Not sure if this is the right place for this question but here goes...
Some time in the past I've stumbled upon some site/article/post/etc that discussed the issue of 2 parties having (or not) some information and being aware of the other party knowing it. Something like:
A: knows X
B: knows that A knows X
A: knows that B knows that A knows X
and so on...
Now in the source I've seen there was a statement that with enough of those "cycles" (like 4 or 5 maybe?) both parties have like a perfect knowledge of the situation - they know and they're aware that the other party knows and so on... So this doesn't (need to) go infinitely, at some point everyone is aware of everything. Apparently, it's a known problem and there's already been some work/reasoning devoted to it.
Unfortunately, I wasn't able to find anything on the internet that concerned this topic and I'm curious. So my question is: has anyone ever heard about something like this? Does this problem have an established name? Can you point me to any articles/sources of information? I'd appreciate it.