Regular type distributions in mechanism design and ρ-concavity

Some of the best-known results in mechanism design depend critically on Myerson's (Math Oper Res 6:58-73, 1981) 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.