Aumann has shown that agents who have a common prior cannot have common knowledge of their posteriors for event $E$ if … common knowledge that the posteriors for $E$ \emph{do} coincide? We show that a necessary and sufficient condition for this … is the existence of a nonempty \emph{finite} event $F$ with the following two properties. First, it is common knowledge …

(statistically) disassociated from each other and how are such disassociations reflected in the agents’ knowledge structure … disassociation under common knowledge (the agents’ types are independent, conditional on some common-knowledge variable). Subjective … that disassociates types is more informative than any common-knowledge variable. With three or more agents, conditions (i …

desired coordination of actions even when a high order of mutual knowledge of payoff functions obtains. We want to make … explicit the role of knowledge about rationality of players, not only that of payoff functions. For this purpose, we use an … embedding belief systems, it is necessary that the upper bound order of mutual knowledge of payoff functions exceeds the upper …