Think about improv for a moment - actually, imagine that you're on the stage, in the middle of some really amazingly great long-form improv. Your troupe does "a serial story", and like any group, you take a lot of cues from the audience when you do it.
Now remove the audience, and replace that audience with a set of rules that does the same stuff, applies similar pressures to the group, rewards them at the same points.
What would those rules look like?
How would they look like tabletop RPG rules (traditional, novel, or outrageous games all apply)?
How would they look different from what we know?