On approximate decentralization of Pareto optimal allocations in locally convex spaces
type: Item
instance of: scholarly article
title: On approximate decentralization of Pareto optimal allocations in locally convex spaces
zbMATH Open document ID: 0645.90008
DOI: 10.1016/0021-9045(88)90054-8
author: M. Ali Khan
author: Rajiv Vohra
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: Extending the second fundamental theorem of welfare economics to economies with a topological vector space of commodities \textit{G. Debreu} [Proc. Nat. Acad. Sci. USA 40, 588-592 (1954; Zbl 0055.380)], supposed that the aggregate production set is a convex set with nonempty interior and applied then the supporting hyperplane theorem. The authors extend this result, renouncing the interiority assumption and replacing it by some weak closure (Choquet condition), local compactness (Dieudonné condition) and order conditions. The main idea of the paper is to find an approximate support (\(\epsilon\)-support) to the closure of a convex set with empty interior which enables the authors to find an approximate version of the Debreu result (an exact result is also included). The paper uses in an essential way recent results in functional analysis obtained by G. Choquet, J. Dieudonné, Ky Fan, E. Bishop and R. R. Phelps.
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 46A03
zbMATH DE Number: 4053301
zbMATH Keywords: Pareto optimal allocations
zbMATH Keywords: locally convex spaces
zbMATH Keywords: welfare economics
zbMATH Keywords: topological vector space of commodities
zbMATH Keywords: Choquet condition
zbMATH Keywords: approximate support
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90054-8
OpenAlex ID: W2080911211
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description: scientific article; zbMATH DE number 4053301