If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A, where the subset is interpreted as the set of "welfare optima". A game form (or "mechanism") implements the social choice rule if, for any...

The authors exhibit an efficient auction (i.e., an auction that maximizes expected surplus conditional on all private and public information). In the case of private value, it is well-known that the Vickrey auction (for one good) or its Groves-Clark extension (for multiple goods) is efficient in...

The paper characterises the choice rules that can be implemented when agents are unable to commit themselves not to renegotiate the mechanism.