Which is hilarious, because I remember very clearly when McDonald's was crushing Burger King and the head of McDonald's said, on the record, "You know what you do when your competitors are drowning. ... step on their head".
Burger joints compete in the "fast food" market which also includes fried chicken joints, taco joints, and the like. They also have more broad competition from the "fast casual" market, "restaurant dining" market, and the "food" market.
The question antitrust has historically asked here is the concentration, and the extent to which have they have pricing power.
I guess burger joints can't be monopolies.