MinMax Theorem

MAS

Let us have sets $X,Y$ and function $f:X\times Y\to \mathbb{R}$. If

• $X$ and $Y$ are standard simplexes and
• $f$ is bilinear, $f(x,y)=x^{T}Ay$ , then ${\max }_{x\in X}{\min }_{y\in Y}f(x,y)={\min }_{y\in Y}{\max }_{x\in X}f(x,y)$