John Allen Paulos in his Who’s Counting column at ABC News:
A bit of information is “common knowledge” among a group of people if all parties know it, know that the others know it, know that the others know they know it, and so on. It is much more than “mutual knowledge,” which requires only that the parties know the particular bit of information, not that they be aware of the others’ knowledge. As Aumann showed, one can prove a theorem that can be roughly paraphrased as follows: Two individuals cannot forever agree to disagree. As their beliefs, formed in rational response to different bits of private information, gradually become common knowledge, their beliefs change and eventually coincide.
Very abstract stuff, but there is an interesting example that demonstrates how the notion might enable us to explain sudden bubbles or sudden crashes in stock markets. These changes, which sometimes seem to be precipitated by nothing at all, might be the result of “subterranean information processing.”
More here.
