"I know this" is different from "I know you know this", which is different from "You know I know this", which is still different from "you know I know you know this"
"I know this" is different from "I know you know this", which is different from "You know I know this", which is still different from "you know I know you know this"
Indeed. See https://en.wikipedia.org/wiki/Common_knowledge_(logic)
“When everybody knows that everybody knows” by Steven Pinker is about this.