I Know You Know I Know



"Captain Amazing: I knew you couldn't change. Casanova Frankenstein: I knew you'd know that. Captain Amazing: Oh, I know. And I knew you'd know I'd know you knew. Casanova Frankenstein: But I didn't. I only knew that you'd know that I knew. Did you know that? Captain Amazing: (clears throat) ... Of course."

- Mystery Men

Paranoia can be a funny thing. It seems no matter how well you've prepared or you how you anticipate possible outcomes, there's always someone who can mess your plan up if he knows about it. Ah, but how do you know he knows? He may be acting like he doesn't know so you won't do anything different that he can't predict. This, inevitably, leads to the following paranoid rant:

"Yes, but if he knows I know he knows, he may do (X) instead. But what if he knows more than I think he does? He could be acting like he only knows that I know he knows, when in fact he knows that I know he knows I know he knows!"

Typical punchline: "...what was I doing again?"

Something of an overblown version of the classic chess axiom "think three moves ahead", this is one of the most common sights in a duel of Chessmasters. A Gambit Roulette may also have them, as the level of paranoia necessary to pull one off suggests he's suspecting everyone of knowing and reacting accordingly. Of course, if there's a Gambit Pileup in the making, that attitude might be justified...

May not feature the exact line, but often uses a scene where one character or the other remarks on how his opponent would react if he knew, and what he's doing in case that happens. In Real Life, humans are capable of keeping track of many degrees of what people know ("I know that he knows that she knows that they know that we know about the party..."), though even when taking the game seriously, they tend to find the string of "knowing" comical.

I Know You Know I Know breaks down logically, and it obeys some rules. Here are the levels of deception, with examples:

Level 0: absolute honesty, no deception.

Level 1: X plays level 1 (hereafter abbreviated X(n)). X(1) has information that Y(0) does not, and utilizes this in a deception.

Level 2: Y(2) knows that X(1) is playing a deception. Y(2) reacts accordingly.

Level 3: X(3) knows that Y(2) is well aware of the deception, and thus plans for the outcome of the first deception being revealed.

Level 4: Y(4) is aware of the above play, and knows that the logical reaction to finding out the deception will play right into X(3)'s hands. Thus, Y(4) plays around X(3).

Level 5: X(5)'s entire deception is a deception, maybe meant only to engage Y(4).

And so on, and so on.

This chain can go on indefinitely. In the really hairy cases, one or more deceptions are being played parallel or maybe even in conjunction with one another, making the abovementioned Gambit Pileup.

From the second level on, the recipient of the deception (in this case Y) has two choices: either Y plays a counter-game so that the deception is revealed, or Y willingly plays the deception to X's logical conclusion. The first option will reveal Y to be playing a higher level, but will foil X's deception. The second option will let X fulfill the deception, but will not reveal Y's level. Reaction from Y is crucial, as this seperates Y from a player of equal level to X. If that was the case, Y would simply be aware of the deception but unable to act upon it. In reacting, Y steps it up a level.

Of course, with each rise in level, the below levels become meaningless, so this gambit only works if X is not playing an even higher level, in which case Y would either be playing into X's hands or letting X win.

X also runs the risk of misjudging Y's level. If Y is playing a higher level than anticipated, then the deception is, as mentioned above, meaningless. If Y is playing a lower level, then X will be Crazy Prepared but never engaged on the higher levels, which may leave X Properly Paranoid.

See also most instances of the Poisoned Chalice Switcheroo. Frequently a consideration in Feed the Mole. In many an Absurdly High Stakes Game this will take the form a (often internal) monolog.

Usually results in an Overly Long Gag. Frequently ends with an "I Didn't See That Coming". May result in Archive Binge-like behavior when plans are laid for both eventualities, and then for both of those eventualities, and then all four of those, and then all sixteen... This may develop into an Gambit Roulette if it hasn't done so already.

Not to be confused with "I Know I Know I Know".

Anime & Manga

 * One episode of Yu-Gi-Oh! does this word-for-word, during Joey's battle with Yugi. He gives a long internal monologue about whether or not the card Yugi placed down was a trap card or if that was too obvious...
 * "Eh. Who cares? I'm just gonna attack."
 * 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.
 * Neon Genesis Evangelion is based around this trope SO MUCH. Gendo Ikari's relation with SEELE IS this. They each know that the other is planning to betray them, so both work with that, but both know that the other knows. They just keep on trying to get one step ahead using their unimportant pawns, such as Shinji, Rei, Asuka, Toji, Kaworu etc etc. Both are surprised when
 * Every fight during the second part of Jo Jos Bizarre Adventure follows this pattern. Jojo attacks, the opponent declares they saw it coming and counters, Jojo explains he saw that coming and twists the attack as needed, and so on until one side or the other goes down.
 * This makes up about a third of Kaiji, the other two-thirds being basic game theory and heroic determination. In particular, the defeat of in the first season is based on Kaiji's realization of when  will stop knowing he knows.
 * Appears in Ghost in the Shell: Stand Alone Complex, strangely not as a part of an Evil Plan, but in a sniper duel. In fact, the whole episode revolves around knowing and predicting enemy tactics. The story is told by one character during a poker game to illustrate to the other players why he is so good at bluffing.
 * This is ALL of Spiral once the Blade Children storyline starts.
 * And all of Death Note from the time L shows up. So, all of it, really.
 * Especially when
 * The series finale may be the largest example of this anywhere. Light and Near are somewhere around eight deep into this, both of them believing that they are one step ahead of the other.
 * The third round in Liar Game becomes this with Akiyama and Yokoya. It's likely that the upcoming fourth round will feature it even more.
 * Most of the point of Legend of Galactic Heroes is like this, with Yang Wenli and Reinhard (and various other pairs) making plans, which may include knowing their opponent's plans (and sometimes involve a plan being an opponent seeing though the plan, with an extra layer of fake planning below it).
 * Eyeshield 21 does something like this during the big game between Ojou and Deimon during the Fall Tournament, with a whole string of characters reacting with shock, then going "Is that what you expected me to say?" when a dramatic play seems to go one way, then the other.
 * A major plot point of a certain Spice and Wolf arc. Holo is a semi-deity, one incredibly adept at quick thinking and long term planning both. Her sharp senses and silver tongue can turn practically any bargain into an incredible deal. So when Lawrence manages to find himself in a make-or-break financial showdown with Amati, (who is also an incredible merchant), he almost breaks down trying to out-think their combined plans.
 * An episode of Pokémon had the group seeing a basket of fruit on the road. Ash wanted to eat it, but Misty points out that it's an obvious trap by Team Rocket. She then points to some fruit growing in the trees, which the gang decided to take... causing them to fall right into a trap set by Team Rocket, who set up the basket knowing it would be ignored.
 * Mirai Nikki And how! Considering its a series thats about people trying to kill each other to become God. And each and every one of them can predict the future. The entire series revolves around this trope.

