Conditional Beliefs and Higher-Order Preferences

Byung Soo Lee

MPRA Paper from University Library of Munich, Germany

Abstract: In this paper, we establish the Bayesian foundations of type structures in which beliefs are lexicographic probability systems (LPS’s)—such as those used in Brandenburger et al. (2008)—rather than standard probability measures as in Mertens and Zamir (1985). This is a setting which the distinction between preferences hierarchies (Epstein and Wang, 1996) and beliefs hierarchies is meaningful and the former has conceptual advantages. Type structures in which beliefs are conditional probability systems (CPS’s) are found to describe fewer hierarchies than LPS type structures can if a nonredundancy requirement is imposed. The two families of type structures are found to be capable of describing the same set of hierarchies in the absence of such a requirement. The existence of “largest”—a notion closely related to universality—LPS/CPS type structures is also shown. Finally, we find that some coherent hierarchies cannot be types but those hierarchies may be needed to express epistemic conditions for iterated elimination of weakly dominated strategies.

Keywords: Preferences hierarchies; type structure; weakly dominated strategies; epistemic game theory; lexicographic probability system; conditional probability system (search for similar items in EconPapers)
JEL-codes: C72 D8 D80 (search for similar items in EconPapers)
Date: 2013-07-17
New Economics Papers: this item is included in nep-gth, nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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