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In the United States, when a student graduates from medical school they start an internship – a period of supervised on-the-job training designed to ensure they’re ready for the rigorous demands of their chosen profession. Every year, over 20,000 students must be paired up with hospitals, and complex algorithms are employed to ensure that the best possible matches are made. This year’s Nobel Prize in Economics recognises the work of two mathematicians who made such a system possible.

The science of matchmaking is a form of game theory – the mathematics of strategy and decision-making. Game theorists have been awarded Nobel Prizes in the past – most notably John Nash in 1994, for his work on non-cooperative systems (as exemplified by Twig film the Prisoner’s Dilemma). The first of this year’s Nobel laureates, Lloyd Shapley, studied alongside Nash at Princeton, and is recognised for his work in cooperative game theory – that is, systems in which participants can work together to influence outcomes. Shapley’s pioneering research with the late David Gale led to the formulation of the Gale-Shapley algorithm in 1962, which uses deferred-acceptance to match members of a cooperative group in a stable way.

The second recipient of this year’s prize is Alvin Roth (pictured), credited with advancing the field’s practical applications in a number of ways. It is Roth who devised the US’s current system of matching interns to hospitals, using the Gale-Shapley algorithm as his basis. In addition, his work has been used to match students to schools, and even organ donors with patients in need of kidney transplants – an especially urgent instance of matchmaking, where the stakes are life and death. Through their individual efforts, Shapley and Roth have not only helped improve numerous markets, but also saved lives.