Generalized KKM theorem, minimax inequalities and their applications

Guoqiang Tian

MPRA Paper from University Library of Munich, Germany

Abstract: This paper extends the well-known KKM theorem and variational inequalities by relaxing the closedness of values of a correspondence and lower semicontinuity of a function. The approach adopted is based on Michael's continuous selection theorem. As applications, we provide theorems for the existence of maximum elements of a binary relation, a price equilibrium, and the complementarity problem. Thus our theorems, which do not require the openness of lower sections of the preference correspondences and the lower semicontinuity of the excess demand functions, generalize many of the existence theorems such as those in Sonnenschein (Ref. 1), Yannelis and Prabhakar (Ref. 2), and Border (Ref. 3).

Keywords: KKM theorem; Variational inequalities; Complementarity problem; Price equilibrium; Maximal elements; Binary relations (search for similar items in EconPapers)
JEL-codes: D63 (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (6)

Published in Journal of Optimization Theory and Applications 2.83(1994): pp. 375-389

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:41217

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