A Robustly Efficient Auction and Informational Size

Résumé

The idea that there exists a trade-off between robustness and the extent to which certain goals of mechanism design can be achieved is intuitive. Nonetheless, the literature on robust mechanism design is silent about it. We explore the problem in the context of an efficient auction problem with interdependent values. We construct a mechanism that robustly achieves efficiency. We introduce a notion of robust informational size and show that agents'informational rents are small if agents are informationally small in our sense. Furthermore, these rents are decreasing in the amount of information available to the designer: the more robust the efficient implementation result, the higher the informational rents. We thus provide an upper bound to the "cost of robustness", formalizing the intuitive idea of a trade-off between robustness and the possibility of achieving implementation.