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A further extension of the KKMS theorem
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Kannai, Yakar and Wooders, Myrna Holtz (1999) A further extension of the KKMS theorem. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.538).
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Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...
Abstract
Recently Reny and Wooders ([23]) showed that there is some point in the intersection of sets in Shapley's ([24]) generalization of the Knaster-Kuratowski-Mazurkiwicz Theorem with the property that the collection of all sets containing that point is partnered as well as balanced. In this paper we provide a further extension by showing that the collection of all such sets can be chosen to be strictly balanced, implying the Reny-Wooders result. Our proof is topological, based on the Eilenberg-Montgomery fixed point Theorem. Reny and Wooders ([23]) also show that if the collection of partnered points in the intersection is countable, then at least one of them is minimally partnered. Applying degree theory for correspondences, we show that if this collection is only assumed to be zero dimensional (or if the set of partnered and strictly balanced points is of dimension zero), then there is at least one strictly balanced and minimally partnered point in the intersection. The approach presented in this paper sheds a new geometric-topological light on the Reny-Wooders results.
| Item Type: | Working or Discussion Paper (Working Paper) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Social Sciences > Economics | ||||
| Library of Congress Subject Headings (LCSH): | Set theory, Topological degree, Algebraic topology, Equilibrium (Economics) | ||||
| Series Name: | Warwick economic research papers | ||||
| Publisher: | University of Warwick, Department of Economics | ||||
| Place of Publication: | Coventry | ||||
| Official Date: | September 1999 | ||||
| Dates: |
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| Number: | No.538 | ||||
| Number of Pages: | 22 | ||||
| Status: | Not Peer Reviewed | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Funder: | Natural Sciences and Engineering Research Council of Canada (NSERC) |
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