Okay, so I know I'm not high up there in the rankings or anything, but personally I do believe that if you put a time limit on it, people aren't going to be rushing to set up matches if they're ahead, even if by only 1 or 2 games.
That being said, I think there should also be a cap at the number that are to be played (it can be a high number, low number, whatever).
As for what is to be "won," I don't think there's really anything - even bragging rights. This, to my understanding, is a friendly war/battle/etc. I don't believe friends boast, but again, that may just be personal opinion.