Upper Semicontinuous Extensions of Binary Relations

Walter Bossert (), Y. Sprumont and Kotaro Suzumura ()

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: Suzumura shows that a binary relation has a weak order extension if and only if it is consistent. However, consistency is demonstrably not sufficient to extend an upper semi-continuous binary relation to an upper semicontinuous weak order. Jaffray proves that any asymmetric (or reflexive), transitive and upper semicontinuous binary relation has an upper semicontinuous strict (or weak) order extension. We provide sufficient conditions for existence of upper semicontinuous extensions of consistence rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, we prove one theorem using a further consistency property and another with an additional continuity requirement.

Keywords: Extensions; upper semicontinuity; consistency (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Date: 2002
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Related works:
Working Paper: Upper Semicontinuous Extensions of Binary Relations (2002)
Working Paper: Upper Semicontinuous Extensions of Binary Relations (2002)
Journal Article: Upper semicontinuous extensions of binary relations (2002)
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