Not sure; I didn't think about that dimension. I suppose that in a real nuclear war, you wouldn't just shout BANG, you'd actually choose a target before launching. So I suppose the natural extension is along the lines of:

• each player shouting BANG has to somehow indicate their target player
• a player may only validly shout BANG up to two seconds after they are first targeted, after which they are dead and can no longer launch attacks
• any player left alive at the end of the exchange wins.

The two-player case is obviously contained in this form as a special case, in which target selection is implicit because there is only one possible choice.

Of course, this means that in a multi-player game it all comes down to alliances and enmities between the players, which I think is a fair reflection of the reality. Not so convinced it'd make a good game though.