Are you asking "is this a good game idea"? If so, it belongs in Game Design, not Writing.
But you didn't say anything about what the game itself would be - what genre, what platform, what play mechanic.
I agree with Tom. You're asking the wrong question, essentially. Instead of asking whether this would be a good idea or not, you should instead ask yourself (or us) how this can become a good idea. It's all about implementation.
As for my own answer, I'd say that you could make it like the Fallout universe - dark satirical humor and you can just about sell any wild idea that you can think of. Only problem is that you'd have to be good at that type of humor.