I don't think we've done this here before (we do it over at AT.com) and I figured I'd bring it over as I know we have a ton of lurkers and maybe this will bring them out and join in some fun.
This is probably pretty self-explanatory, but I'll give it a go...
You post, "The person after me is/owns/likes/has/hasn't/etc. __________."
In order to make the next post, you should fit the previous description. Obviously you don't want to make your stipulation too restrictive or bizarre or it might bring the thread to a screeching halt.
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The person after me watched a movie this weekend.