A flexible minimax theorem
The paper deals with a generalization of the von Neumann's minimax theorem in topological spaces, i.e., some sufficient conditions are suggested for the equality of minimax and maximin. The conditions are given in an abstract form that is also specified in the paper. Namely, the conditions assume compactness of any Lebesgue set of the pay-off function with respect to \(y\) for any \(x\), pseudoconnectedness of such set intersection, and their jointness for different \(x\). For any of the latter two conditions, the author proves other sufficient conditions and compaires them with the previous results. Thus, there are unified various minimax theorems, including one for quasiconcave functions (with respect to \(x\)) in the sense of interval spaces.
scientific article; zbMATH DE number 556296
scientific article