Minimax theorems and saddling transformations

Abstract

A transformation mapping games onto games that have saddle values (for short, saddling transformation) was first considered by von Neumann. By introducing mixed strategies, he showed that the bilinear extension of a finite game has a saddle value. This paper is concerned with saddling transformations of topological type in the setting of the quasi concave-convex payoffs and with their compositions. It yields new minimax theorems which are extensions of the Sion theorem.