Formulation of Incomplete Information and Redundant Type Structure

A type structure is non-redundant if no two types of a player represent the same hierarchy of belief over the given set of basic uncertainties, and it is redundant otherwise. Under a mild assumption (which is both necessary and su¢ cient), we show that any redundant structure can be identi…ed with a non-redundant structure with an extended space of basic uncertainties. The belief hierarchies induced by the latter non-redundant structure, when “marginalized” onto the partial space of basic uncertainties, coincide with the hierarchies induced by the former structure. We argue that the analyst must make use of a non-redundant structure unless he believes that he misspeci…ed the players’space of basic uncertainties, and redundant structures can provide di¤erent equilibrium predictions only in so far as they re‡ect the idea that there are hidden uncertainties entertained by players but unspeci…ed by the analyst. JEL classi…cation: C72, D80, D82.