Before revision:  In this work, we go one step further and show that for many fundamental two-sided markets-e.g., bilateral trade, double auctions, and combinatorial double auctions-it is possible to design near-optimal mechanisms with provable, constant-factor approximation guarantees with just a{\em   single sample from the priors! In fact, most of our results in addition to requiring less information also improve upon the best known approximation guarantees for the respective setting .
After revision:  In this work, we go one step further and show that for many fundamental two-sided markets-e.g., bilateral trade, double auctions, and combinatorial double auctions-it is possible to design near-optimal mechanisms with provable, constant-factor approximation guarantees with just a{\em single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information .