Before revision:  In particular, we find that when this rate is controlled in a certain range , the two goals can be achieved to \sqrt{n \log n}, the mechanism can be AEABB and AE } at the same time asymptotically. The proposed mechanisms are robust in two ways: first, they depend on the valuation distributions only through certain moments ; second, they allow for asymmetric and irregular valuation distributions.
After revision:  In particular, we find that when this rate is controlled in a certain range , the two goals can be achieved to \sqrt{n \log n}, the mechanism can be AEABB and AE } at the same time as long as the cost does not grow too rapidly. One advantage of the proposed mechanisms is their informational robustness as they depend only on certain moments of the valuation distributions.