The author discusses the development of an algorithm-based mechanism by Gale and Nobel Prize–winners Roth and Shapley. They proposed a concept of deferred matching that has real-life applications in such areas as doctors’ residency programs and college admissions.
The author discusses transactions that are difficult to execute with a price tag, such as kidney donations, marriages, college admissions, and so on. In "College Admissions and the Stability of Marriage" (American Mathematical Monthly 1962), Gale and Shapley presented a mechanism of algorithm-based selection for transactions in which decision making by contracting parties is based on factors other than just money.
How Is This Article Useful to Practitioners?
Gale (now deceased) and Nobel Prize–winners Shapley and Roth devised a mechanism for the selection of marriage partners in which each man and woman ranks his or her preferred partner. Each man proposes to his most-preferred woman. Each woman rejects all proposals except that from the highest-ranking man, who is kept on hold in case she is proposed to by an even higher-ranking man. This cycle continues until all women are partnered. Although this system will not ensure ideal outcomes for all parties, it will ensure that no one ends up with a low-ranking spouse in terms of each individual’s preference.
This system, called "cooperative game theory," has little application for real-life marriages, but the algorithm-based solution was proposed to improve the college admission system and was instrumental in designing the National Resident Matching Program in the United States. The "deferred acceptance" program has transformed the placement of doctors in hospital residency programs. Before the matching program, competition would force hospitals to hire doctors well before graduation, resulting in poor doctor–hospital compatibility in many cases.
Economists generally get a lot of flak for coming up with theories that are difficult to understand and execute in real life. However, as the practical application of cooperative game theory has proved, sometimes simple arguments using simple mathematics can bring solutions for otherwise complicated problems.