I understand the max-min inequality, basically
The Von Neumann's theorem states that, for the inequality to become an equality
f(.,y) should always be convex for given y and
f(x,.) should always be concave for given x, which also makes sense.
This video says that for a zero-sum perfect information game, the Von Neumann's theorem always holds, so that minimax always equal to maximin, which I did not quite follow.
Why do zero-sum perfect information games satisfy the conditions of Von Neumann's theorem?
If we relax the rules to be non-zero-sum or non-perfect information, how would the conditions change?