I haven't written about agenda for a while, for various reasons. But I was just struck with this though and I wanted to share.
*A Nar GM is like a guy in an improv jazz band. He might be a "first amongst equals" because he has special responsibilities, but really he's just playing a different instrument. Everyone plays off each other, calling each other out. There is no written music and we follow each other's cues instead. The GM might take on the role of a conductor, aiming the spotlight around and deciding which two or three instruments should play together, but he lets them play it out themselves, not according to preset notation.
He (and possibly everyone else) is asking (implicitly): So if you're in this arrangement, what do you do? What if I change the tempo? And if I bring in the trumpet, how do you react?
*A Gamist GM is like a coach (or in a more extreme version, a drill sergeant). He's hard on you, making you climb stuff and crawl in the mud and jump over high obstacles but he's not doing it because he hates you. He's doing it because he's your fan, and he wants you to succeed. But to do that that he has to be fair and keep raising the bar, making stuff harder, not giving you an easy time.
He is asking (implicitly): Can you do this? What if I make it harder? Ok, how about we try again and see if you can do it with less trouble this time?
*A Sim GM is like a guy writing fanfiction. (Ok, so maybe this is a less-than-favorable comparison in relation to the other two, but it's not intended that way). Ok, maybe he's a genre author. The players are his readers, but they're also telling him what to write. They know the "original" and they know what must go in there, what fits, what rules exist, what kind of characters are right, what kind of story arc should roll out. You know examples where the fans get angry because they think the author(s) handled a character wrong? Instead of a free jazz band the group is more of a cover band, but also the fanbase.
I find it harder to frame Sim in terms of question, but the GM is (implicitly) asking stuff like: Is this what your character's arc needs? What would Frodo do? What's the right way for this to go down? (maybe someone has better examples)
As always it isn't exactly accurate to map specific techniques and behaviors directly to agendas, but I thought these were good analogies of what goes on at the table.