The Von Neumann's Minimax theorem gives the conditions that make the max-min inequality an equality.I understand the max-min inequality, basically min(max(f))>=max(min(f)).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.QuestionsWhy 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?
Illustration of Von Neumann's Minimax theorem in games?
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