Assuming that (for whatever reason) two PCs decided to settle their disputes by means of a fair contest it seems like it would be difficult to determine which character had the 'initiative' to take the first action or which of them wins in a straight contest of brawn.
Let's take a look at a scenario I can very much envision happening in my current game. Lady Vega (a Hardholder) has had yet another disagreement with Goat (a Chopper) and his gang. Both of the characters respect each other and are bullheaded and confident enough to challenge the other to some sort of fair fight or other contest of strength rather than skulking about in the shadows or causing a full-on gang fight.
Given Lady Vega runs a pseudo-medieval society she insists on a duel (with swords) to resolve their latest dispute and Goat, confident in his own strength, agrees. Some time later Goat and Lady Vega are stood in the castle courtyard surrounded by cheering crowds and are about to throw down.
How could I determine which of them has the 'initiative' in the fight, assuming both of their players want their character to act first?
I feel like the flow of the duel would sort itself out past this initial sticking point, but I'm unsure how to get the fiction rolling in a manner that's fair to both contestants. I could simply ask them to make an opposed roll (+sharp probably) but, while trivial in other systems, this seems out-of-place and heavy-handed in the fiction-driven environment of AW.