Obituary

Leonid Hurwicz

American economist and mathematician who was awarded the 2007 Nobel prize

Leonid "Leo" Hurwicz, who has died at the age of 90, was professor emeritus of economics at the University of Minnesota and the creator of mechanism design, the "reverse engineering" side of economics. Ordinarily, economists try to predict what outcomes are likely to arise from institutions such as markets, regulations, and taxes. But mechanism design theorists do the opposite: they begin with the desired outcome and ask whether an institution (ie, a mechanism) could be designed to achieve it.

To take a domestic illustration: Mother wishes to divide a cake between her two children, Alice and Bob, and to ensure that neither envies the other. Bob should not prefer Alice's piece to his own, nor vice versa. If Mother knows that the children see the cake the same way she does, she can simply divide the cake equally and give each child a piece. But if Bob might think his piece is smaller than Alice's then the simple solution will not work.

However, there is a procedure that will work: Mother can have Bob divide the cake and then let Alice choose which piece she wants, leaving the other for Bob. This mechanism achieves a fair division because it induces Bob to divide the cake so that the pieces are equal in his eyes. He will cut the cake so that whichever piece Alice selects, he is happy with the other. Alice will be happy too, since she gets to choose.

This illustrates some of the key features of mechanism design. The designer (Mother, in this case) does not have enough information in advance to identify which outcome will achieve her goal. Thus she must proceed indirectly through a mechanism, the divide-and-choose procedure, whose very execution, in effect, generates the information needed. To complicate matters, the participants (Alice and Bob) do not care about the designer's goals; their ends are to get as much cake as possible. Therefore, the mechanism must be consistent with their ends; it must be incentive-compatible.

Leo was the first to formulate all these concepts - mechanisms, their information-generating role, and incentive compatibility - in pioneering papers in 1960 and 1972. This was the work cited by the Nobel committee in awarding him the 2007 economics prize, together with Roger Myerson and myself.

Like many other economists, he had been fascinated by the "planning controversy" of the 1930s and 40s. Oskar Lange and Abba Lerner argued that centralised planning - properly conceived and carried out - could replicate and even surpass the performance of the competitive market, while Ludwig von Mises and Friedrich von Hayek remained staunchly sceptical of this claim. Leo recognised the importance of the debate, but found it unsatisfactory because all its principal terms remained undefined. It was his attempt to give unambiguous meanings to such concepts as "centralisation" and "decentralisation" that ultimately led him to mechanism design.

The line of work Leo inspired has led to a broad consensus among economists that Von Mises and Von Hayek were correct for settings in which there are large numbers of economic agents on both the buying and selling sides of the market - so that no single agent has much power - there are no significant "externalities" of consumption or production (so my consuming or producing a good does not directly affect you), and there are no serious asymmetries of information about the good (eg, sellers do not know more about it than buyers do). However, alternative mechanisms can, in general, be devised that improve on the pure market when any of the three conditions fails to hold.

Born in Moscow, to Polish-Jewish refugees, during the year of the Russian revolution, Leo returned with his family to Poland and graduated in law from Warsaw University in 1938. He then studied at the London School of Economics, with Von Hayek and Nicholas Kaldor, and with Von Mises at Geneva's Graduate Institute of International Studies.

In the US from 1940, he was at Harvard and the Massachusetts

Institute of Technology, where he became a research assistant to Paul Samuelson, and at the University of Chicago, where he was an assistant to Lange. After the US entered the second world war, Leo was a faculty member at Chicago's Institute of Meteorology, while lecturing in statistics in the economics department and on electronics to the US army's signal corps. In 1942 he began an association with the Cowles Commission for Research in Economics which lasted into the 1960s.

In 1951, after positions including professorships at Iowa State College and the University of Illinois, he joined Minnesota, where he remained for the rest of his career. But he travelled too, as visiting professor or fellow at universities including Stanford, Bangalore, Indonesia, Tokyo, Harvard, Berkeley, Santa Barbara, the California Institute of Technology and Michigan. He was the recipient, Nobel aside, of many awards, including the US National Medal of Science (1990) and six honorary doctorates.

The last two decades have seen a trend toward privatisation, the shift of public assets to the private sector. In eastern Europe, privatisation was induced by the fall of the Soviet Union and the imperative of transforming the old socialist states into market economies. In Britain and the US, the rationale was efficiency - where certain assets could be used more productively by private companies than by government. Privatisation requires mechanisms for transferring assets from one sector to the other. Thus, mechanism design has played an important role in some very practical issues.

I first learned about Leo's work from the great economist Kenneth Arrow, when I was a mathematics student at Harvard in the early 1970s. The experience persuaded me to switch from maths to economics. A few years later, Ken introduced me to Leo and we became friends and collaborators. He was a remarkably gentle, warm and gracious man with a devilish, deadpan sense of humour.

A few days ago I got a note from his daughter Sarah, who told me that at a 1993 summer school in Jerusalem, Leo was so beloved by graduate students that they followed him around like the pied piper. He was my pied piper too.

He married Evelyn Jensen in 1944. She survives him, as do their two daughters and two sons.

· Leonid Hurwicz, economist, born August 21 1917; died June 24 2008