Combat in Arkheim is resolved instantly. You can watch the fight either directly (for fights in your town) or in the Reports (all fights on the map).
Several Warlords of several players can team up for a battle, however, they will always fight in turns, one vs. one.
The warlord with the most combat strength on each side will fight each other.
The top troop stacks of both those warlords compare initiative.
The higher initiative strikes first and kills enemy troops according to strength and multiple modifiers. The warlord immediately loses morale according to his losses.
Then the enemy troop stack strikes back.
Now the second row of troop stacks compares initiative and strike accordingly, then the third.
After the third troop stack attacks, several items or abilities might trigger, then the fight continues with the top troop stacks.
If at any point a warlord hits 0 morale, he will flee from battle.
In a fight with several warlords, the next warlord pair will start their battle in the same way. A victorious warlord might thus fight several times in one combat.
The side with no warlords left loses the overall combat.