In bilevel and robust optimization we are concerned with combinatorial min-max problems, for example from the areas of min-max regret robust optimization, network interdiction, and two-stage adjustable robust optimization. Even though these areas are well-researched for over two decades and one would naturally expect many (if not most) of the problems occurring in these areas to be complete for the classes \(\varSigma ^p_2\) or \(\varSigma ^p_3\) from the polynomial hierarchy, almost no hardness results in this regime are currently known. However, such complexity insights are important, since they imply that no polynomial-sized integer program for these min-max problems exist, and hence conventional IP-based approaches fail. We address this lack of knowledge by introducing at least 72 new \(\varSigma ^p_2\) -complete and \(\varSigma ^p_3\) -complete problems. The majority of all earlier publications on \(\varSigma ^p_2\) - and \(\varSigma ^p_3\) -completeness in said areas are special cases of our meta-theorem. Precisely, we introduce a large list of problems for which the meta-theorem is applicable (including clique, vertex cover, knapsack, TSP, facility location, and many more). We show that for each of these problems, the corresponding min-max (i.e. interdiction/regret) variant is \(\varSigma ^p_2\) - and the min-max-min (i.e. two-stage) variant is \(\varSigma ^p_3\) -complete.