Card Games

 * Proper Poker strategy, especially at higher levels, requires this kind of thinking and trying to stay one step ahead of your opponent(s). At its highest levels, the whole thing can get ridiculous, break down, and require game theory to come up with an ideal solution.
 * Blackjack strategy (eg, "counting cards") and trying not to let casinos notice you thinking too much is a meta-gambling example which can, at its extreme, surpass anything you've read in a spy novel.
 * Really, any competitive game is like this. Playing to Win has an excellent summary of it.
 * Trading card games can have a variety of rules, exceptions, and so on to keep things interesting, but Yu-Gi-Oh! is well-known for the numerous and sometimes surprising ways the action can be altered, and the official rules tell you to expect this by saying that if a card says something contrary to the rules, you follow the card. There are cards to alter almost any aspect of the game: from draw to battle to endgame, so any action you take can begin this kind of mindgame.

Comics
"Charlie Brown: Ha! I know what she's got on her mind! Every year she pulls the same trick on me... she jerks the ball away just as I try to kick it... Well, this time I think she has a different idea. I think she's going to try to fool me by not jerking the ball away! This time she knows I know she knows that I know she knows I know what she's going to do... I'm way ahead of her! (Hilarity Ensues) Lucy: I figured you knew that I knew you knew I knew that you knew I knew you knew, so I had to jerk it away!"
 * Cerebus does this several times, usually involving Lord Julius, a Clown Prince of MagnificentBastardy. Astoria also does this to Cerebus.
 * Peanuts has used this joke quite a few times, when Charlie Brown is on the pitcher's mount, trying to figure out whether the hitter is expecting his fast ball. There was another incident involving Lucy's football-pulling stunt:


 * When Black Widow stops the hijacking of a NASA space shuttle she and the agent in charge of the hijacking keep one-upping the other after they reveal a part of their scheme to the other, each explaining how it "changes the game." First, Black Widow reveals that she is working with the CIA and has been impersonating the man's partner. The man, commenting that that changes the game, explains that he has just detonated the explosive in his partners head, probably killing a few of his interrogators. Widow, saying that that changes the game, explains that she is still going to take this man in for questioning, though now she will make sure to hurt him while doing so. The hijacker, after commenting that that changes the game, explains that he is now crashing the shuttle to stop her. After that the game stops changing and Widow just beats the tar out of the man, but you have to wonder what game they started with and what they were playing when they finished.
 * Garfield had a case of this, when Garfield was trying to get a spider to come a bit closer so he could hit him with a (not very well concealed) newspaper. After a pileup of "Make me Make you"s, they forget what they were talking about... and the process was restarted in the last panel.

Fan Works

 * In Harry Potter and The Methods of Rationality, Harry learns methods of deception at higher levels, such that this becomes invoked. If you want to pretend that you don't know anything about something, you don't say "I don't know", you act as you anticipate your opponent anticipating your actions if you didn't know--in this case, pretending to clumsily fish for more information on the topic.
 * Played with in My Immortal. When Ebony Enoby travels back in time, she knows that Snape Snoop possessed James Samaro and made him kill Lucious Lucian. She, however, did not "want them to know [she] knew." Whether or not Tom knew she knew is not made clear, but it is likely, as "Suddenly it's a Sitcom," the dramatic reading snarked at this bit.
 * Tom knew she knew that he knew that Snoop worked for Volxemort and possessed Samaro and... it kind of melts from there.
 * In a recent chapter of Dragon Age: The Crown of Thorns, Theron Mahariel, the Dalish Elf Warden, contemplates how he's been passively spying / been allowed to eavesdrop on some secret talks between the Guile Hero dwarven noble protagonist and Alim Surana, One-Man Army mage. The extent of the I know he knows I don't, etc., has to be seen to be believed. And it's only slightly played for laughs.

Films -- Animation

 * Disney's Hercules has a variation. Hades is telling The Fates his Evil Plan, but they keep interrupting him by saying they already know his plan, because they're the Fates and they know everything. Hades eventually snaps and shouts ''I KNOW you know! I know! I get it! I get the concept!

Films -- Live-Action
"Martin: And never let him know that you know what he thinks you don't know you know... y'know?"
 * The Princess Bride has this between Vizzini and the Man in Black, as he attempts to figure out which goblet contains the poison. (See the Literature entry below.) Subverted in that Vizzini isn't really trying to reason it out; he's just throwing possibilities at the Man in Black to see if any of them gets a reaction. If he were really playing I Know You Know I Know, he'd have realized that just as he wasn't about to leave the outcome to chance, the Man in Black wasn't about to leave it to chance either...
 * If Vizzini were paying attention to his own line of reasoning, he might have realized that he was getting dangerously close to the truth (as shown by the Man in Black getting increasingly nervous in this scene in the book) that.
 * The Lion in Winter played this straight, albeit slightly lampshaded, complete with the line itself from Prince Geoffrey: "I know. You know I know. I know you know I know, we know that Henry knows and Henry knows we know it. We're a knowledgeable family."
 * Monkeyed around with in Mystery Men; see the page quote.
 * The Swedish movie The Shark Who Knew Too Much opens with the main lead chased by a helicopter while shouting this sort of dialogue. Given that he's spent his whole life masquerading as a group of identical triplets who can't stand each other's presence just to trick his father into giving him shareholder majority of the company, it's obvious there's a lot of deception involved.
 * In Sneakers, Martin is interrupted while breaking into an office. In the course of inventing a plausible explanation for why he's there, he finds himself inadvertently entangled in one of these:

