I’m having a little trouble seeing the details here. Would writers be cross-posting their bits and pieces as they go, or is the idea for each participant to present a completed story based on the “starter”? What’s the purpose of the replies - critique? What would the writers’ motivation be - to test-drive stories, to improve their abilities with give and take from their peers, to publish?
Sounds like fun. From what I’ve seen it might be that some of it is being done at the Unaboard (www.unaboard.com) and at Elfkin477’s page (check her Interactive story board). There may be more; those are the only ones I’m aware of.
The only slight, possible hassle is the issue of rights. If you publish something on the web, “first electronic publication rights” can no longer be offered for sale - if you’re writing for sale, that could make things a touch difficult. The way around this is to make the site members only, and make it clear that it’s strictly for the purposes of writing exercises and critique, similar to what Critters does (www.critters.org).
Sounds like fun to me, I’m always up for a writing challenge
On another board (not this one or my story board) one of the challenges that went well was the challenge starter gave each person a single word, and the writers then wrote a 500 word story that had to include the word. You might want to consider writing games as well, like the ones I’ve started in mpsims:
http://boards.straightdope.com/sdmb/showthread.php?threadid=78541&highlight=worse+Mary ← long finished
If you do do it on the SD boards, you might want to check with the mods as to which forum it belongs in, since a lot of round-robin type stories (like the surreal continuing story) end up in mpsims instead of here for reasons I can’t quite explain.