**Female Nietzschean's most likely compete but not the same way and not for the same reasons as males but it is never really explored in the show.**

In the show we really never see a lot of Nietzschean females so I do not believe there is explicit canon, that being said.

Nietzschean society seems to be matriarchal at least when it comes to breeding and since males can have as many wives as they can attract it is doubtful that females have to prove their worthiness as a mate.

One episode had a barren female say that by proving herself in combat she would raise the status of her brothers.

The episode with the princess has her mention that her eggs have been removed and frozen to be implanted in lesser females, of course I am not sure how agreeing to a suicide mission actually proves your superiority.