There's
-first order knowledge(n=1), where you know the rules of the game.
-second order knowledge(n=2), where you know that your opponents know the rules also.
- third order (n=3), where you know they know that their opponents know the rules

you can see where this is going - Common knowledge assumes that, in an ideal game, a player is aware of ALL levels possible. It's like reaching Nirvana - literally becoming the Buddha of playing that game!

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Incidentally we see this over and over in The Dark Knight. The Joker always uses the advantage of rigging the 'battle for Gotham's soul' based on knowing what Batman and the Police know about the clues he had left behind for them - then using that to manipulate them to great effect. There is even the subexample of the ferry scene where the two groups are aware of the rules of the game and know that the group on the other boat are aware too. I bet The Joker was a game theory enthusiast.
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I think this a great tool to be aware of when plotting - figuring out who knows what and when and the figuring out how they act accordingly. You can create some very clever villians who are masters of knowing who knows and predicting behavior - using that intellect for evil gains.

Hmm...maybe we should do a writing challenge - write a story of two antagonistic characters who know that they both know they know that they both know. Know what I'm sayin'? I know you do. And now, I know you know that I know you do know - know what I'm saying?...

Great post KDW!