Common knowledge

There is a distinction between mutual knowledge and common knowledge.

• Mutual knowledge: knowledge that everyone knows.

• Common knowledge: not only knowledge that everyone knows, but something that everyone knows that everyone else knows (and that everyone knows that everyone else knows that everyone else knows, and so forth).

The answer to the seeming paradox of the blue-eyed islander puzzle (the visitor didn't seem to reveal new information yet caused a chain of events to happen) is that the visitor did bring new knowledge. "There is at least one blue-eyed islander" went from being mutual knowledge to common knowledge.

Links

• https://xkcd.com/blue_eyes.html

• https://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/

• https://terrytao.wordpress.com/2011/05/19/epistemic-logic-temporal-epistemic-logic-and-the-blue-eyed-islander-puzzle-lower-bound/