From the following set of preferences for four men and four

From the following set of preferences for four men and four women, find the stable matching that is female-optimal. The men are denoted A.B.C.D. and the women are denoted a, b, c, d. You may find the matching by hand or you can implement the proposal algorithm yourself, but you must show your work. Do not use a website or program (that you did not create) that will do it for you.

Solution

Stable matching means, the matching should be in favor of both men & women as more as possible. But since, it should be female-optimal, we will have to give \"women preferences\" more preference.

case 1 : a : C > B > D > A
-> Since for women \'a\', the first preference is man C. So we will check for C\'s preference.
   C: b >c>a>d
But, for man C, women \'a\' is the third preference, so it is not stable match.

-> Now, we shall look for second preference if women \'a\'. It is man B.
   B: a>c>d>b
   for man B, women \'a\' is his first preference. so it is a stable match.
   HENCE, women \'a\' matches with man \'B\'.

similarly we can look for other matches also. So, the answer is below :
a -> B
b -> C
c -> A
d -> D