We analyze a setting common in privatizations, public tenders, and takeovers in which the ex post efficient allocation, i.e., the first best, is not implementable. Our first main result is that the open ascending auction is not second best because it is prone to rushes, i.e., all active bidders...

We characterize the incentive compatible allocation that maximizes the expected social surplus in a single-unit sale when the efficient allocation is not implementable. We then show that allowing for the possibility that the good remains unsold may increase the expected social surplus even when...

We study the second best in a single unit sale to two bidders. This is the allocation that maximizes the expected social surplus subject to the biddersʼ incentive compatible constraints when the first best is not implementable. We prove that Maskinʼs (1992) result that any first best...

We show that the commitment to not allocate may be exploited by a seller/social planner to increase the expected social surplus that can be achieved in the sale of an indivisible unit.

We characterize the incentive compatible allocation that maximizes the expected social surplus in a single-unit sale when the efficient allocation is not implementable. This allocation may involve no selling when it is efficient to sell. We then show that the English auction always implements...