I can’t think of the exact name of the game, but I recall in a few introductory creative writing classes/creative writing clubs doing this exercise where one person writes one line of a poem/story/etc. and then each subsequent person writes one line until it goes all the way around and the page is filled with an often offensive, chaotic, and hilarious jumble.
The game rarely produces works of merit, but I always found it fun, mostly because I was usually the first jackass to break continuity, introduce a random character, event, or object, or bring forth any number of complications. I loved how it brought out the mischief in everyone.
But the game is important in another way, too, in that it suggests how a poem (in this case) can abruptly or subtly shift in the small space of line or even within the line. A poem of several authors rather than one will most likely come out messy, nonsensical, and inconsistent in the realm of this game, but the product is illuminating nonetheless. From these scrambled poems we can ponder the multiple screaming voices within our own heads that compete for space on the page. Will one voice calmly scribe the poem, or will our rampant mental contradictions battle on the page? The results will differ greatly.