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Some PbtA games do and some don't, so it's a good question! GM PbtA works pretty much how you'd think, generally, but I'll be doing GMless. Avery Alder has some good (free!) examples of GMless PbtA in the form of Perfect, Unrevised and Dream Askew. (The PDFs credit her by a different name; she's since changed it.) 

The Law players from PU and the Psychic Maelstrom/Society Intact/etc from DA resemble the Lost Love/Memento/etc I have in mind.

Note that these games are not exactly like mine is going to be, lol!