Thanh Nguyen and Milan Vojnovic
We consider the optimal prior-free auction design for allocating a set of indistinguishable items to a set of buyers where the objective is to maximize seller's revenue. The key design requirement is that the auction must always fully allocate all items to buyers, which prevents using the traditional approach based on reserve prices. This is an important class of auctions both in theory and practice.
We study two types of auctions: generalized first-price and truthful. We show a revenue upper bound $o(v_1/\log(v_1/v_2))$ for both classes of auctions. This resolves an open question of Mirrokni, Muthukrishnan and Navad. We also give optimal auctions that match the upper bound and extend the results to the case of multiple items.
Our results answer the basic question of how much revenue can an auction generate without reserve prices. We also found that in our setting even by relaxing the truthfulness condition of the auction design to a Nash implementation, one cannot gain much larger revenue.