Daniel BuenoThis branch of mathematics studies the behavior of decision makers, or players, whose actions – according to the established rules – affect one another. Each rational player acts according to how he or she believes the others will act. This theory may also be applied to various fields such as political science, psychology and evolutionary biology.
An offshoot of game theory often used in economics is matching theory (pairings) that deals with situations in which there are two finite and distinct sets – like men and women, or schools and students – and may help form couples or evenly distribute students among universities.
Matching theory, which was described in 1962 by Americans David Gale and Lloyd Shapely, had already been used (as Gale discovered 15 years later), to allocate physicians among residency programs in the US for over a decade. The proof that the algorithm used since 1951 was the same as the 1962 one was published by Gale in partnership with Brazilian mathematician Marilda Sotomayor. From the standpoint of economics, the American Alvin Roth showed that the balance achieved by the market of physicians and hospitals is the same as that asserted by game theory. Matching theory, whose significance earned Shapley and Roth this year’s Nobel Prize in Economics, was made more accessible to non-mathematicians thanks to the book published by Roth and Sotomayor in 1990. Today, Roth devotes himself to the study of its applications while Sotomayor works on the theory, heading the school established by David Gale.
Specialist consulted
Marilda de Oliveira Sotomayor, FEA-USP
