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.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Generalizations of the FKKM Theorem and Ky-Fan Minimax Inequality, with Applications to Maximal Elements, Price Equilibrium, and Complementarity|
|Keywords:||FKKM Theorem; Inequality; Maximal Elements; Price Equilibrium; Complementarity|
|Subjects:||D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement|
|Depositing User:||Guoqiang Tian|
|Date Deposited:||13. Sep 2012 18:35|
|Last Modified:||14. Feb 2013 10:17|
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