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The Buy Price in Auctions with Discrete Type Distributions

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  • Yusuke Inami

    ()
    (Graduate School of Economics, Kyoto University)

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    Abstract

    This paper considers second-price, sealed-bid auctions with a buy price where bidders' types are discretely distributed. We characterize all equilibria, restricting our attention to equilibria where bidders whose types are less than a buy price bid their own valuations. Budish and Takeyama (2001) analyzed the two-bidder, two-type framework, and showed that if bidders are risk-averse, a seller can obtain a higher expected revenue from the auction with a certain buy price than from the auction without a buy price. We extend their revenue improvement result to the n-bidder, two-type framework. However, in case of three or more types, bidders' risk aversion is not a sufficient condition for the revenue improvement. Our example illustrates that even if bidders are risk-averse, a seller cannot always obtain a higher expected revenue from the auction with a buy price.

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP657.pdf
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    Bibliographic Info

    Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 657.

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    Length: 19pages
    Date of creation: Jul 2008
    Date of revision:
    Handle: RePEc:kyo:wpaper:657

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    Keywords: Auction; Buy price; Risk aversion;

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    1. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, Econometric Society, vol. 55(3), pages 633-46, May.
    2. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1473-1518, November.
    3. Hidvegi, Zoltan & Wang, Wenli & Whinston, Andrew B., 2006. "Buy-price English auction," Journal of Economic Theory, Elsevier, Elsevier, vol. 129(1), pages 31-56, July.
    4. Budish, Eric B. & Takeyama, Lisa N., 2001. "Buy prices in online auctions: irrationality on the internet?," Economics Letters, Elsevier, Elsevier, vol. 72(3), pages 325-333, September.
    5. Timothy Mathews & Brett Katzman, 2006. "The role of varying risk attitudes in an auction with a buyout option," Economic Theory, Springer, Springer, vol. 27(3), pages 597-613, 04.
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