To be announced

Abstract

In a Vickrey auction, if one bidder can invest to increase his value, the combined mechanism including investments is still fully optimal. By contrast, there exist monotone allocation rules that are arbitrarily close to the the allocative optimum, but such that the associated mechanism with investments by one bidder cannot guarantee any positive fraction of the full optimum. We show that if a monotone allocation rule that guarantees some fraction of the allocative optimum also \excludes bossy negative externalities," then the same guarantee applies to the combined mechanism with investments. We show moreover that a mild weakening of this property is necessary and sufficient for the result.