Common Knowledge and Game Theory

Abstract

Perhaps the most important area in which common knowledge problems arise is in the study of rational expectations equilibria in the trading of risky securities. How can there be trade if everybody's willingness to trade means that everybody knows that everybody expects to be a winner? (see Milgrom/Stokey [1982] and Geanakoplos [1988].) Since risky securities are traded on the basis of private information, there must presumably be some "agreeing to disagree" in the real world. But to assess its extent and its implications, one needs to have a precise theory of the norm from wich "agreeing to disagree" is seen as a deviation. The beginnings of such a theory are presented here. Some formalism is necessary in such a presentation because the English language is not geared up to express the appropriate ideas compactly. Without some formalism, it is therefore very easy to get confused. However, nothing requiring any mathematical expertise is to be described.