Sion's minimax theorem

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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 quasiconcave on , , and
lower semicontinuous and quasi-convex on ,

then,

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