Despite attractive theoretical properties, Vickrey auctions are seldom used due to the risk of information revelation and fear of cheating. CVAs (Cryptographic Vickrey Auctions) have been proposed to protect bidders' privacy or to prevent cheating by the bid taker. This paper focuses on incentive issues for certain CVAs. First, it defines the CVAs of interest and identifies ideal goals for this class of CVAs. One of the criteria identifies an incentive problem that is new to the literature on CVAs, the disincentive of bidders to complete the protocol once they have learned that they lost the auction. Any auction protocol that requires losing bidders to do additional work after learning they have lost the auction must provide the losers with proper incentives to follow the protocol. Second, this paper shows that for a class of CVAs, some losers must continue to participate even though they know they have lost. Finally, it describes two new CVA protocols that solve the protocol-completion incentive problem. Both protocols use bidder-bidder comparisons based on a modified Yao's Millionaires' protocol. The first protocol performs O(n2) bidder-bidder comparisons, while the second protocol performs O(n) comparisons.
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Acknowledgements The authors thank Chee Yap for pointing out the 4-way comparison scheme and Felix Brandt for his helpful comments on our early draft. The first author thanks the Max-Planck-Institute for Computer Science in Saarbrücken, Germany, where he met Chee Yap. The second author was partly supported by a research grant from the Yonsei Management Research Center. Finally, we thank the referees for comments that substantially improved this paper.
All Science Journal Classification (ASJC) codes
- Economics, Econometrics and Finance (miscellaneous)
- Human-Computer Interaction