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Equivalent Results in MinimaxTheory

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  • J.B.G. Frenk

    ()
    (Econometric Institute, Faculty of Economics, Erasmus University Rotterdam, and Tinbergen Institute)

  • G. Kassay

    (Department of Mathematics, Babes Bolyai University, Cluj)

  • J. Kolumb�n

    (Department of Mathematics, Babes Bolyai University, Cluj)

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    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.

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    File URL: http://papers.tinbergen.nl/02009.pdf
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    Bibliographic Info

    Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 02-009/4.

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    Date of creation: 06 Feb 2002
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    Handle: RePEc:dgr:uvatin:20020009

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    Web page: http://www.tinbergen.nl

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    Cited by:
    1. Friedman, Craig & Sandow, Sven, 2006. "Utility-based performance measures for regression models," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 541-560, February.
    2. Frenk, J.B.G. & Kas, P. & Kassay, G., 2004. "On linear programming duality and necessary and sufficient conditions in minimax theory," Econometric Institute Research Papers EI 2004-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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