On the Nobel Prize in Economics
Wednesday 24 October 2012
A comment by Mario Pascoa, Professor of Economics, University of Surrey.
The 2012 Nobel prize in Economics was awarded to Lloyd Shapley and Alvin Roth, for “the theory of stable allocations and the practice of market design”. The subject of stable allocations complements another central subject in economics, the efficient allocation of resources. An allocation is efficient if there is no other allocation that can make at least one person better off without hurting others. An allocation is stable if no group of persons can improve upon it using their own resources.
While efficiency describes a property that is desirable from the point of view of trying to use resources in the best possible way for the society, stability addresses whether an allocation can be sustained given the interests and power of the different groups that can be formed. Efficiency is a more idealistic concept, stability deals with conflict and cooperation. Efficiency can be addressed in an individualistic framework and, in that framework, one can check whether it can be implemented when individuals act strategically (in a non-cooperative way, as John Nash (1950) suggested). Stability has to be addressed in a coalitional framework.
As the Nobel prize committee recognizes, Lloyd Shapley is “the most important researcher in the field of cooperative game theory”. In this field, the most used solution concept is the core, which is what is left after elimination of all allocations that can be improved upon by some coalition. Shapley showed in different contexts that the core is non-empty and how core allocations can be achieved. One important issue is whether market equilibria are stable (and whether they are the only stable outcomes), but a just as important issue is the stability of allocations when prices cannot be used, such as in matching men and women, medical doctors and hospitals, students and schools, organ donors and patients. Shapley together with David Gale proposed in 1962 an algorithm for two-sided matching. The core of the transferable utility version, known as the assignment game, was extensively studied by Shapley and Shubik.
Alvin Roth built on Shapley’s work and made two seminal contributions, checking whether stable allocations are incentive compatible and devising the practical implementation of stable allocations in several contexts, particularly in the health industry. Revealing true preferences may not be the best strategy for a matching candidate and, therefore, procedures should be deigned in order to make stability strategy-proof.
In coalitional games individuals are still important and Shapley (1953) made an important contribution in this respect. He proposed a way to measure the value of an individual in terms of the average of that individual’s contribution to the power of the different coalitions. This concept has been widely used in cost allocation problems and in political science.
As a former student of Lloyd Shapley I am particularly happy for this long awaited honor. My supervisor was J. Ostroy, but Lloyd was a member of the thesis committee and I benefitted much from his advice. At my doctoral defense, Lloyd questioned whether my result on the purification of equilibrium strategies for large games could be achieved without the strong anonymity assumption I had made, that only the distribution of strategies should matter, not how different agents act. It turned out that, two years later, it came to my mind a way to dispense with that assumption. This had interesting implications for my work on monopolistic competition, as it allowed me to replace Oliver Hart’s hypothesis that brands are picked unrelatedly by consumers by a plain assumption on the dispersion of consumers’ choices, which is what makes monopolistic competition different from oligopoly.
