Your boss will point to a colleague as your competition.
Your company will pitch you against your counterpart in a different company.
Your teacher will put your dearest friend in the opposite side.
Your parents might make you compete with your own sibling.
Do you want to compete with the person sitting next to you, the person sitting in a different building/place or with yourself is always up to you.
Side Note: Competition is only in your head. What if you kick it out and work for perfection instead is worth a thought!