""As I said before, I've allowed you to keep your wicked life for two reasons. And the second reason is so you can tell him [Bill] in person everything that happened here tonight. I want him to witness the extent of my mercy by witnessing your deformed body. I want you to tell him all the information you just told me. I want him to know what I know. I want him to know I want him to know. And I want them all to know they'll all soon be as dead as."
 * The villain of Under Siege 2 does this while explaining to the muscle of the operation that he's going to demonstrate the power of his earthquake-shooting satellite by using it on a fertilizer plant in China: "[The fertilizer plant] is actually a secret chemical weapons testing facility. We know this. The Chinese know that we know. However, we pretend we don't know, and they pretend they don't know that we know that they know we know. But know that we know. In the end, everyone knows."
 * Inverted in a long-distance sort of way in We Were Soldiers, where throughout the entire battle, Colonel Hal Moore emphatically knew what his Vietnamese counterpart was going to try, whereas the Vietnamese CO emphatically did not.
 * Specifically because the Vietnamese were using more or less standard tactics, and Moore, using a never-before-testing air cavalry method, was forced to make up tactics as he went along.
 * The Bride says this at the end of Kill Bill:
 * Specifically because the Vietnamese were using more or less standard tactics, and Moore, using a never-before-testing air cavalry method, was forced to make up tactics as he went along.
 * The Bride says this at the end of Kill Bill:

"White Goodman: Cuz I know you. And you know you. And I know that you know that I know that you know you."
 * Hot Lead and Cold Feet has Don Knotts' Sheriff deliver this line regarding his arch-nemesis, Rattlesnake: "'Cause he's here and I know he's here. And he knows I know he's here! But he doesn't know I know he knows I know he's here, but I know. So I got the edge!"
 * In Dodgeball:

"Bob the Turk: I warn you, do not make me do something that I would not do, unless someone made me do it because they didn't do something someone told them to do. Gus Cardinale: Don't worry, Bob, I would never do something to make someone do something to someone, because that someone didn't do something that someone wanted them to do. Bob the Turk: I'm glad we understand each other. Gus Cardinale: ... Me too. (cue Aside Glance)"
 * From the description above, the classic quasi-comedy The Court Jester. Everyone knows the pellet with the poison's in the flagon with the dragon, but the vessel with the pestle has the brew that is true!
 * A variation in the movie Why Me?

"I've written papers on "Little did he know." I've taught classes on "Little did he know." I once gave an entire seminar based upon "Little did he know." Sonofabitch, Harold. "Little did he know" means there's something he did not know. That means there's something you don't know. Did you know that?"
 * From the Harry Potter Alternate DVD Commentary Gag Dub Wizard People, Dear Readers: "Then, dear readers, Harry notices a tear in Snake's pants and blood all over her leg, and Snake notices that Harry has noticed, and he notices she noticed that! I mean, there is a trade of noticing going on that is just bewildering."
 * Played with hilariously by Professor Hilbert in Stranger Than Fiction, when Harold mentions his narrator said "Little did he know":

"Barbara Novak: You know I have no interest in seeing you. Catcher Block: But you know you have to, and you know I know you have to. I'm sure you know how things are at KNOW ever since your new NOW. Barbara Novak: I have no way of knowing how things are now at KNOW. I knew how things were at KNOW before NOW. Catcher Block: Then you should know now at KNOW things are a lot like they are at NOW; we have to interview every applicant for every job, and so do you or you'd be going against NOW's definition of discrimination and you wouldn't want the readers of NOW or KNOW to know that, now would you? And later: Barbara Novak: Scooped you again. Catcher Block: I knew you would. Barbara Novak: I knew the minute Catcher Block: And I knew you knew Barbara Novak:"
 * In the film (and play) Romanoff and Juliet, The General (Peter Ustinov) goes back and forth between the U.S. and Soviet ambassadors, discovering the layers of intrigue: The Soviets have broken the American code. The Americans know this, and are feeding the Soviets misinformation. The Soviets are aware that it is misinformation and are pretending to be fooled by it.
 * 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!"
 * Down With Love, several times, one of them also counting as a Hurricane of Puns, as the discussion concerns two magazines called "Know Magazine" and "Now magazine"

"Akeem: Listen, I know what I like, and I know you know what I like, because you were trained to know what I like, but I would like to know, what do you like?"
 * And Barbara's entire speech at the end where she reveals
 * Coming to America has this happen as Prince Akeem meets his bride-to-be:


 * Seen in The Three Musketeers 2011. The musketeers have to break into the Tower of London. Milady, who's worked with them in the past, knows their methods, and can give Buckingham the information. They know she knows their methods and will tell Buckingham. She knows they know she knows and will tell Buckingham.

Literature
"Han: From now on, we can't trust anything we see. Anything we see, anything we hear, anything we think we ought to do. Not with Thrawn back on the scene. 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.
 * A hilarious example exists in The Princess Bride with mid-level villain Vizzini. He goes through all sorts of permutations on which goblet has the poison in it, based on his observations and the defeat of his minions. In the end,.
 * The Dune series is renowned for its incredibly intricate layers-upon-layers of this kind of gambit.
 * 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.
 * Dune Messiah continues the pattern, only this time it's Paul's enemies pulling a 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.
 * Children of Dune sets up a three or four-way struggle for control of the Imperium, with the demon-possessed Alia on one side, the Bene Gesserit on another, the remnants of the Corrinos as a third, and an unknown quantity in the form of Paul's children, Leto and Ghanima. Leto is captured by people whom he believes to be working for the Bene Gesserit, only to have it turn out that Alia is secretly calling the shots. He himself, however has a deeper plan that eventually trumps all of theirs and renders them moot.
 * Parodied mercilessly in the National Lampoon's Doon, where two characters have a half-hour long conversation without knowing what the other is talking about.
 * The big reveal in Book XI of The Brothers Karamazov relies on this type of logic played seriously. You can almost see it coming when it is occurring at an earlier point in the novel (some hints are dropped that something is going on at either rate), but when you learn precisely what took place in one character's mind as a result of seemingly-irrelevant events, it forces you to re-evaluate everything else that has happened.
 * Also used by the author in Crime and Punishment, where the Nietzsche Wannabe protagonist and the Inspector Javert who inspired Columbo play this game.
 * Edgar Allan Poe plays this one straight in one of his mystery stories, "The Purloined Letter". Private eye Auguste Dupin actually explains that this is the reason he can outwit the police and get his man. The police know who stole the document; the thief knows the police know. The difference between Dupin and the police is that Dupin knows the suspect knows the police know, and the police don't know that.
 * Vetinari plays this game subtly off-screen in Discworld. Specifically, his package to Uberwald was clearly tampered with, as expected, and he specifically uses codes that are almost unbreakable. (As for himself? He always poisons both glasses. It doesn't matter who knows what, he gets out ahead either way!)
 * 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.
 * The climax of the third book brings this to an epic level. Thrawn knows that the New Republic wants to capture an important bit of technology, of which only three are known to exist, all on Imperial worlds. The New Republic knows that Thrawn knows this. They also know that one system is heavily protected while another is only lightly defended. Thrawn knows that they know this. The New Republic knows that Imperial Intelligence is very good and will pick up disinformation that shows an attack on the lightly protected system is in the works. Meanwhile they actually plan to attack the heavily-fortified one. Thrawn knows that the New Republic knows that his intelligence is that good, and that the "secret plans" are a deception, so he disregards those attack plans and prepares for the real attack.
 * In the Hand of Thrawn Duology, set a decade later, a trio of Imperials conspire very successfully to make it look like Thrawn is Back From the Dead. When Han Solo finally sees the (fake) Grand Admiral and has his suspicions deftly countered, it's a shock. Thrawn was, after all, alarmingly good at anticipating what people would do.

