So - I've been thinking a lot about using a mancala board as the main tool for a resolution mechanic; it occurs to me that there's an additional idea I had that might be good to throw in on top.
Basically, you have Friends.
Well, let's back up. As our good friend Sheikh recommended here, you have skill levels in the mancala resolution -game thing. Sooo here's how we frame them: each character has a set of things they're good at OR resources they alone (or alone-ish) can exploit.
There are three types of characters: the Main (the star!), Cotagonists (co-stars/first among equals), and the Omnes (everybody else). If you have a Main, a clear outlier (in importance) among the characters (someone like Elric, Dr. House, or Dexter [from Dexter, natch]), then that character gets three skills/assets, with ratings of 6 and 1. If you have Cotagonists, they have skill ratings of 4, 3, and 1.
Omnes have pretty much one rating for everything they do, based on their importance in the story/to their protagonistic nemesis. That rating can be anywhere between 1 and 6, with 6 being reserved for the central antagonist in the story. Alternately, obstacles or other not-person barriers to the players could be rated accordingly - the Sea of Swords ( a vast swath of rock formations, zero water, and maybe bandits) merits a 4 if it's a grand but not final obstacle to getting deeper into the Southlands. I dunno.
So. You pick your assets, and now we make Friendships a little more clear. Friendships have two steps in 'em - two times you can take advantage of this relationship before that person wants nothing to do with you. Theoretically, a given Friend could be a group of people instead.
The point of Friendships, beyond the social assets they provide (i.e it's good to be cozy with some people), is that they provide assets you don't have. This is super-important - in conflict, retreat is (nearly) always an option, so if you hit a wall, you can go back and find someone to help you. If you use a Friend's asset in place of your own on the mancala board, reduce your connection to that Friend by one step.
If you reduce your connection to zero steps, that relationship is either over or on hiatus - that Friend doesn't want to have anything to do with you or refuses to help you. You can get back in their good graces again, though - with Laurels! A Laurel is any sort of favor, gift, honor, or what have you that the Friend would actually appreciate, as defined by whoever's playing that Friend. One Laurel restores one step.
I advise that player to push for all they can get from the situation, but what they demand must be something the other player is capable of giving. I see no problem at all with demanding something the supplicant can't currently give - that'd be the beginning of a quest, I suppose!
Two more things about Laurels - first, you can determine what's "fitting" in one of three ways: the supplicant may decide privately what he's going to give the Friend, and maybe give it unasked as well, in play; both parties may discuss, out of character, what would be appropriate, and run a scene wherein the giving occurs, if necessary; OR the Friend may announce, in play, what his/her desire or demand might be.
So - talk about it out of character, or one party springs it on another. Or talk about it in-character, I guess, but only if it's interesting.
Second thing: new or brief Friendships - if you can only make contact with a stranger, or someone who will only interact with you for a short time (someone you meet on the road, or suchlike), then you and the player of the Omnes can discuss what you might need to give this person to get them to do you a favor. Once you've gained, and used up, one step with this person, it's likely that the relationship, such as it is, will dissolve on the spot, but it may be that the Omnes character is well-liked by the group, and either sticks around or returns sometime later in some form.
So. That, combined with a mancala-based resolution mechanic, and I think we have a game starting to form. :)