National Intern Matching Program

History Internship introduced around the turn of the 20 th century – A concentrated exposure to clinical medicine to students – Cheap labor for hospitals – The number of positions offered greater than the number of graduating medical students

Competition for students 1944: standard appointment date advanced to the beginning of the junior year A multiple-agent Prisoner’s Dilemma – Hospitals all preferred as late an appointment date as possible – Each preferred to appoint its interns earlier than its competitors

Collective Action Association of American Medical Colleges: neither transcripts nor letters of reference would be released prior to the end of the junior year for students seeking internships commencing in 1946

A New Problem Students inclined to wait as long as possible before accepting the position he had been offered, in the hope of eventually being offered a preferable position Students who were pressured into accepting offers before their alternate status (waiting list) was resolved were unhappy if they were ultimately offered a preferable position.

Hospitals whose candidates waited until the last minute to reject them were unhappy if their preferred alternate candidates had in the meantime already accepted positions. Unhappier still when a candidate who had indicated acceptance subsequently failed to fulfil his commitment after receiving a preferable offer.

Attempted solution AAMC proposed in 1949: – Appointments should be made by telegram at 12:01 AM, November 15, with applicants not required to accept or reject them until 12:00 noon the same day. – 12-hour waiting period rejected by the American Hospital Association as too long

A more centralized matching procedure : trial-run algorithm 1952: National Intern Matching Program – Students ranked in order of preference the hospital programs – Hospitals similarly ranked their applicants – All parties submitted these rankings to a central bureau – Voluntary participation – Over 95% students and hospitals participated – NIMP remains in use with an adjustment to accommodate married couples in 1999 (contribution by Alvin Roth)

Empirical study NIMP is stable. Regional matching procedures in England – 2 out of 8 algorithms are stable and they survive. – Among the remaining 6 algorithms, 4 of them have been abandoned. – 2 unstable ones which are unstable work in two smallest of the UK markets; probably more difficult for a student and consultant to prearrange a match under social pressures.

Stability

A B C α 1, 3 2, 2 3, 1 β 3, 1 1, 3 2, 2 γ 2, 2 3, 1 1, 3 The 1 st number gives the ranking of women (A, B, C) by the men (α, β, γ), the 2 nd number is the ranking of the men by the women. Q: Is there any stable assignment? Example

Tasks Existence of a stable assignment in the internship market? The algorithm of NIMP Does it give a stable assignment? Is the assignment Pareto efficient? Will the algorithm ever end?