Truthful auctions with optimal profit

Abstract

We study the design of truthful auction mechanisms for maximizing the seller's profit. We focus on the case when the auction mechanism does not have any knowledge of bidders' valuations, especially of their upper bound. For the Single-Item auction, we obtain an "asymptotically" optimal scheme: for any k ε Z + and ε > 0, we give a randomized truthful auction that guarantees an expected profit of Ω(OPT/ln OPT ln ln OPT...(ln (k) OPT) 1+ε), where OPT is the maximum social utility of the auction. Moreover, we show that no truthful auction can guarantee an expected profit of Ω(OPT/ln OPT ln ln OPT...(ln (k) OPT). In addition, we extend our results and techniques to Multi-units auction, Unit-Demand auction, and Combinatorial auction. © 2006 Springer-Verlag.