The Yannelis-Prabhakar Theorem on Upper Semi-Continuous Selections in Paracompact Spaces: Extensions and Applications

M. Khan and Metin Uyanık

Papers from arXiv.org

Abstract: In a 1983 paper, Yannelis-Prabhakar rely on Michael's selection theorem to guarantee a continuous selection in the context of the existence of maximal elements and equilibria in abstract economies. In this tribute to Nicholas Yannelis, we root this paper in Chapter II of Yannelis' 1983 Rochester Ph.D. dissertation, and identify its pioneering application of the paracompactness condition to current and ongoing work of Yannelis and his co-authors, and to mathematical economics more generally. We move beyond the literature to provide a necessary and sufficient condition for upper semi-continuous local and global selections of correspondences, and to provide application to five domains of Yannelis' interests: Berge's maximum theorem, the Gale-Nikaido-Debreu lemma, the Gale-McKenzie survival assumption, Shafer's non-transitive setting, and the Anderson-Khan-Rashid approximate existence theorem. The last resonates with Chapter VI of the Yannelis' dissertation.

Date: 2020-06
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Economic Theory, 2021

Downloads: (external link)
http://arxiv.org/pdf/2006.16681 Latest version (application/pdf)

Related works:
Journal Article: The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications (2021)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2006.16681

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().