This seems like one of those things a genius would wonder about, and so here I am, trying to be a genius.
What would a second person game be like?
We've all heard of first and third person games. These descriptions refer to the perspective the player is given: either as the protagonist, or as a disembodied camera following the protagonist. Second person, however, would imply that the user takes the perspective of not the protagonist, but someone would would refer to the protagonist as "you".
Taking this definition more broadly first, there are several types of media which currently addresses the protagonist as you. The more well known are those "choose-your-own-adventures" book. Translating that into a game would make it similar to a God game, where you provide all the opportunities for the computer-controlled characters, and watch what they do. Since there are multiple paths through the story (one would hope), it would be ideal if you can somehow configure the protagonists, giving them traits and attributes which will then be used to decide which path through the story they take.
The game will therefore be much closer to writing a piece of interactive fiction than any conventional game. This in fact is also a good description of the second type of existing media: the role of a dungeon master in table top role playing games. The concept is the same, except this time it's other people who are controlling the protagonists, while the "player" controls the story telling, the NPCs, and pretty much everything else in the game.
Taking this concept further, a second person game is a game where the player controls everything but the protagonist. Technically it will only be "second person" if the player controls an animate object (since otherwise it will be third person), but it is still an intriguing idea.
My final question is, what kind of story could this format tell? I could imagine the player being mean, and denying everything the protagonist asks for. For the protagonist to succeed though, the player would have to keep giving ground, or at the very least play a very supporting/passive role. It would certainly be very strange.
What prevents the character(s) the player is controlling from turning into the protagonist?