Hierarchies of conditional beliefs derived from commonly known priors

In this paper, we consider a finite set of agents with commonly known full-support priors on the fundamental space of uncertainty. Then, we show that if the hierarchies of conditional beliefs á la Battigalli and Siniscalchi (1999) are derived from these priors, then all types of the same agent yield the same hierarchy. We also show that the previous result does not necessarily hold when the priors are not full-support. Moreover, if the collections of conditioning events does not cover the underlying space of uncertainty, there are always commonly known (non-full-support) priors such that every agent''s conditional belief hierarchies are derived from these priors.