The following tables depict the preferences of three universities regarding a set of applicants, and the preferences of the applicants regarding the universities. Every university also has a specified quota for the number of students that it can accept. These preferences are strict preferences, i.e., there are no instances of indifference.
Find a stable matching A between the universities and the applicants that is preferred by all the applicants to any other stable matching; i.e., for any stable matching B, an applicant who is matched to two different universities under A and B prefers the university to which he is matched under A to the university to which he is matched under B.
(a) The preferences of the universities (from left to right) and each university's quota of students (between the round brackets) are:
University X (4): j bakgdcef hi.
University Y (2): dbhaj f kecig.
University Z (3): f cj bhdegika.
The preferences of the applicants (from left to right):
(b) The preferences of the universities (from left to right) and each university's quota of students (between the round brackets):
University X (6): abcdef ghijklmn.
University Y (6): nmlkj ihgf edcba.
The preferences of the applicants: Applicants a, b, c, d, e, f, g, h, i, j prefer University X to University Y , and applicants k, l, m, n prefer University Y to University X.