Han: Who knows? That's what drives you so crazy about him. You try to do something and odds are it's exactly what he wanted you to do. You stand still and don't do anything, and he runs a smartrope around you."

"Silk: Does he know that you know? Ambassador: Yes, but I don't think that he's aware that I know that he knows that I know."
 * Zhuge Liang's Empty City Ruse (from the fictionalized parts of Romance of the Three Kingdoms) relies on this.
 * Zhuge Liang is the master of this trope. Various plans include:
 * Empty City: Zhuge Liang sits alone in an empty city playing his harp while a rival army comes up. They know that Zhuge is a genius and is obviously up to something. Knowing they would know this, the city really is empty, and the whole thing was a stall tactic. That worked.
 * Two Roads: Cao Cao is leading his army through a mountain pass when he comes to a fork in the road, one direction he can see a lot of smoke as you would expect from army camp fires; down the other he sees very little smoke. Obviously, the big smoke path is a ruse and the little smoke path is an ambush. Actually? I Know You Know I Know, the big path is the real army.
 * Played with in Twilight. Edward and Alice Cullen play a Chess game by using their abilities to figure out what move the other is going to make next... and countering... and being countered... and countering again... and so on.... The game is finished in their minds before two pieces are physically moved.
 * A children's book titled Finding Buck McHenry, about a man who may or may not be a retired pro baseball player, has the young narrator going, "I knew. And he knew that I knew. And I knew that he knew that I knew. Stop. You're making yourself dizzy."
 * In Mistress of Dragons, Draconis knew that Edward knew that Draconis knew that Edward didn't trust him. I had to spend 5 minutes interpreting that.
 * In "Riding the Bullet", by Stephen King, the main character is on the verge of freaking out when he dizzies his own mind with how he can't let the dead guy next to him know that he knows that he knows that he's dead (or something, I'm quoting from memory).
 * Sometimes both parties can "win" at this (or at least, two out of three can). In one short story in Future on Ice (edited by Orson Scott Card), an immortal being finds two soldiers who're lost and starving to death, and it gives them each two boxes. It's observed them and claims it knows how they think, and if it predicted of one of them that he'd only open one box, it gave him food in one box, and in another box a device that will allow the user to become immortal if he so chooses. If it predicted one would open both boxes, one box will have food and the other will be empty.
 * In Neal Stephenson's Cryptonomicon, Detachment 2702 exists to generate enough random noise to cover up the fact that the Allies have broken German and Japanese ciphers. It stands to reason that if the Axis finds out, they'll switch to a new cipher, so being able to act on the information they got without revealing they have this information becomes very important.
 * Discussed in the Belgariad. The Drasnian ambassador to Nyssa is bribing the staff of the Tolnedran embassy for information as part of his intelligence network. The Tolnedran ambassador knows this, and occasionally feeds his staff fake information as a result. The Drasnian ambassador knows this.

"Sarah: You know they're lying. Doctor: Of course I know. And they know that I know. And I know that they know, and they know that I know that they know [etc., etc.]"
 * The BBC Doctor Who book The Doctor Trap has an entire plot based off this. The villain is convince the Doctor knows something the villain doesn't. Not really. The titular trap, the Doctor explains is Confused? Yeah, join everyone else in the book.
 * A Fourth Doctor book has the Doctor going on and on like this, until Sarah Jane Smith tells him to shut up.


 * Subverted by Ephraim Kishon in a story with a bagel salesman. The narrator thinks he wants to fool him into buying lower quality bagels, and goes through lengths with this trope, only to find out at the end that all the bagels always were fresh, and he suspected an innocent guy lying.

Live-Action TV
"Sir Humphrey: Yes, but even though they probably certainly know that you probably wouldn't, they can't certainly know that although you probably wouldn't there's no probability that you certainly would!"
 * Nearly every sitcom with wacky secret hijinx ever. Especially when someone hatches a Counter Zany.
 * Data does this in the Star Trek: The Next Generation episode "Peak Performance", right here. Troi points out he's overanalysing.
 * In an episode of Friends, "The One Where Everyone Finds Out", Phoebe and Rachel find out about Monica and Chandler's secret relationship, and something of an arms race begins regarding whether or not "they know we know they know we know!" Joey gets caught in the middle (since he's known for a while), and eventually throws up his hands when he can't keep track of who knows what.
 * Parodied in the same episode, when Monica walks into the apartment and dramatically says, "They know." Cue the confusion.
 * Similar to the above example (but fewer levels), Richie in The Class must determine how Duncan's date went for Nicole, but since he's a Bad Liar, he ends up revealing Nicole's secret, then Duncan's secret, then both.
 * During Draft Day betting at Sports Night Dana and Casey try to figure out if the other knows anything about Tommy Castro's knees, and if so, do they know that the other person actually doesn't know anything about... etc. Ends when Casey explains the entire I Know You Know I Know situation to Dan, while wired so Dana can hear him.
 * The Doctor Who one-off comedy special The Curse of the Fatal Death has the Doctor and the Master engaging in a round of this. Since both have access to time machines, it quickly gets complicated.. ("624 years in a sodding sewer!")
 * Also in the regular series episode "Let's Kill Hitler", between the Doctor and River.
 * Happens quite a few times in Yes Minister. Especially funny due to Sir Humphrey's penchant for Sesquipedalian Loquaciousness.

