Superhero management sim
I had forgotten Double Fine was getting into iOS development with Middle Manager of Justice. Following a number of great sim games that fit very well with these mobile platforms, this tasks players with managing superheroes in an office environment. You'll send them out to fight crime, make sure they're always working out, and generally micromanage the hell out of your staff.
During my time trying out Middle Manager of Justice, I promoted my Masked Mummy to Junior Assistant Hero and filled out a bunch of Justice Request forms. Like a mid-level boss! This isn't necessarily the type of thing I'd expect from a studio like Double Fine, but the writing is at times pretty funny, if nothing else. The fact that it's a free download doesn't hurt, either. Give it a shot.