I think that the dispute shouldn't have any materialistic value. The winner and the loser of the duel should only gain or lose honor and prestige. 

Due to the fact that they are both vulnerable nations and know that if one of them attacks then the "Empire beyond the mountain" will see that as an opportunity to expand.
Both of the nations know that even if they lose, they have no reason to comply with the winners demands, because the winner cannot do anything to enforce them.(The loser is in a more favorable position, because it is always easier to defend than to attack).