I Know You Know I Know: Difference between revisions

{{trope}}

 

 

* 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 [[Gambit Pileup|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.

* 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 [[Alternate Character Interpretation|far better at it]] than humans.

* The [http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/ Blue-Eyed Islanders puzzle] relies on this to an insane level, in that it ultimately depends on {{spoiler|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}}.

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