"Amy: The last couple of times Decker got really close you pulled the same trick, hiding right under his nose. Making him think we're half-way out of state. He's gonna figure that game out. Hannibal: Yeah. But he'll figure I figured that, so he'll figure that I figured the other way, which is why we're staying here. Amy: That makes no sense. Hannibal: Decker will understand it."
 * Used in the Stargate SG-1 episode "Ripple Effect",
 * Used dramatically in Stargate Universe with Chloe revealing that she knows about the thing that he knows, it's just that... the 'thing'.. is Eli being in love with her whilst she's in love and in a relationship with one of Eli's best friends.
 * A common sight in Survivor, with the convoluted backstabbing, double-dealing, and mind-gaming that the players perpetrate on one another.
 * Relied on by Shawn in Psych, as it is unclear whether/how much most of the main cast believes his psychic stint. Lampshaded in the theme song, in fact, it's (almost) the name of the theme song.
 * It's also unclear who the "you" addressed in the lyrics "I know you know that I'm not telling the truth/I know you know you just don't have any proof" is. Lassiter? Vick? Jules? Henry? The audience?
 * Also, there have been some very high-stress or time-sensitive moments where Shawn doesn't even bother to try and make his psychic schtick look plausible in front of Vick, which implies that she operates on I'll Pretend I Didn't Hear That (plus her no-nonsense, down-to-earth persona makes her steadfast reliance on Shawn's vibes seem very out-of-place).
 * Played with in NCIS when Gibbs asks for Ziva's weapon. And her backup weapon (revolver in ankle holster). And her backup backup weapon (a knife). He then hands the knife back to her, and points out that he wanted her to know he knew.
 * Recently used in Chuck, after the staff of the buy more is told to behave Morgan goes through this to try and work out whether or not they should misbehave due to the person telling them knowing they'd know he knows they know he knows how they'd act.
 * Burn Notice talks about this during season 2. Michael, having started to become much more enlightened as to Carla's objectives and methods, begins to spy on her. Unfortunately, as he points out, he can't do anything different because it would clue her in to the fact that he already knows a little of what's going on.
 * On The A-Team, B.A. Baracus is terrified of flying, so they have to drug him every time they go on a flight. One time, they put it in his burger. Another time, he realized that they needed to drug him, so he took Murdock's burger. And promptly passed out afterwards. Finally, at one point he was switching everyone's burgers, trying to figure out which one was drugged, and ultimately decides that the one burger they wouldn't have put it in is the one they gave him first... only for it to be revealed that this time, they'd drugged his milk.
 * How exactly did this guy get into Army Special Forces again?
 * Also from The A-Team:

"Assistant: I know you know I told Danny. Matt: I know you know I know."
 * 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.
 * Used mostly seriously on Studio 60 On the Sunset Strip. Matt's assistant has told Danny about Matt's pill-popping. After Danny confronts Matt, she quietly walks into the room.

"Cory: Ohhhhh, you're a smug one aren't you George huh. You know you know, I know you know, I don't know how you know, but I know that you know. Mr. Feeny: Alright I know, I know everything. Now what in the world are you talking about? Cory: NOTHING!! THIS GETS OUT, I'LL HUNT YOU DOWN LIKE A DOG!!"
 * Shows up in Fringe with Milo Stanfield, a savant who can predict the future enough to cause accidents to kill people set off by dropping a pen. It's impossible for Fringe Division to outthink him, because if they try, he'll predict it, and if they predict he'll predict it and choose a different option, he'll predict that too. Astrid describes the situation with at least six recursions of "he'll predict that we predict".
 * Invoked in Sherlock's "A Study in Pink". The assassin tempts Sherlock into a battle of wits involving two identical pills: one poisoned, the other harmless. He tries to lure Sherlock in with this form of logic, but Sherlock refuses the terms of the argument, knowing that no matter what choice he makes, the odds of success are still 50/50. He takes a third option and is ready to walk away from the whole thing, but gets lured back to the table because he has to know if he can win. And the twist of it is, the show never says if he made the right choice.
 * Played with on Boy Meets World. Cory thinks that Mr. Feeny knows that Topanga proposed to him, even though Mr. Feeny doesn't actually know:

"Myka: And, for the record, I knew that you slipped this in my pocket at the cemetery. HG: I thought you’d know. Myka: I knew that you’d think that."
 * Myka and H.G. have a good one in Warehouse 13 quickly becoming complex making Myka's partner tell them to stop a small part below

Music
"I know you know I know So what's the point in being slow Let's get this show on the road today"
 * The Kelly Clarkson song "Walk Away" has the lyrics:

"I know that you don't think I know that I know what I know I don't think that you know i think that I know that you don't"
 * Bob Dylan's song "Tell Me, Momma".
 * Hank Green's "I Know (A Song in Ten Words)", heard here.

"Little does she know that I know that she knows That I know she's two-timin' me Little does she know that I know that she knows That I know she's cheatin' on me"
 * Tex Perkins' I Know Y'Know I Know.
 * Done almost verbatim in the Kursaal Flyers song "Little Does She Know", which was a British top 20 hit in 1976. The chorus is:

"And I knew that you knew that I knew that You knew that I knew that you knew that I knew that you knew that I knew"
 * '60s psychedelic-pop group the Love Generation had a minor hit with the Jimmy Webb-penned "Montage", which wraps up thusly:

"''Need I say I love you Need I say I care Need I say that emotion's Something we don't share
 * The Rutles: "I know you know what you know, but you should know by now that you're not me..."
 * "Throwing It All Away" by Genesis starts with the lines:

I don't want to be sitting here

Trying to deceive you

'Cause you know I know, baby

That I don't wanna go''"

"''We cannot live together We cannot live apart That's the situation We've known it from the start Every time that I look at you But I can't see the future

'Cause you know I know, baby

That I don't wanna go''"


 * "Come to the Sunshine", a '60s sunshine-pop ditty written by cult favorite (and future Beach Boys Smile collaborator) Van Dyke Parks and recorded by Harpers Bizarre, has in its chorus the line You know, I know, you know, that I love you.

Pro Wrestling

 * On an episode of Monday Night RAW, before a scheduled match with Triple H, Mick Foley's Dude Love and Mankind appeared on the screen to introduce Cactus Jack. (It was sort of a thing.) Towards the end, Dude Love asks Mankind if "you're thinking what I'm thinking," and Mankind cheerfully replies "I think I am thinking what I think you think I think you're thinking!"

