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, 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.convex analysis;game theory;finite dimensional separation of convex sets;generalized convexity;minimax theory

Capabilities and Equality of Health I

The concept of capabilities, introduced originally by Sen with the aim to provide a better basis for the theory of inequality, has inspired many researchers but has not found any simple formal representation which might be instrumental in the construction of a comprehensive theory of equality. In the present paper, we present a formalization of the concept of capabilities based on Lancasterian characteristics, whereby a functioning of an individual is a method for transforming an initial position to a final outcome. In this context, we investigate whether preferences over capabilities as sets of functionings can be rationalized by maximization of a suitable utility function over the set of functionings. Such a rationalization turns out to be possible only in cases which must be considered exceptional and which do not allow for interesting applications of the capability approach to questions of health or equality. The conclusion which can be obtained from the predominantly negative results is that a formal description of capabilities much involve ideas which go beyond the simple representation as a family of choice sets.capabilities; characteristics; equality of health

Convex sets strict separation in Hilbert spaces

Convex sets separation is very important in convex programming, a very powerful mathematical tool for operations research, management and economics, for example. The target of this work is to present Theorem 3.1 that gives sufficient conditions for the strict separation of convex sets.info:eu-repo/semantics/publishedVersio