Discussing “College admissions and the stability of marriage” of D.Gale and L.S.Shapley.
Gale and Shapley paper confirmed that the issue of marriage and college admissions is equivalent. From the first theorem: “An assignment is optimal if every applicant is at least as well off under it as under any other stable assignment”, the authors make a few assumptions that carry throughout their paper. The first of these is that there are no ties in how students and colleges or men and women rank their preferences. Additionally, every student and college, and man and woman, ranks every college and student, and woman and man, omitting only those which they would never consider under any circumstances. Then, they give optimal solution for college admissions is “deferred-acceptance procedure”. Second theorem is: “Every applicant is at least as well off under the assignment given by the deferred acceptance procedure as he would be under any other stable assignment”. While presenting the deferred-acceptance procedure, Gale and Shapley made some simply assumptions about the interests of agents (colleges and applicants or men and women: (1) they have fixed priority and are not affected by exogenous factors, (2) strict priorities (3) priority colleges equals to substitutes. In my opinion, these assumptions have some limitations
First, the fixed interest assumption is impractical for many reasons. In marriage, Love is a fickle element. In college administrations, preferences will also change. For example, a person who apply for a specific college often do not known tuition fee until the end of the application process (because of scholarships, grants and financial aid that few students pay full tuition). Therefore, for price-sensitive students, priorities may not be defined until the application process...
