PvP fighting is... eh.

Either you should agree with the person on the result before/during the fight, or a third party needs to step in to decide the path of the fight. Realistically speaking, if characters are balanced, then it'd be near impossible to check-mate someone. People have the advantage of lots of time to deduce and decide on what moves their character could possibly do to counter their opponent's. It quickly ends up nowhere if there's no way to decide when the battle should end.