The classic question.
Rules: This is a fight in an arena, you are unarmed, you cannot leave the arena until every other animal is dead, and while the animals are as intelligent as normal they do understand that they’re fighting you and will try to do so, they won’t just run away.
Cougars get all their advantage from being able to launch a sneak attack from some sort of cover. Put one out in the open and it's vitals are going to be far more exposed than mine, and a well placed attack would likely mean a short fight