@Pablei I found interesting how does the abstract matching theory can find practical solutions to real-world problems. In this respect, I have also heard about the NRMP, which is aimed at allocating students who have recently graduated from med school to hospitals. I have been reading more about these topics and I found another matching mechanism which refers to the German university admissions system and it is briefly resume below:
"The centralized admissions procedure for public universities in Germany is used to allocate places in human medicine, dentistry, veterinary medicine, and pharmacy. The basic outline of the admissions procedure is as follows:
- In the first round, up to 40 % of total capacity is allocated among special applicants.
- In the second round, all remaining places are allocated according to universities’ preferences among those applicants not assigned in the first part.
In the actual procedure, the group of special applicants consists of applicants who have earned an excellent average grade in school , and of applicants who have waited a long time since finishing high school"
In the second round the procedure uses two matching mechanisms, the Boston and the college optimal stable mechanism. Assuming universities are not strategic, the paper results show that complete information equilibria are characterized by a stability notion that takes the specific constraints of the German university admissions system into account,
I would like to leave its reference in case you are interested in reading more about it.
Alexander Westkamp."An analysis of the German university admissions system”, Economic Theory, 2013