Radio
Alice: Yes. Bob: Yeah I thought so. Well I didn't say that. Alice: Yes you did! You said you couldn't believe I said what I said about what I thought you said (but which we do agree you didn't say) because you thought I said I said what I said not because you didn't do what you said you'd do but because you said you'd do it, and that makes me feel that you feel that I feel that you don't feel what I feel. Bob: You know I feel you feel I feel what you feel. Alice: Yes but I don't feel you know I know that and that's why I said what I said. Bob: What did you say? Alice: That sometimes, I think you're a little over-analytical-- Bob: Bollocks.
 * John Finnemore's Souvenir Programme, Ep. 3, gives us this brilliant example. Warning: Any and all attempts at comprehension may result in brain damage.
 * Bob: Okay. I want you to listen very carefully and tell me if I've got this right. You're angry about what you think I said about what you said about what you thought I said (but we now both agree I didn't say) about what you thought I thought you thought about what I did when you did what you did when I didn't do what you thought I said I would do but what I thought I said I would try to do, is that right?

Sport

 * The general concept of second intention fencing takes this to ridiculous levels, until someone decides to interrupt all of the feints and counterattacks with a simple straight lunge.
 * In baseball, when one team manages to figure out the second team's signals they'll usually try to only act on that knowledge at a critical point in the game. The second manager might intentionally allow them to try and steal the signal so at the critical point they think they know what's being planned. Which could cause paranoia in the first manager if the signal seemed too easy to steal, leading to suspicion of a setup. Which the second manager would know, so...
 * In another baseball example, catcher Carlton Fisk once managed to confuse a batter by talking about how he knew the batter knew the pitcher was ignoring Fisk and only throwing fastballs down the middle, and the pitcher knew Fisk knew the batter knew but wouldn't listen to when Fisk said he was signalling for curveballs (he was actually signalling for fastballs...down the middle). After an epic performance which included Fisk screaming at the pitcher to throw the curveball and going out to the mound, yelling and waving his arms around, the batter was so screwed up trying to figure out who knew what was supposed to happen he could only watch a third strike fastball go right down middle.

Tabletop Games

 * In the Magic The Gathering novel Test of Metal, Jace and Tezzeret play this game, each trying to anticipate the other's moves while knowing the other is doing the same thing and knowing the other knows this.

Theater

 * In Arsenic and Old Lace, the bluffing game regarding which characters know about the murders committed by the other characters reaches truly epic levels.
 * Jonathan Larson's semi-autobiographical musical, tick, tick... BOOM, contains a song called "Therapy". Essentially, the song is a dialogue between two characters detailing how, if they'd known that the other knew what they knew... things would be different. It's really quite brilliant.
 * What makes it even better is that, in the end, the other character is proven right. To make this clearer, "I feel bad that you feel bad about me feeling bad about you feeling bad about what I said about what you said about me not being able to share a feeling." Whatever it was that she said about him not being able to share a feeling was probably accurate; he apparently isn't good at it.

Video Games
"Indigo: ... So, they've decided to set a trap. However, I know that it's a trap, and I must assume that they know I know it's a trap. So really, it's more of an invitation. An invitation to ambush. Shall I send your RSVP?... Oh, and do play along some if you get the chance. That should really help to freak them out."
 * When dealing with conspiratorial spy-types, it's always important to keep track of who knows what, and how they know it. City of Heroes plays with this by having the character knowingly sent into a trap, just to cause confusion among the enemy.

"Subject 1: I know what you're thinking Subject 2: I know that you know what I'm thinking! Subject 1: I know that you know that I know what you're thinking! Subject 2: i know that you know that I know that you know what I'm thinking!"
 * City of Heroes loves this, especially with scanner/newspaper missions. Villains (or heroes) will call out your character for a fight, set an ambush, and attempt to take you down. The fact that you know it's an ambush in no way deters you from walking right into it, but, in spite of insurmountable odds, you always eventually walk out too.
 * The Dinosaur King DS game descends into this sometimes with the hints that opponents give about their next move.
 * From the final mission of the Whiteboard War game Chop Raider: "We're not going to force you to do it, but we know you won't decline."
 * The "ESP Center" wonder from Civilization: Call to Power.

"Boyd: -unless they know we know we know they know, so we won't go! Raz: So... I shouldn't go to the book depository? Boyd: Of course you're going to the book depository!"
 * The new indie game Achron is built upon this trope and time-travel. Every minute or so, a time "wave" occurs so any changes you made to that last big fight will be etched into the game and your opponent will have a chance to fix it or leave it. Or maybe you just pretended to change it, and he sends troops back to fight what he thought you sent back. But then, you did send stuff back, but maybe not to there, so he doesn't know that you know that he knows you sent troops back. Or does he?
 * Fighting gamer and game designer David Sirlin calls it "Yomi Layers" with "I know you know I know" being the third layer. He explains it in-depth in this article.
 * Boyd pulls a variation of this midway through The Milkman Conspiracy, much to Raz's confusion:


 * Frozen Synapse requires players to think like this constantly.
 * This is often done by the players themselves during wifi Pokémon battles. Ha, you've sent out your Gyarados against my Starmie? I'll just use Thunderbolt to exploit your 4x weakness to electricity! But you know I'll do that. So you'll switch in a ground type that will be immune, so I should use Surf. But you know that I know that you know, so you'll leave in Gyarados, letting it soak up the not-very-effective hit in exchange for hitting me with Giga Impact; therefore, I should use Thunderbolt after all. But you know that I know that you know that I know, so you'll switch out, and--
 * Tthe opponent is in the exact same situation because you could Take a Third Option: switch out yourself into say a Grass-type that could handle either Water or Ground (and other options exist, so unless all of the opponent's Pokemon have already been revealed, you never know what may be brought out next).
 * Platform Game: Any type of this game can have this trope come into play with various types of trap like the Pressure Plate trap or Kaizo Trap. One example is in Limbo, which has one a Pressure Plate trap, and then another right after. This leads to the I Know You Know I Know because any semi-competent Genre Savvy gamer is going to go "Well, it's obvious that the 2nd trap is an inverted version of the first... but wait.. if the designer knows that, he'll make the trap the opposite of the inversion, so I should do the same thing I did on the first trap.. but he knows that I know that.." this loops around until the player simply chooses one at random, and likely dies anyway.

Web Animation

 * Red vs. Blue has an example in the final episodes of Revelation: as Washington and co. approach a base known to be inhabited by Tex, he stops the jeep some distance away, pointing out that the open area ahead is the perfect spot for a sniper ambush. Doc asks, since Tex received the same training he did, wouldn't she know he'd know that and plan accordingly? Wash: "You're overthinking it." And then the buried landmines go off.

Web Comics
"Thief: You realize of course this means Fighter is the smartest. Black Mage: I want to cry, but there aren't enough tears."
 * Eight Bit Theater
 * Often happens to Red Mage. This panel shows a prime example.
 * This panel is another great example.

