The Theory of stable allocations and the practice of market design. The Nobel Prize in Economics 2012 for Alvin E. Roth and Lloyd S. Shapley

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2012 was awarded jointly to Alvin E. Roth and Lloyd S. Shapley for their contributions to the theory of stable allocations and the practice of market design. The theory of stable allocations consists of a family of models that study assignment problems in which two disjoint sets of agents (or a set of agents and a set of objects) have to be matched. For example, men to women, workers to firms, students to schools, or patients to live donor kidneys. A matching is stable if no subset of agents can improved upon their proposed matches by rematching only among themselves. Stability is an essential property if matching is voluntary. The practice of market design consists of applying those two-sided matching models to specific assignment problems with the aim of proposing improvements on how they are solved. This paper presents a brief description of the academic career of the laureates and describes their contributions by presenting the most basic two-sided matching model and some of its market design applications, including the organization of a centralized system to propose kidney transplantations to use kidneys of live donors that are incompatible with their respective patients, the yearly assignment of North-American medical students to hospital internship programs, and children to schools in cities such as Boston and New York