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The buy price in auctions with discrete type distributions

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  • Inami, Yusuke

Abstract

This paper considers second-price, sealed-bid auctions with a buy price where bidders' types are discretely distributed. We characterize all equilibria in which bidders whose types are less than the buy price bid their own valuations. Budish and Takeyama (2001) analyze the two-bidder, two-type framework. They show that if bidders are risk-averse, then the 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. In case of three or more types, however, bidders' risk aversion is not a sufficient condition for a revenue improvement. We point out that even if bidders are risk-averse, the seller cannot always obtain a higher expected revenue from the auctions with a buy price.

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  • Inami, Yusuke, 2011. "The buy price in auctions with discrete type distributions," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 1-11, January.
    • Handle: RePEc:eee:matsoc:v:61:y:2011:i:1:p:1-11
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    References listed on IDEAS

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    1. Stanley Reynolds & John Wooders, 2009. "Auctions with a buy price," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 9-39, January.
    2. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
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    4. Budish, Eric B. & Takeyama, Lisa N., 2001. "Buy prices in online auctions: irrationality on the internet?," Economics Letters, Elsevier, vol. 72(3), pages 325-333, September.
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    6. Timothy Mathews & Brett Katzman, 2006. "The role of varying risk attitudes in an auction with a buyout option," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 597-613, April.
    7. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    8. Hidvegi, Zoltan & Wang, Wenli & Whinston, Andrew B., 2006. "Buy-price English auction," Journal of Economic Theory, Elsevier, vol. 129(1), pages 31-56, July.
    9. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, September.
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    Cited by:

    1. Zhonghao Shui, 2023. "Rejection prices and an auctioneer with non-monotonic utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 925-951, September.
    2. Matzke, Andreas & Volling, Thomas & Spengler, Thomas S., 2016. "Upgrade auctions in build-to-order manufacturing with loss-averse customers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 470-479.

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    Keywords

    Auction Buy price Risk aversion;

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