Equivalent Results in Minimax Theory

26 Pages Posted: 26 Aug 2006

See all articles by J. B. G. Frenk

J. B. G. Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

G. Kassay

Babes-Bolyai University - Faculty of Mathematics and Computer Science

J. Kolumbán

affiliation not provided to SSRN

Date Written: 24 2002 1,

Abstract

In this paper we review known minimax results with applications ingame theory and show that these results are easy consequences of thefirst minimax result for a two person zero sum game with finite strategysets published by von Neumann in 1928: Among these results are thewell known minimax theorems of Wald, Ville and Kneser and their generalizationsdue to Kakutani, Ky-Fan, König, Neumann and Gwinner-Oettli. Actually it is shown that these results form an equivalent chainand this chain includes the strong separation result in finite dimensionalspaces between two disjoint closed convex sets of which one is compact.To show these implications the authors only use simple propertiesof compact sets and the well-known Weierstrass Lebesgue lemma.

Keywords: convex analysis, game theory, finite dimensional separation of convex sets, minimax theory, generalized convexity

JEL Classification: M, M11, R4, C7

Suggested Citation

Frenk, J.B.G. (Hans) and Kassay, G. and Kolumbán, J., Equivalent Results in Minimax Theory (24 2002 1,). ERIM Report Series Reference No. ERS-2002-08-LIS. Available at SSRN: https://ssrn.com/abstract=370953

J.B.G. (Hans) Frenk (Contact Author)

Erasmus University, Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 0 10 408 1257 (Phone)
+31 0 10 408 9162 (Fax)

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

G. Kassay

Babes-Bolyai University - Faculty of Mathematics and Computer Science ( email )

Str. Mihail Kogalniceanu nr. 1
Cluj-Napoca, RO-400,084
Romania

J. Kolumbán

affiliation not provided to SSRN

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