This exact scenario, with whatever permutations, has gone on in in the mind of every person who has played the game in real life, at least once. In Timothy Zahn's The Thrawn Trilogy ( Star Wars Expanded Universe books), part of Magnificent Bastard Thrawn's effectiveness in battle is based on his reputation: his enemies know fully well he's a a nigh-unparalleled master strategist and tactician, so from their perspective each and every move he makes is like Schrodinger's Gambit, existing in a state of It's A Trap and It's Not A Trap until they open the box and the waveform collapses. Dr. Necrosis: But how could you predict I wouldn't expect you're foreseeing my anticipation of your assuming my not-believing? Ha! Answer me that.

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In an episode of The Invisible Man (2000), Darien gets implanted a spy nanobot by a former girlfriend working for the evil agency Crysalis (the details of how the nanobot was implanted are a bit embarrassing to him). The Agency finds out, so they Know that Crysalis know. So they plan to use him as a decoy, but later the secret is ruined, so Crysalis knows that the agency knows that Crysalis knows. And obviously, the Agency knows. Especially when L and Light start working together to catch Kira, who is actually Light. L was always slightly better at the up close and personal mindgames, but Light fared better in the end. The New Series Adventures novel The Doctor Trap has an entire plot based off this. The villain is convinced the Doctor knows something the villain doesn't. Not really. The titular trap, the Doctor explains is what they think you know that they don't. Confused? Yeah, join everyone else in the book.

There is a formal system called modal logic that can be used to model what certain agents in a system know (including what they know/do not know about what the other agents know/do not know).

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Lando: Thrawn or no Thrawn, the Empire is still down to eight sectors. Maybe this is really all he's going for, hoping to confuse Coruscant so badly it just freezes up. What are you waiting for? Who knows me better? How much do you know about me? How well do my friends, family and crush know me? Grab your partner or BFF and take the How Well Do Know Me quiz.Dune Messiah continues the pattern, only this time it's Paul's enemies pulling The Plan aimed at forcing him to choose between his beloved and his Imperium. He knows they are doing this, but falls into the trap anyway, only to be rescued from it by the son who will later replace him as the most powerful prophet in the universe. Also used by the author in Crime and Punishment, where the Nietzsche Wannabe protagonist and the Inspector Javert who inspired Columbo play this game. From Little Big Man comes the great quote "You want me to think that you don't want me to go down there, but the subtle truth is you really *don't* want me to go down there!" Break the ice with your colleagues and open up to each other with these Who Knows Me Better Questions for Work! You might even become closer along the way! 91. What is my job title? Have I ever ranted about work with you? 96. Do I like participating in non-work activities at the office?

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I Know You Know I Know breaks down logically, and it obeys some rules. Here are the levels of deception, with examples: The series finale may be the largest example of this anywhere. Light and Near are somewhere around eight layers deep into this, both of them believing that they are one step ahead of the other. There's an entertaining panel in the manga where other characters witnessing a "conversation" between Light and Near begin to wonder why neither of them are saying anything.The first book alone features a subverted Red Herring Mole (someone suspected of being a traitor who is both too obvious to be the real mole as well as Beneath Suspicion, but actually turns out to be the traitor), followed by an elaborate mind game played by Thufir Hawat to set the Harkonnens against one another, and capped with Paul successfully bluffing and counter-bluffing the combined forces of the Bene Gesserit, the Imperium, and the Spacing Guild. The Blue-Eyed Islanders puzzle relies on this to an insane level, in that it ultimately depends on a 100-story tall tower of hypotheticals. Let's say that K(0) is the knowledge that there exists someone on the island with blue eyes; and K(N+1) is the knowledge that everyone knows that K(N). So if I know K(1) it means I know everyone knows there's someone with blue eyes on the island; if I know K(2) it means I know everyone knows everyone knows there's someone with blue eyes on the island; and so on. The crux of the riddle rests on how, from being given K(100), everyone on the island deduces they have blue eyes by a mind-numbing 100-day process of collapsing hypotheticals. The crux of the whole thing is "common knowledge", defined as I Know You Know I Know to infinity. Prior to the outsider's statement, the islanders all knew at least one of them was blue-eyed, and that all the other islanders knew that, but only up to N, not infinity. Once the fact becomes common knowledge, the hypotheticals can begin collapsing, but not before.