Common Knowledge

(noun) something known by most people

"Some of you have blue eyes."

Nothing Happens

All the
blue-eyed people leave the island!

In four days, all the blue-eyed people leave the island!

Common Knowledge

There is common knowledge of p in a group of agents G when

• all the agents in G know p
• they all know that they know p
• they all know that they all know that they know p
• and so on ad infinitum.

Induction

We know something at time t.

We can say something about time t+1.

What did the islanders deduce?