Perhaps even more confusing than the iterative reasoning of common knowledge is the idea reflected in the following scene. If a player is only boundedly rational, and thinks a limited number steps ahead, can we iterate the "I know how many steps ahead you know" reasoning, too? Rick Daley explains the set up for the scene:

"Captain Amazing is losing his sponsors (notably Pepsi) because he can't find any more good fights. So, he decides to sponsor the parole of one of his worst enemies, Casanova Frankenstein, who has spent the last 20 years in an insane asylum. The first thing Casanova does is blow up the asylum. Captain Amazing shows up moments later."

CF: Captain Amazing! What a surprise!
CA: Really? I'm not so sure about that. Your first night of freedom and you blow up the asylum. Interesting choice. I knew you couldn't change.
CF: I knew you'd know that.
CA: Oh, I know that, and I knew you'd know I know you knew.
CF: But I didn't. I only knew you'd know that I knew. Did you know that?
CA: Of course.