Deterministic single object auctions with private values

We study deterministic single object auctions in private values environments. We show that a deterministic allocation rule is implementable (in dominant strategies) if and only if it is a generalized utility maximizer. With a mild continuity condition, we show that a deterministic allocation rule is implementable and non-bossy if and only if it is a virtual utility maximizer (with appropriate tie-breaking). Both our results extend the seminal result of Roberts (1979) from unrestricted domain to the restricted domain of single object auctions.