Upper Semicontinuous Extensions of Binary Relations
AbstractSuzumura 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.
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Bibliographic InfoPaper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-01.
Length: 16 pages
Date of creation: 2002
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extensions; uer semicontinuity; consistency;
Other versions of this item:
- Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Upper semicontinuous extensions of binary relations," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 231-246, May.
- Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2002. "Upper Semicontinuous Extensions of Binary Relations," Discussion Paper Series a423, Institute of Economic Research, Hitotsubashi University.
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-06-04 (All new papers)
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