The communication complexity of private value single item auctions

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The communication complexity of private value single item auctions

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Grigorieva,Elena
Herings,Jean-Jacques
Müller,Rudolf
Vermeulen,Dries (METEOR)

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Abstract

In this paper we present a new auction, the bisection auction, that can be used for the sale of a single indivisible object. We discuss the issue concerning the information revelation requirement of this auction and the associated amount of data that needs to be transmitted. We show that in the truthtelling equilibrium the bisection auction is economical in its demand for information on the valuations of the players. It requires the players to transmit less information bits to the auctioneer than the Vickrey and English auctions. In particular, we prove that for integer valuations uniformly distributed on the interval [0,L) the bisection auction of n players requires in expectation transmission of at most 2n + log L information bits by the players. Compared with the corresponding number in the Vickrey auction which is n log L, and in the English auction which is on average at least (1/3) nL, the bisection auction turns out to be the best performer.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 052.

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Date of creation: 2004
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Handle: RePEc:dgr:umamet:2004052

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This paper has been announced in the following NEP Reports:

NEP-ALL-2005-01-02 (All new papers)
NEP-GTH-2005-01-02 (Game Theory)

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Grigorieva,Elena & Herings,P. Jean-Jacques & Müller,Rudolf & Vermeulen,Dries, 2002. "The private value single item bisection auction," Research Memoranda 051, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
Other versions:
- Elena Grigorieva & P. Herings & Rudolf Müller & Dries Vermeulen, 2007. "The private value single item bisection auction," Economic Theory, Springer, vol. 30(1), pages 107-118, January. [Downloadable!] (restricted)
Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February. [Downloadable!] (restricted)
Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March. [Downloadable!] (restricted)
Rothkopf, Michael H. & Harstad, Ronald M., 1994. "On the role of discrete bid levels in oral auctions," European Journal of Operational Research, Elsevier, vol. 74(3), pages 572-581, May. [Downloadable!] (restricted)
Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1991. "Protecting the winner : Second-price versus oral auctions," Economics Letters, Elsevier, vol. 35(3), pages 243-248, March. [Downloadable!] (restricted)
Other versions:
- Engelbrecht-Wiggans, R. & Kahn, C.M., 1990. "Protecting the Wnner: Second-price Versus Oral Auctions," University of Chicago - Economics Research Center 90-8, Chicago - Economics Research Center.
Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July. [Downloadable!] (restricted)
Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November. [Downloadable!] (restricted)

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