The easy answer is yes. You must give plenty of examples. And from as many aspects of your life as possible. University experience certainly, but also include situations from your early life in order to demonstrate that competition is natural to you. Sporting activities are an obvious source here.

Show that you are competitive on your own as well as within a team situation. You should also suggest that you are successfully competitive. Failing in competition will not look very good.

Bring into your answer how other people see you. Do they regard you as a competitive person and if so is that a good or a bad thing? Are you the kind of person others look to when they are faced with a challenge?