Abstract
The actions that individuals take depend on common knowledge among individuals. We set this connection in a framework of fuzzy events on a sigma field over a set of sample points. If we identify a set in a sigma field with its characteristic function, then events in the usual sense of probability theory are also fuzzy events. We give a new definition of a partition of fuzzy events making it possible to pursue the theorems which are extensions of the agreement theorems. These theorems are of some interest in areas in which people's beliefs about each other's beliefs are of importance, such as financial markets theory. Moreover, the significance of our formal system for economics is that the theory stresses the inability of a person to discriminate clearly between an event and its negation. A theory with such an emphasis might be found useful by researches studying “incomplete contracts”. By means of examples, guidance is provided regarding the significance of the theory for finance.
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