In the context of stable matchings I am currently trying to understand the Gale-Shapely Algorithm (traditional marriage algorithm).
I have proved it s correctness and I have shown that its male optimal in the sense that each boy will end up in the best stable match. (i.e. any matching where he would be with a girl he prefers would not be stable), however I am struggling a little to come up with a good strategy to show the algorithm will return a female pessimal matching. (i.e. among all stable matchings each female will be matched to the least preferred boy)
A hint to get me started would be very appreciated.