About: Sion's minimax theorem

In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion. It states: Let be a compact convex subset of a linear topological space and a convex subset of a linear topological space. If is a real-valued function on with upper semicontinuous and quasi-concave on , , and lower semicontinuous and quasi-convex on , then,