A death match between the presidents / prime ministers of the rival countries. The country of the winner of that match will win the war, and the country of the loser has to deal with the following consequences.
I once asked my dad, wouldn't it be better if wars were determined by rock-paper-scissors? He explained, that even if, the citizens of the losing country would probably get so upset, they would take matters into their own hands and start a riot, which would effectively lead to regular war.
(He explained it better than that, but it was long ago and I only remember the general sense of what he said)