 Epistemic equivalence of extended belief hierarchiesElias Tsakas Games and Economic Behavior, 2014, vol. 86, issue C, 126-144 Abstract: In this paper, we introduce a notion of epistemic equivalence between hierarchies of conditional beliefs and hierarchies of lexicographic beliefs, thus extending the standard equivalence results of Halpern (2010) and Brandenburger et al. (2007) to an interactive setting, and we show that there is a Borel surjective function, mapping each conditional belief hierarchy to its epistemically equivalent lexicographic belief hierarchy. Then, using our equivalence result we construct a terminal type space model for lexicographic belief hierarchies. Finally, we show that whenever we restrict attention to full-support beliefs, epistemic equivalence between a lexicographic belief hierarchy and a conditional belief hierarchy implies that an arbitrary Borel event is commonly assumed under the lexicographic belief hierarchy if and only if it is commonly strongly believed under the conditional belief hierarchy. This is the first result in the literature directly linking common assumption in rationality (Brandenburger et al., 2008) with common strong belief in rationality (Battigalli and Siniscalchi, 2002). Keywords: Epistemic game theory; Conditional belief hierarchies; Lexicographic belief hierarchies; Type spaces; Epistemic equivalence; Common strong belief; Common assumption (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:86:y:2014:i:c:p:126-144 DOI: 10.1016/j.geb.2014.03.008 Access Statistics for this article Games and Economic Behavior is currently edited by E. Kalai More articles in Games and Economic Behavior from Elsevier |
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