Knowledge and common knowledge in a distributed environment
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
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People, no matter how rational they are, usually act on the basis of incomplete information. If they are rational they recognize their own ignorance and reflect carefully on what they know and what they do not know, before choosing how to act. Furthermore, when rational agents interact, they also think about what the others know, and what the others know about what they know, before choosing how to act. Failing to do so can be disastrous. When the notorious evil genius Professor Moriarty confronts Sherlock Holmes for the first time he shows his ability to think interactively by remarking that "all I have to say has already crossed your mind"; Holmes, even more adept at that kind of thinking responds "then possibly my answer has crossed yours." On account of Moriarty's limited mastery of interactive epistemology, he let Holmes and Watson escape from the train at Canterbury, a mistake which ultimately led to his death, because he himself went on to Paris after calculating that Holmes would normally go on to Paris, failing to deduce that Holmes had deduced that he would deduce what Holmes would normally do and in this circumstance get off earlier.