Dominant Strategy in Medical School MATCH
For the last 30 years, AAFP has been analyzing data from the National Resident Matching Program — a program introduced to bring a semblance of order to the previously chaotic system of matching medical school graduates with appropriate residency programs. Solving this problem was done in a very market-like fashion. First, the Medical graduates are asked to announce their value for a residency program by ranking their top programs. Then the residency programs rank the medical students they want. A program analyzes these rankings, and gives a student to their top resident program, so long as that program wanted them as well. This serves to maximize the social welfare of the two-party system.
A big issue that is brought up in the analysis of the MATCH, is the idea of strategically ranking programs. Should you rank your top choice as first, even if it’s a very competitive program? Similarly, should the programs rank the top medical student as their first choice, even if many programs are gunning for that student? Lets take a look at the MATCH-ing mechanism.
First, the MATCH looks at all the applicants, and takes their top program. If that program also wanted them, a match is made. However, if another applicant choice that program as their first choice, and the program ranked this new student higher, then these two are matched, and the previous match is pushed down. If a match gets pushed down past the number of applicants the program is accepting, then they are “unmatched” and perhaps sent to a different school (the next one on their list, per se). So what should you do?
It seems that it’s largely a dominant strategy for both the student and the program to rank their counterparts truthfully. Take an example of this: if the student ranks truthfully, they will always get their top program, if their top program matched them. The only way they will not get that program, even if the program choose them, is if the program admitted all the preferred students. In this case, each of those students had a higher value to this program, and so the trade off (loss of the students choice, for the gain of the programs choice) is overall beneficial to the total welfare. If the student does not rank his programs truthfully (i.e. putting a preferred program lower in value) then they run the risk of getting a lower value program, when they could have matched with the preferred one. This is a lower payoff for the student, and as such, social welfare is not maximized.
In this sense, it is always beneficial to rank the program you want the highest, and rank others in descending order. Same goes for the residency programs, they only stand to lose if they don’t bid truthfully for the desired students.