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

DOI:
https://doi.org/10.1090/S0002-9939-1994-1211591-2

MathSciNet review:
1211591

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1211591-2

Keywords:
Compactly open,
open graph,
closed graph,
lower semicontinuous,
upper semicontinuous,
class ,
-majorant,
-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