Initial Knowledge and Announced Posteriors in the Posterior Communication Process

概要

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We investigate the communication process where a group of players with common prior and different private information announce repeatedly their posteriors of an event. We examine the relationship between the posteriors announced in this communication process and the players' knowledge of others' posteriors at the beginning of the process. That players' knowledge is described in terms of the initial knowledge which specifies both the players' posteriors and who knows that who knows that ... that who knows whose posterior. For each initial knowledge, a measure is defined over the class of the events which satisfy that initial knowledge requirement. We show that the class of all the initial knowledge is divided into two types: For one type of initial knowledge, an identical sequence of posteriors is announced in the process for almost all the events which satisfy that initial knowledge requirement; For the other type of initial knowledge, every set of the events which satisfy that initial knowledge requirement and for which an identical sequence of the posteriors is announced in the process is measure zero.
静岡県立大学の論文