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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Approximation method and equilibria of abstract economies

Authors: Kok-Keong Tan and Xian-Zhi Yuan
Journal: Proc. Amer. Math. Soc. 122 (1994), 503-510
MSC: Primary 90A14; Secondary 47N10
MathSciNet review: 1211591
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Abstract: By applying an equilibrium existence theorem for a qualitative game due to Ding and Tan and by employing an "approximation" method used by Tulcea, we obtain an equilibrium existence theorem for an abstract economy (generalized game) in which the constraint correspondences are not assumed to have open graphs nor open lower sections (which are generally assumed in the literature). Our result generalizes the corresponding results of Shafer and Sonnenschein (1975), Borglin and Keiding (1976), Yannelis and Prabhakar (1983), Tulcea (1986), and Chang (1990) in several ways.

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PII: S 0002-9939(1994)1211591-2
Keywords: Compactly open, open graph, closed graph, lower semicontinuous, upper semicontinuous, class $ L_C$, $ L_C$-majorant, $ L_C$-majorized, one-person game, qualitative game, generalized game, abstract economy, equilibrium point, paracompact, topological vector space, locally convex space
Article copyright: © Copyright 1994 American Mathematical Society