1. National Intern Matching Program

2. 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

3. 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

4. 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

5. 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.

6. 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.

7. 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

8. A more centralized matching procedure 1950-1951: 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)

9. 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.

10. Stability

11. 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

12. 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?