Equivalent Results in Minimax Theory

Hans Frenk, G. Kassay and J. Kolumban

ERIM Report Series Research in Management from Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam

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

Keywords: convex analysis; finite dimensional separation of convex sets; game theory; generalized convexity; minimax theory (search for similar items in EconPapers)
JEL-codes: C7 M M11 R4 (search for similar items in EconPapers)
Date: 2002-01-24
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Citations: View citations in EconPapers (2)

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