Three results on communication, information and common knowledge

Abstract

I extend the results on communication, information and common knowledge by proving the following : 1. If n individuals with partitional information structures communicate their posterior probabilities of an event sequentially, one to one at a time, according to a scheme whim never excludes anyone permanently, and they revise in a nonmyopic way, then they eventually reach common knowledge. 2. If n individuals with partitional information structures form posterior probabilities of a given event and the minimum of their posteriors is common knowledge as well as the number of times it is attained then all posteriors must be equal. 3. Balancedness, the property of non-partitional information structures necessary and sufficient to prevent "Agreeing to Disagree", is in fact a very unrestrictive requirement. A new property, subnestedness, implies balancedness.