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High Quality Content by WIKIPEDIA articles! In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John Von Neumann's minimax theorem. It states: Let X be a compact convex subset of a linear topological space and Y a convex subset of a linear topological space. If f is a real-valued function on Xtimes Y with f(x,cdot) upper semicontinuous and quasiconcave on Y, forall xin X, and f(cdot,y) is lower semicontinuous and quasi-convex on X, forall yin Y.