Imagine- you have a friend and you are convinced your party is better than theirs. They think otherwise. How do you prove this? You can challenge them, of course! A request similar to that of a friend request maybe, located on their profile. A time limit could be issued? You could fight other player's parties. Only if they accept, of course. I see how party experience could be an issue, leveling up only through battling friends could be over-powered and take away from the RPG point of the game. One way to get around this is to not give experiment points. Another could be you'd get half of what you get from a natural battle. Say you get 100 points from defeating a level 15 pet in the map. If the pet is level 15, you'd get 50 points. I am leaning more towards the second option. There are other things you have to consider, but I would love to be ble to battle my friends.