equilibrium of competitive markets with all the markets clearing without any reference to money, and of course profits are zero in that situation! A system of generalised barter is sufficient to determine all prices.
But then that is theory. We know money buys goods and money at the end of the day is what we receive our incomes in. We know there are imperfections and monopolies and restrictions put on markets by regulations. It is easy to think that markets are more messier than not since we never notice their good side but only notice when they fail.
What we have in the award to Roth and Shapley is another view of what markets are about. Indeed, the phenomena they have explored would not even be called markets ordinarily, such as finding a marriage partner or matching kids to the schools they would best fit. Or even matching kidney donors to recipients. Shapley worked as a mathematician on game theory and ?Shapley values? have been meat and drink to game theorists for decades now. Shapley was exploring co-operative games and gave an expression to what benefit?value?a player would expect from playing such games. As negotiations continue, players transfer value payments among each other (so-called side payments). In equilibrium, when the game is over, each player would have his or her marginal contribution to the total benefit from the coalition.
This was a mathematical result but the idea of negotiation and search among alternatives is a powerful one. The idea is that markets are meant for matching needs and availabilities. Money may be a shadowy substance or a real payment. In matchmaking among a group of men and women lined up against each other (speed dating), the idea is to find the best match for each person overall. You may be stuck on one person to begin with but she may not prefer you but someone else who may not rank her as highly as some other woman and so on. We can arrive at a final equilibrium with a bit of give and take. Each player has to sacrifice a little of their preferred choice and move to the next best until everyone is happy. The original work by Shapley and David Gale proved that you will arrive at such an equilibrium.
So markets exist to match need to availability or, as we more usually say, demand to supply. But the matchmaking may be in large markets with homogenous commodities in large supply and known prices or the item being ?bought and sold? may be something more intimate. It is the matching of preferences to what is available which is at the heart of markets.
The orthodox theory of General Equilibrium makes large demands on rationality and the amount of information available to all participants in the markets. This is mainly to facilitate the mathematics. But some people take it literally and assert, as under Rational Expectations, that people actually behave like that. Friedrich Hayek broke with these ideas in a brilliant lecture he gave to the LSE Students Economics Society. He said that the fundamental economic problem was that knowledge was scattered among the many participants. No one did or could know everything about the economy?not even the Planning Commission! Each of us knows something locally?our preferences, our abilities , our resources. The trick is to pool the scattered knowledge together. As he said, the Division of Knowledge problem is as basic to economics as Division of Labour. Markets pool the scattered knowledge together by using prices as signals to which people can respond.
What Shapley and Roth allow us to do is to take this insight further in smaller group situations where the item being exchanged is not available in large quantities. But at the same time, with the market being small, you can signal much more intensively the complex demand you have. The best example involves kidney transfers. You may need a kidney but the one available may not be suitable. Roth designed a scheme whereby you can cross-match kidneys and patients across a much larger number of kidneys and patients then is possible for a single hospital. That is a market and many people are alive thanks to its workings.
Shapley and Roth inspire us to take this idea of markets and use it in many more situations, especially where there may be artificial scarcity merely because the information available is not being shared widely. This will improve our schools and hospitals and even some marriages.
The author is a prominent economist and Labour peer
