Regular type distributions in mechanism design and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\rho $$</EquationSource> </InlineEquation>-concavity

Some of the best-known results in mechanism design depend critically on Myerson’s (Math Oper Res 6:58–73, <CitationRef CitationID="CR22">1981</CitationRef>) regularity condition. For example, the second-price auction with reserve price is revenue maximizing only if the type distribution is regular. This paper offers two main findings. First, a new interpretation of regularity is developed—similar to that of a monotone hazard rate—in terms of being the next to fail. Second, using expanded concepts of concavity, a tight sufficient condition is obtained for a density to define a regular distribution. New examples of regular distributions are identified. Applications are discussed. Copyright Springer-Verlag 2013