Theoretical Economics, Volume 6, Number 2 (May 2011)

Theoretical Economics 6 (2011), 269–287

Agreeing to agree

Ehud Lehrer, Dov Samet


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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