Truthful auctions with optimal profit

  • Authors:
  • Pinyan Lu;Shang-Hua Teng;Changyuan Yu

  • Affiliations:
  • Department of Computer Science and Technology, Tsinghua University and Microsoft Research Asia, Beijing, China;Department of Computer Science, Boston University;Department of Computer Science and Technology, Tsinghua University and Microsoft Research Asia, Beijing, China

  • Venue:
  • WINE'06 Proceedings of the Second international conference on Internet and Network Economics
  • Year:
  • 2006

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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∈Z+ and ε0, we give a randomized truthful auction that guarantees an expected profit of $\Omega(\frac{OPT}{\ln OPT \ln\ln OPT \cdots (\ln^{(k)}OPT)^{1+\epsilon}})$, where OPT is the maximum social utility of the auction. Moreover, we show that no truthful auction can guarantee an expected profit of $\Omega(\frac{OPT}{\ln OPT \ln\ln OPT\cdots \ln^{(k)}OPT})$. In addition, we extend our results and techniques to Multi-units auction, Unit-Demand auction, and Combinatorial auction.