Generalized KKM theorem, minimax inequalities and their applications
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).
|Date of creation:||1994|
|Date of revision:|
|Publication status:||Published in Journal of Optimization Theory and Applications 2.83(1994): pp. 375-389|
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Web page: https://mpra.ub.uni-muenchen.de
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- Wayne Shafer & Hugo Sonnenschein, 1974.
"Equilibrium in Abstract Economies Without Ordered Preferences,"
94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
- Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
- Tian, Guoqiang, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 949-58, October.
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