There have certainly been Fortnite competitions, but you can't really say that it's designed for competition -- and that's a problem when Epic is spending big money on tournaments. You won't have to wait too long to see a mode, however. Epic Games is developing a "robust competition system" that will have players square off against each other within the same match, and "be recognized for their accomplishments." It didn't say how this system would work (a ladder, perhaps?), but it would arrive sometime later in the fall.