Language and Common Knowledge

Last time's discussion veered off onto the fertile lands of Game theory. Let's explore it further. Perhaps you've read a book like Strategy of Conflict (http://www.amazon.com/The-Strategy-Conflict-Thomas-Schelling/dp/0674840313) by Thomas Schelling? Or a blog post on LW such as Game Theory As A Dark Art (http://lesswrong.com/lw/dr9/game_theory_as_a_dark_art/).

I am intending this meetup to be a broad and open-ended discussion, with little to no maths, and concerning topics like conflict, cooperation, mechanism design, stable strategy.

I am especially interested in Common Knowledge. I quote fromScott Aaronson (http://www.scottaaronson.com/blog/?p=2410), who quotes from Steven Pinker:

"But seriously, let me give you an example I stole from Steven Pinker, from his wonderful book The Stuff of Thought (http://www.amazon.com/The-Stuff-Thought-Language-Window/dp/0143114247). Two people of indeterminate gender—let’s not make any assumptions here—go on a date. Afterward, one of them says to the other: “Would you like to come up to my apartment to see my etchings?” The other says, “Sure, I’d love to see them.” [...]

In our case, the puzzle is this: both people on the date know perfectly well that the reason they’re going up to the apartment has nothing to do with etchings. They probably even both know the other knows that. But if that’s the case, then why don’t they just blurt it out: “would you like to come up for some intercourse?” (Or “fluid transfer,” as the John Nash character put it in the Beautiful Mind movie?)

So here’s Pinker’s answer. Yes, both people know why they’re going to the apartment, but they also want to avoid their knowledge becoming common knowledge. They want plausible deniability. There are several possible reasons: to preserve the romantic fantasy of being “swept off one’s feet.” To provide a face-saving way to back out later, should one of them change their mind: since nothing was ever openly said, there’s no agreement to abrogate. In fact, even if only one of the people (say A) might care about such things, if the other person (say B) thinks there’s any chance A cares, B will also have an interest in avoiding common knowledge, for A’s sake.

Scott Aaronson continues:

"I think that a large fraction of the infamous social difficulties that nerds have, is simply down to nerds spending so much time in domains (like math and science) where the point is to struggle with every last neuron to make everything common knowledge, to make all truths as clear and explicit as possible. Whereas in social contexts, very often you’re managing a delicate epistemic balance where you need certain things to be known, but not known to be known, and so forth—where you need to prevent common knowledge from arising, at least temporarily. "

• When is it useful for something to not become common knowledge?

• How has language evolved to facilitate common knowledge or -ignorance?