Agreeing to Agree or Why We Cannot Agree on the Odds that Your Firm is More Profitable than Mine
20 Pages Posted: 18 Jul 2004
Date Written: September 2003
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 do coincide? A necessary and sufficient condition for this is the existence of a nonempty finite event F with the following two properties. First, it is common knowledge at F that the agents cannot tell whether or not E. Second, this still holds true at F, when F becomes common knowledge.
Keywords: Agreement theorem, common knowledge
JEL Classification: D82, D70
Suggested Citation: Suggested Citation