Agreeing to agree

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,: School of Mathematical Sciences, Tel Aviv University
,: Faculty of Management, Tel Aviv University
Authors registered in the RePEc Author Service: Dov Samet

Theoretical Economics, 2011, vol. 6, issue 2

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 (search for similar items in EconPapers)
JEL-codes: C70 D82 (search for similar items in EconPapers)
Date: 2011-05-03
References: Add references at CitEc
Citations: View citations in EconPapers (11)

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Working Paper: Agreeing to agree (2003)
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