Malcolm Gladwell's article this past May examined the "I-know-they-know-I-know-they-know" regress as it relates to spying and national intelligence. If country X knows that country Y is intercepting their communications, isn't country X likely to communicate intentionally wrong information? It's an interesting read.
On a more personal level, social situations where I know the other person knows something about me but they are not aware that I know that they know, or variations thereof, are always intriguing and challenging. Interactions bulging with meta data.
Andre Aciman, in a long, interesting essay in The American Scholar, touches on similar themes when, as an aside, he talks about his favorite French novels which have sentences or paragraphs like:
Her lover knew, by the way she showed every conceivable proof of love for him, that she was determined to say no to him.
Her future husband could tell, by the way she blushed whenever they were alone together, that she felt neither love, nor passion, nor desire for him; her blushes came from exaggerated modesty, which in her coy, girlish way she was pleased to mistake for love. The very means meant to conceal her blushes is precisely what gave them away. Her husband guessed by how happy his wife was when she heard that their friend was not going to join them on their trip to Spain that he was the one with whom she’d have betrayed him if only she had the courage.
The frown with which she seemed to dismiss the man she wished she didn’t love told him everything he longed to know. Even the abrupt, rude manner with which she snapped at him as soon as they were alone was a good sign: she was more in love with him than he had ever hoped.
I thought that if anything could rekindle your feelings for me, it was to let you see that mine too had changed, but to let you see this by feigning to wish to conceal it from you, as if I lacked the courage to acknowledge it to you.