I've noticed that if I punch one of my buddies I can start a "duel", but I have not yet initiated one (due to many midgets who deserve my bullets more). What happens when you duel? Is there any benefit for winning or penalty for losing?
Dueling lets you test your muscle against your fellow players. For the most part, it is for fun. Especially since it isn't balanced very well. Some classes are better at dueling than others, and your character and item levels have huge affects on the outcome.
There is a Badass Challenge called "Haters Gonna Hate" that rewards you for duel wins. The max rank for the Challenge is after 50 wins. You get the first level for winning your first duel, next rank for winning 5, and so on, up to 50.
There is no penalty for losing. After a duel your shields and health are restored for the most part. Though any ammo you used during the duel is lost, and special power timers and other timers used are not instantly reset but have to going through their usual time to refill. But all of that is easily recovered with a little bit of time and opening of boxes.
There is a challenge for winning duels. Other than that, just bragging rights.