On the impossibility of black-box transformations in mechanism design

A fundamental question in algorithmic mechanism design is whether any approximation algorithm for a single-parameter social-welfare maximization problem can be turned into a dominant-strategy truthful mechanism for the same problem (while preserving the approximation ratio up to a constant factor). A particularly desirable type of transformations—called black-box transformations— achieve the above goal by only accessing the approximation algorithm as a black box.

A recent work by Chawla, Immorlica and Lucier (STOC 2012) demonstrates (unconditionally) the impossibility of certain restricted classes of black-box transformations— where the tranformation is oblivious to the feasibility constrain of the optimization problem. In this work, we remove these restrictions under standard complexity-theoretic assumptions: Assuming the existence of one-way functions, we show the impossibility of all black-box transformations.