Posted by: Jae Hyun Park | September 10, 2010

Lect 5: Stable Marriage Problem-II

(Guest post by Jae Hyun Park)

In Lecture 5, we learned how to distinguish between stable and unstable matchings.

For instance, Let M={m,m’} and W={w,w’} and their prefences are…

Lm : w>w’ , Lm’ : w’>w

Lw: m>m’,  Lw’ :  m’>m

Now we can have two types of perfecting matchings from the men and women given above.

1. (m,w) (m’,w’) which is stable since both men and women are satisfied with their current partners

2.(m’,w) (m,w’) which is unstable since m’ and w’ prefer each other to their current partners and same for m and w. Hence eveybody will break up with their current partners in order to match up again.

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