Glossary of game theory terms.

Common Knowledge

An item of information in a game is common knowledge if all of the players know it (it is mutual knowledge) and all of the players know that all other players know it and all other players know that all other players know that all other players know it, and so on. This is much more than simply saying that something is known by all, but also implies that the fact that it is known is also known by all, etc. Consider a simple example of two allied armies situated on opposite hilltops waiting to attack their foe. Neither commander will attack unless he is sure that the other will attack at exactly the same time. The first commander sends a messenger to the other hilltop with the message "I plan to attack in the morning." The messenger's journey is perilous and he may die on the way to delivering the message. If he gets to the other hilltop and informs the other commander - can we be certain that both will attack in the morning? Note that both commanders now know the message, but the first cannot be sure that the second got the message. Thus, common knowledge implies not only that both know some piece of information, but can also be absolutely confident that the rest no it, and that the rest know that we know it, and so on.

updated 22 August 2006