Conditional Beliefs and Higher-Order Preferences

In this paper, we provide the Bayesian foundations of type structures--—such as those used for epistemic analysis of iterated admissibility by Brandenburger et al. (2008)--—in which beliefs are LPS’s (lexicographic probability systems) rather than standard probability measures as in Mertens and Zamir (1985). This turns out to be a setting in which the distinction between preference hierarchies (Epstein and Wang, 1996) and belief hierarchies is meaningful and the former has conceptual advantages. In particular, using preference hierarchies allows us to identify conditions under which the distinction between LPS beliefs about types and LCPS (lexicographic conditional probability system) beliefs about types is a meaningful one. Furthermore, we construct “universal” LPS/LCPS type structures and find that they describe the same finite-order preferences even though the universal LPS type structure describes more hierarchies. Finally, we give an epistemic condition for iterated admissibility using coherent hierarchies that cannot be types.