Sizing up other investors is more than a matter of psychology. New logical notions are needed as well. One of them, "common knowledge", due originally to the economist Robert Aumann, is crucial to understanding the complexity of the stock market and the importance of transparency. A bit of information is common knowledge among a group of people if all prties 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 others' knowledge.

As I'll discuss later, this notion of common knowledge is essential to seeing how "subterranean information processing" often underlies sudden bubbles or crashes in the markets, changes that are precipitated by nothing at all and therefore are almost impossible to foresee. -- John Allen Paulos in A Mathematician Plays the Market