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.

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Erasmus Research Institute of Management
hdl.handle.net/1765/158
Tinbergen Institute Discussion Paper Series , ERIM Report Series Research in Management
ERIM report series research in management Erasmus Research Institute of Management
Erasmus Research Institute of Management

Frenk, H., Kassay, G., & Kolumban, J. (2002). Equivalent Results in Minimax Theory (No. ERS-2002-08-LIS). ERIM report series research in management Erasmus Research Institute of Management. Retrieved from http://hdl.handle.net/1765/158