Choosing a mate based on competition is female hormone driven behaviour. Thus you have the phenomenon of groupies.
Such a scenario as you describe leaves out the important part of how men don't compete with who they see as above them in such domains. It's just disrespectful behaviour to chase after your bros' girl, and deserves a straight up punch in the face.
It does happen, and it happened to me with one girl, and I "won" the competition and that was the end of it, he stood aside. Men respect the choices of women, unless they are conniving, bitchy manipulative cunts, and if you have friends like that, you have got problems that you are not acknowleding.
Men are the trophies, not the women. And anyway, the kind of women who chase you because other women are chasing you are not worth your time, they will drop you at the very moment you can be replaced.