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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 KnasterKuratowskiMazurkiwicz 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 RenyWooders result. Our proof is topological, based on the EilenbergMontgomery 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 geometrictopological light on the RenyWooders 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 
Number:  No.538 
Number of Pages:  22 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Funder:  Natural Sciences and Engineering Research Council of Canada (NSERC) 
References:  [1] Albers, W. (1979) \Core and kernel variants based on imputations and demand profiles" in Game Theory and Related Topics, O. Moeschlin and D. Pallaschke, eds. North Holland, Amsterdam. 
URI:  http://wrap.warwick.ac.uk/id/eprint/1637 
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