The 2012 Nobel Prize in economics was awarded to Alvin E. Roth and Lloyd S. Shapley for the theory of stable allocations and the practice of market design. This theory concerns a central economic problem: how to match different agents or redistributed individual owned objects as well as possible. For example, students have to be matched with schools, and donated human organs with patients in need of a transplant. How can such matching be accomplished as efficiently as possible? What methods are beneficial to what groups?Lloyd Shapley used cooperative game theory to study and compare different matching methods. A key issue is the existence of a matching that is stable in the sense that no two unmatched agents would prefer each other over their matched counterparts. Gale and Shapley proved that in a two-sided market, e.g., man and woman, or students and schools, there is a stable matching, and they derived a specific method, the so-called Gale-Shapley algorithm – that always ensure a stable matching. They also studied agents' motives for manipulating the matching process.Alvin Roth recognized that Shapley's theoretical results could clarify the functioning of important markets in practice, and applied the matching theories to actual market. He also helped redesign existing institutions for matching new doctors with hospitals, students with schools, and organ donors with patients. These reforms are all based on the Gale-Shapley algorithm, and the Shapley-Scharf theory of the core of markets with indivisible goods.