Theoretical Economics 6 (2011), 269–287

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### Agreeing to agree

*Ehud Lehrer, Dov Samet*

#### Abstract

Aumann has shown that agents who have a common prior cannot
have common knowledge of their posteriors for event $E$ if these
posteriors do not coincide. But given an event $E$, can the agents
have posteriors with a common prior such that it is 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 at $F$ that the
agents cannot tell whether or not $E$ occurred. Second, this still
holds true at $F$, when $F$ itself becomes common knowledge.

Keywords: Agreeing theorem, common knowledge, common prior, no trade theorem

JEL classification: C70, D82

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