Munich Personal RePEc Archive

Generalizations of the FKKM Theorem and Ky-Fan Minimax Inequality, with Applications to Maximal Elements, Price Equilibrium, and Complementarity

Tian, Guoqiang (1990): Generalizations of the FKKM Theorem and Ky-Fan Minimax Inequality, with Applications to Maximal Elements, Price Equilibrium, and Complementarity. Published in: Journal of Mathematical Analysis and Applications , Vol. 170, (1992): pp. 457-471.

[img]
Preview
PDF
MPRA_paper_41225.pdf

Download (735kB) | Preview

Abstract

This paper generalizes the Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem of Ky Fan (“Game Theory and Related Topics,” pp. 151–156, North-Holland, Amsterdam, 1979; and Math. Ann.266, 1984, 519–537) and the Ky Fan minimax inequality by introducing a class of the generalized closedness and continuity conditions, which are called the transfer closedness and transfer continuities. We then apply these results to prove the existence of maximal elements of binary relations under very weak assumptions. We also prove the existence of price equilibrium and the complementarity problem without the continuity assumptions. Thus our results generalize many of the existence theorems in the literature.

UB_LMU-Logo
MPRA is a RePEc service hosted by
the Munich University Library in Germany.