Non-bossy single object auctions

Abstract

We study deterministic single object auctions in the private values environment. We show that an allocation rule is implementable (in dominant strategies) and non-bossy if and only if it is a strongly rationalizable allocation rule. With a mild continuity condition, we show that an allocation rule is implementable and non-bossy if and only if it is a simple utility maximizer (with appropriate tie-breaking). All our characterizations extend the seminal result of Roberts (“Aggregation and Revelation of Preferences”, pp. 321–348, 1979) from the unrestricted domain to the restricted domain of single object auctions.