CHAMPION WARFARE:
There must be a pre-battle champion warfare where both sides choose their champions (max of 3 for each side) who engage in one-on-one combat resulting in morale boost for winning side and morale penalty for losing side. After that, losing side reassess the outcome of the battle. If odds are seriously against them due to that morale penalty, they offer their surrender to winning side, or continue to pursue battle otherwise. Winning side may accept or reject their offer and continue battle/slaughter in case of rejection while losing army starts retreating.
In some cases, like siege Assaults, battles can be resolved through champion warfare, e.g. messenger from defending party is sent out to the attacking party during town/castle siege to determine the outcome of the siege by champion warfare. If defending party wins, attacking party will abandon the siege but if attacking army takes lead, defending army will surrender the town/castle to attacking army.
Power balance of both fighting armies, personality traits of army commanders, relation between fighting kingdoms and relation between army commanders to be few of the determinants of whether both parties agree on the champion duels or not.