Is there a limit to the sequence "I know that you know that I know..."?
Consider this hypothetical example. A and B are spies on opposing sides. B gets hold of some secret information about A’s side. B will be trying to deliver this information to his side.
1. B knows
A finds out that B has the information. A need not know the details of the information. A knows enough to try to stop B.
2. A knows that B knows.
B finds out that A is going after him, and will keep track of A’s whereabouts and try to stay away.
3. B knows that A knows that B knows.
It seems that each extra level of knowledge has diminishing impact. At this point, I am not sure if it makes much difference if A knows that B knows that A knows that B knows. Do you think this is the general case?
Consider the case where A tells something to B. Can we assume all levels of A knows that B knows that…?