Conditional Beliefs and Higher-Order Preferences
AbstractIn 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 48551.
Date of creation: 17 Jul 2013
Date of revision:
Preferences hierarchies; type structure; weakly dominated strategies; epistemic game theory; lexicographic probability system; conditional probability system;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D8 - Microeconomics - - Information, Knowledge, and Uncertainty
- D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-07-28 (All new papers)
- NEP-GTH-2013-07-28 (Game Theory)
- NEP-MIC-2013-07-28 (Microeconomics)
- NEP-UPT-2013-07-28 (Utility Models & Prospect Theory)
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