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It's pretty simple. You have seven days and seven missions to survive through. Of course the Game takes place on a different plane of Shibuya. The Reapers can't touch the Players, though, but they can make completing things... Difficult.
[So cheery and upbeat!]
Failure means erasure. Make it through Day Seven and maybe the Composer will give your life back to you. If not, you can either become a Reaper or play again.