Tools from advanced real analysis and the Prékopa-Borell Theorem are combined to derive a tight sufficient condition for regularity (R. Myerson, Optimal auction design, Mathematics of Operations Research 6, 1981, pp. 58-73). The conventional log-concavity condition arises as a special case. The approach allows various generalizations, for instance to multidimensional types. Regularity is verified explicitly for numerous new families of parameterized distributions. Economic applications are outlined, in particular to the robustness of the modified Vickrey auction.
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