This paper develops a methodology for characterizing expected revenue from auctions when 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...

Risk and time are intertwined. The present is known while the future is inherently risky. Discounted expected utility provides a simple, coherent structure for analyzing decisions in intertemporal, uncertain environments. However, we document robust violations of discounted expected utility,...