2 research outputs found
Equivalent Results in Minimax Theory
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, KĂÂśnig, 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.convex analysis;game theory;finite dimensional separation of convex sets;generalized convexity;minimax theory
Equivalent Results in Minimax Theory
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, KĂśnig, 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