Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2002-02-06
Number: 02-009/4
Author-Name: J.B.G. Frenk
Author-Email: frenk@few.eur.nl
Author-Workplace-Name: Econometric Institute, Faculty of Economics, Erasmus University Rotterdam, and Tinbergen Institute
Author-Name: G. Kassay
Author-Workplace-Name: Department of Mathematics, Babes Bolyai University, Cluj
Author-Name: J. Kolumbán
Author-Workplace-Name: Department of Mathematics, Babes Bolyai University, Cluj
Title: Equivalent Results in MinimaxTheory
Abstract: In this paper we review known minimax results with applications in game theory and showthat these results are easy consequences of the first minimax result for a two person zero sumgame with finite strategy sets published by von Neumann in 1928. Among these results are thewell known minimax theorems of Wald, Ville and Kneser and their generalizations due to Kakutani,Ky-Fan. Konig. Neumann and Gwinner-Oettli. Actually it is shown that these results form anequivalent chain and this chain includes the strong separation result in finite dimensional spacesbetween two disjoint closed convex sets of which one is compact. To show these implicationsthe authors only use simple properties of compact sets and the well-known Weierstrass Lebesgue lemma.
File-Url: https://papers.tinbergen.nl/02009.pdf
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Handle: RePEc:tin:wpaper:20020009