(1) Institut für Mathematische Statistik, Universität Karlsruhe, Englerstr. 2, Postfach 6380, D-7500 Karlsruhe
Abstract:
In the present paper conditions for the strict determinateness of two-person zero-sum games are considered. In order to get such minimax theorems we first study games with concave-convex pay-off function. If a game does not have this convexity property one usually passes to a mixed extension where both players are allowed to use probability measures (-additive randomizations) or, more generally, probability contents (finitely additive randomizations) as mixed strategies. By means of a very general minimax theorem for such finitely additive randomizations it can be shown that the problem of strict determinateness of -additive randomizations is equivalent to an integral representation problem. The latter is investigated in the last paragraph.Diese Arbeit enthält einen Teil der Ergebnisse der Habilitationsschrift des Verfassers.