Common knowledge

A long time ago I blogged about the notion of common knowledge in game theory. Yesterday, over at the Cheap Talk blog, Jeff Ely put up a post with an interesting problem that hinges on the concept (Cheap Talk is a good blog for lovers of game theory):

Two generals, you and me, have to coordinate an attack on the enemy.  An attack will succeed only if we both attack at the same time and if the enemy is vulnerable.

From my position I can directly observe whether the enemy is vulnerable.  You on the other hand must send a scout and he will return at some random time. We agree that once you learn that the enemy is vulnerable, you will send a pigeon to me confirming that an attack should commence.  It will take your pigeon either one day or two to complete the trip.

Suppose that indeed the enemy is vulnerable, I observe that is the case, and on day n your pigeon arrives informing me that you know it too.  I am supposed to attack.  But will I?

Go to Cheap Talk to find out.

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