Bleg! Negotiate with the most powerful or with everyone

I've never done a bleg before... a bloggers begging for more information... but I'm in the dark here about whether political science/IR has any received wisdom (or empirical results) on whether peace negotiations (let's leave it a durable cease-fire for now) are more likely achieved through negotiations between the two main parties or among larger numbers of actors at the table. On the one hand it is intuitive to think that admitting more parties to the JEM-NCP talks, knowing that some of them (say) hate JEM's guts, will make it more difficult to negotiate a real cease-fire between JEM and NCP, and so NCP can say they were negotiating in good faith and the other parties could not agree. On the other hand, such intuition rarely holds up to game theory, which is driven by the modeling assumptions. The various impossibility results suggest that maybe it is pointless to think about theory; there just cannot be good predictions about preference aggregation in the absence of lots of structure about how the parties interact, which by definition is not possible in a negotiation where everyone can walk away. So if you were increasing the number of parties, and knew that differences among the parties were high but unlikely to lead to conflict (are JEM and SLA really going to fight each other in serious battles? Doubtful.), but yes likely to lead to fruitless negotiations (what NCP wants, perhaps?) then how do you structure talks to minimize the bad outcome (from mediator's point of view).... I'm not looking for common sense (I could sit here for hours doing the "on the one hand" thing... I'm an economist after all)... I'm looking for any established results.