Revenue Comparisons for Auctions When Bidders Have Arbitrary Types

This paper develops a methodology for characterizing expected revenue from auctions in which bidders' types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence results. Another application shows that first-price auctions yield higher expected revenue than second-price auctions when bidders are risk averse and/or face financial constraints. This revenue ranking also extends to risk-averse bidders with general forms of non-expected utility preferences.