"Quantum Cop: This Quantum Vector Collector will tell us exactly where Quantum Crook is. Quantum Crook: This Quantum Vector Collector Inspector will tell us when my opposite tries to find us. Quantum Cop: To avoid being snooped, I had you add a Quantum Vector Collector Inspector Detector. ... Quantum Cop: Excellent. He's in Mt. Fuji and doesn't know we're coming. Quantum Crook: Excellent. He knows where we are, and thinks we don't know he's coming."
 * Red Mage parodies this trope in this comic to reach the conclusion that he actually knows how to cast Life 3, despite stating in the same sentence the fact that he knows that he can't. Red Mage used Right for the Wrong Reasons, except he should be wrong. But somehow it works.
 * Mr. Square Has a prime example, wherein Mr. Square says, verbatim "I know that you know that I know what you know about knowing that I know, but you don't know that my knowledge of you knowing is not secret, I WANT you to know that I know so you don't know what I don't....you know?" in this comic
 * Casey and Andy does this at one point in an almost Two Scenes, One Dialogue where the two discuss how they'll counteract each other's plans in increasingly complex manners, whether the other knows about the plan or not.

"TAG: I know you know I know. I did not say more because I did not know whether you should know that I know that you know."
 * Schlock Mercenary:

"Vaarsuvius: ...which in turn means that he knew that you would know that, and that you would know that he would know that you knew. Elan: Which means... that I'm totally confused."
 * Subverted in that both participants of the conversation are AIs, and have no problem following this.
 * Employed in Evil, Inc by Evil Atom on 2008-June-12.
 * Squid Ninja shows how to deal with it rationally.
 * The Last Days of Foxhound has a very amusing example in this strip.
 * A later look into his mind shows that Ocelot thinks like this all the time. Raven lampshades it at that point.
 * Happens twice in Irregular Webcomic Here when Adam and Jamie become omniscient, and here when Head Death talks with Head Paradox.
 * The entire point of this Nedroid strip.
 * It was bound to happen, sooner or later, in The Order of the Stick. Vaarsuvius does it in strip #789:

"Doc Scratch: Naturally, the Thief [Vriska] knew this was her intent all along. ... And the Seer [Terezi] knew the Thief knew all this as well. Just another pair of cheaters attempting to play with their cards face up. Amateurs. Each was gambling, not with any vehicle of probability, which had been eliminated from the equation, but with each other's intentions."
 * Homestuck: The duel between Terezi and Vriska in Act 5. Terezi proposes that they flip a coin to decide whether Vriska stays or goes. Both parties realize that Terezi is employing Double-Speak, so "go" really means "die". Both parties know that Vriska can alter probability and make the coin fall on whichever side she wants. Terezi expects Vriska to call her bluff, by making the coin land on "go" and then turning to leave. Vriska does precisely that, expecting that Terezi won't have the stomach to stab her in the back. This is even lampshaded by Doc Scratch, who narrates their fight.

Web Original

 * Used without being named in one of Ayla's Whateley Universe stories, "Ayla and the Network". The ENTIRE plot is various groups having a Gambit Roulette. The winner is the one who can end the "I know you know" game.
 * Experienced players in Mitadake High pull this kind of thing all the time when debating whether or not to give out their PDA Numbers. Unless the host has disabled the computers due to abuse, in which case there's no risk whatsoever.
 * In the party/forum game of Mafia, this is known as "WIFOM logic", stemming from the "Wine In Front Of Me" scene from The Princess Bride. In truth it's a Logical Paradox that yields no useful information.
 * In some of the more complicated Mafia/Werewolf games, this can be a genuine issue. Oftentimes the evil team will have to deliberately and knowingly kill one of their own, because otherwise the good team will not only know that the person is evil, but that the other members of the evil team know that. It's now common knowledge that the evil team will do that, but it's still more effective than the alternative.
 * Mind My Gap: Virgil Horn almost quotes this trope word for word on the loading screen.
 * The Skeptics Guide to the Universe podcast has a regular feature called "Science or Fiction?" in which the host gets his fellow casters to try and determine which of three science news items is fake (two are true). Occasionally he'll throw in one that's so ridiculous that it has to be fake, but the panelists are reluctant to pick it, naming this trope as a reason why.

Western Animation
"Zorak: Maybe that's just what they want us to think! Space Ghost: Hey, you know what? I think that's just what they want us to think! Zorak: I think, that they think, that we think, that that's just what they want us to think! Space Ghost: Brak, what do you think? Brak: I just, I don't even have the slightest idea what you're talking about."
 * Kronk does this in one episode of The Emperors New School. He is faced with a choice of two levers and is instructed to pull the one he wouldn't pick, due to his ineptitude with levers. He does an I Know You Know I Know for a while until Kuzco interrupts by saying "Yeah, this went on for another two hours," and fast-forwards through the whole thing.
 * Done in Foster's Home for Imaginary Friends, where Bloo is setting up a humiliating surprise party for Mac, and all his efforts play right into Bloo's hands, even when he thinks he's doing the opposite of what Bloo thought he'd do.
 * Taken to extremes in the Danger Mouse episode "The Statue of Liberty Caper", where Danger Mouse and Baron Greenback both try to outwit each other with regards to the location of a trapdoor in the floor, leading Danger Mouse to say "I guessed that you'd guess I guessed you guessed I'd guessed you'd guessed and out-guessed your guess, I guess".
 * End's up as something of a Crazy Prepared in that by the time the scene has finished Dangermouse has saved Penfold's Auntie, Penfold (twice) and the famous buildings of the Americas due to utilising the extreme number of guesses to blow up Greenback's shipboard comupter.
 * Kim Possible: Kim and Ron notice that Shego left a far too obvious clue that she had stolen the McGuffin, so clearly she and Drakken were setting up a trap. Unless they wanted them to think it was a trap and avoid it, in which case the way to confound them was to go ahead into it, except it was a "trap-trap": Drakken knew that they knew that Drakken knew that they knew that it was a trap.
 * Played straight (as straight as anything on that show, anyway) on Cartoon Planet during the following conversation about network executives:

"Julien: So you see, we have the crates with the real fish, while yours are filled with only the phony fish cake. So hahaha-ing. Skipper: Oh, nice try, Ringtail. But I know how much you hate the smell of fish. I was expecting a move like that, which is why I switched the crates before you even got back to the zoo. Julien: Ah, but I was expecting you to be expecting that, so we switcheroo-ed the crates on the pier before the fish got loading on to the truck. Haha! Skipper: Doesn't really matter, because I just switched these crates during your last flashback. Julien: Well I switched them while you were saying you switched them. Skipper: And I switched them last the time you blinked. Julien: Yes, but I pretended to switch them so you actually switched them back. Skipper: Oh, but I double switched. Julien: And I triple switched. Skipper: I million zillion switched. Julien: And I switched them to infinity! So you have to shut up a little bit. Skipper: Ah, but what you didn?t see coming is that [pulls off costume] I am actually you!
 * Played awesomely on an episode of Chowder where the title character is trying to stop his Hyde-like Sleep-Eating form from finding the stash of food he hid, thinking about three steps ahead of himself, sadly to no avail.
 * In The Penguins of Madagascar, things get out of hand when Skipper tries to get back real fish instead of the tasteless fish cakes the penguins have been forced to eat. Julien tried to sabotage the operation.

