SUMMARY OF "ON AUMANN'S NOTION OF COMMON KNOWLEDGE- AN ALTERNATIVE APPROACH"

We provide a bayesian model of knowledge which is based on the of infinite recursion of beliefs. The framework allows a direct formalisation of statements such as "everyone knows that (everyone knows) m that an event A has occurred " and "A is common knowledge". An important and novel feature of our approach is that we explicitly formalise the statement "the information partitions are common knowledge" when we demonstrate the equivalence of our approach to the seminal contribution of Professor Aumann. This allows us to circumvent the self-reference which exists in that definition. The main theorem of the paper shows that given an Aumann structure, there exists a structure in the infinite recursion such that an event is common knowledge in the sense of Aumann if and only if it is common knowledge in our sense