So Player i's payoff "Ui," depends on all the choices in the class, in this case, including her own choice. Of course, a shorter way of writing that would be "Ui," it depends on the profile.
Happily, we think Sling really nailed the app's UI -- the on-screen translucent controls are pretty cool and generally work well without obscuring the view.
As with The Loop (and most of the remainder of the Kin's UI, for that matter), contacts are presented as a comic book-style grid that can be managed with a two-finger tap gesture.