Minimax theorem
In the mathematical area of game theory and of convex optimization, a minimax theorem is a theorem that claims that max x ∈ X min y ∈ Y f ( x , y ) = min y ∈ Y max x ∈ X f ( x , y ) {\displaystyle \max _{x\in X}\min _{y\in Y}f(x,y)=\min _{y\in Y}\max _{x\in X}f(x,y)} under certain conditions on the sets X {\displaystyle X} and Y {\displaystyle Y} and on the function f {\displaystyle f} . It is always true that the left-hand side is at most the right-hand side (max–min inequality) but equality only holds under certain conditions identified by minimax theorems.