Julien: Okay, nicely played. But if you are me, then by processing of elimination, [also pulls off costume] I must be you!

Skipper: Maybe, maybe. But if you are me, and I am you, then we must both be?"

"Yumi: Are you thinking what I think you're thinking?"
 * An episode of Samurai Jack had Jack and Aku agreeing to a final duel with no swords or special powers. Naturally, Aku cheats, which Jack prepared for by bringing his sword and hiding it. But Aku knew Jack would know that he cheated, and had a minion find the sword. But Jack knew that Aku knew that Jack knew that Aku would cheat, so he planted a decoy sword. But Aku knew that Jack knew that Aku knew that Jack knew that Aku would cheat, so he had his minions look for more swords. But Jack knew that Aku knew that Jack knew that Aku knew that Jack knew that Aku would cheat, so he had his sword.
 * This Hey Arnold! clip.
 * In the Code Lyoko episode "Contact", Odd and Yumi have an instance of this.


 * Used in the Young Justice show. The team is using a former Justice League hideout that was compromised. As explained by Robin; "They know we know they know."
 * The Flintstones has one of these. It's something to the effect of "Even though he knows she knows he knows he knows she knows he *doesn't* know..."

Real Life
"THunt_Goblins: I say stuff to Danielle, then I tweet what I said, then I tell her that I tweeted it and now I'm tweeting that I said I tweeted what I said. THunt_Goblins: And I just told Danielle that I tweeted THAT."
 * A semi-real life example, meaning it's actually an urban myth, is Winston Churchill's Coventry dilemma. Allegedly, Churchill had to allow the city of Coventry to be bombed, to prevent the Nazis from finding out about the British spies in Germany.
 * In reality, the British tried to jam the Germans' radio guidance system, but had to take a guess at the frequency to use. They got it wrong.
 * When Alexander Litvenenko died, some of the speculation on who killed him got to this level. Welcome to the Cold War.
 * CIA chief of counter-intelligence James Jesus Angleton spent the 60s and 70s turning the CIA upside down looking for a KGB mole. Some agents began to suspect that Angelton was a mole, on the grounds that starting a witch-hunt for a KGB mole is exactly the sort of thing a KGB mole would do.
 * Comes up in economic theory, as a result of the tendency of economists to use "rational economic actor" to mean a nigh-omniscient agent who outdoes Spock in terms of rigid logic.
 * 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).
 * There is an active research field known as adversarial reasoning: essentially, building models that allow you to predict the actions of an adversary. Once the adversary happens to get a hold of your model it becomes rather useless, as he can make sure he does something other than what is predicted. So you simply create a new model - one that takes into account the fact that your adversary has the old model that he thinks tells him what you think he is going to do! The eventual end state is left as an exercise for the reader.
 * One classic example from the Second World War: an agent was sent to Great Britain by the Germans, who intended that the British intelligence service capture him and use him as a double agent, at which point he could tell the Germans how British counterintelligence functioned. He proceeded to explain this plan to the Brits, who then had him send back two different sets of reports to Germany. One contained what the Brits wanted the Germans to know; the other contained what the Brits wanted the Germans to think the Brits wanted them to know.
 * During World War II, the allies realized that one could confuse enemy radar by dropping small pieces of aluminum, i.e, chaff, but didn't do this because they were concerned that if they did, the Germans would figure this out. As it turned out the Germans had also discovered this but weren't doing it because of the same logic.
 * Studies of animal intelligence sometimes use this trope as an analogy to model a species' cleverness in social interaction. Humans are the only species known to be able to do five levels of I/you know/think, while great apes seem able to manage four (e.g. they can bluff and be subtle about it so the other ape won't catch wise). Or the apes are far better at it than humans.
 * The Blue-Eyed Islanders puzzle relies on this to an insane level, in that it ultimately depends on.
 * How is there both "no reflective surfaces" and "eye colors"? The liquid in eyes is reflective, just look into someone else's eyes and you'll find out what color it is. Well that was easy, onto the next logic puzzle!
 * Have you ever tried seeing the color of your own eyes in someone else's?
 * In Game Theory, the concept of Nash Equilibrium is a means to overcome this kind of stalemate.
 * The Two Generals' Problem plays with this. Two generals have their armies surrounding a target. Each can send a message to the other saying they're ready to attack, but the other might not get it. They can't just send a message and go, because the other general might not get it and won't know. They can't just wait for the other to respond, because then the second message could be lost, and they won't know the other knows. The end result is that, no matter how many messages are sent, they won't be any more sure than if they just sent one message and hoped it arrive. While this situation is impossible to solve in theory, there's a lot of ground gained there by taking the engineering approach and looking for a solution that will work well in practice.
 * The problem is enhanced by the possibility that the defenders may be intercepting and corrupting messages. If it's merely a question of messages getting through, sensible organisation should only require a couple of confirmations before further messages become irrelevant.
 * More specifically, the practical solution is to evaluate the probability of success of a single message transmission, and to then repeat the transmission until the probability of failure has been reduced to a calibrated trivial percentage (say the message has a 1/10 chance of failing, then after sending it once you can be 90% sure that both generals have heard the message, after the first response it's up to 99%, then you might want to send a third one to bring it up to 99.9%, then stop if you can live with a one in a thousand chance of failure, or keep going if you can't).
 * The best solution is for the second general to fire a flare above the city to signify having received the first message.
 * How about agreeing on a series of colored flares: the first general sends up a flare (say, red) meaning that he's ready to attack, and the second responds with the same color to indicate that he will attack as well. Stealth is an issue, but...
 * Courtesy of Tarol Hunt of Goblins fame, we have the following two tweets: