In my recent post about medical graduates applying for multiple specialties in the National Resident Matching Program (NRMP) I briefly mentioned sloppily “sub-algorithms” of the main resident match. To be more specific, whereas it is true that all residents are matched by means of a single algorithm, possible placement of students is fairly restricted by their choice of specialty. In fact, among all students who (also) applied for -to stress it once more- Neurology in 2013, the average number of specialties student applied to fell short of two. As discussed, there is contradictory advice to students about the optimal strategy in terms of multiplicity of specialties.
On a slightly different note, there might be some evidence for a trade-off between distributional goals and market efficiency related to the strategic problem of students. Consider the following situation: A neurology and a neurosurgery department each have an open position. They compete for two students, each of which has a certain value as a neurologist and as a neurosurgeon. Assume both students chose a single field according to their comparative advantage, i.e. the field in which they are relatively better than the other student. If the abilities of students in their respective fields do not exorbitantly differ firms will be absolutely pleased with this situation since they should be able to hire their only candidate by offering slightly more than an outside option and reap the majority of the output. Society should also be happy since the allocation would be perfectly efficient. Unhappy campers would only be found among the residents who would start their career on moderate wages. In this particular situation both would be better off to register for both specialties to induce firm bidding which leads to increased wages but decreases market efficiency due to uncertain outcomes. The interesting question is: Does this logic generalize?