Matching: from Lloyd Shapley's models to Alvin Roth's market design.

Summary Alvin Roth and Lloyd Shapley were awarded the 2012 Royal Bank of Sweden Prize in Economic Science in memory of Alfred Nobel for their work on the centralized organization of certain economic markets, which depend on matching agents of two distinct types (students and schools, for example). Shapley co-authored, with David Gale, the seminal paper in the field, which proposed an algorithm for achieving stable matching. Roth led the redesign of the hospital internship assignment process in the United States and the design of a market related to kidney transplantation. After reporting on these contributions, we also discuss Shapley's seminal role in game theory.