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Rejection prices and an auctioneer with non-monotonic utility

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  • Zhonghao Shui

    () (Graduate School of Economics, Kyoto University)

Abstract

This paper considers an auctioneer who has a non-monotonic utility function with a unique maximizer. The auctioneer is able to reject all bids over some amount by using rejection prices. We show that the optimal rejection price for such an auctioneer is lower than and equal to that maximizer in first-price and second-price sealed-bid auctions, respectively. Further, in each auction we characterize a necessary and sufficient condition that by using the optimal rejection price not only the auctioneer but also bidders can be better off, compared to a standard auction. Finally, we find that the auctioneer strictly prefers a first-price sealed-bid auction if he is risk-averse when his revenue is lower than the maximizer or if the distribution of revenues which are lower than the maximizer in a standard first-price sealed-bid auction is first-order stochastic dominant over the one in a standard second-price sealed-bid auction.

Suggested Citation

  • Zhonghao Shui, 2019. "Rejection prices and an auctioneer with non-monotonic utility," KIER Working Papers 1008, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:1008
    as

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP1008.pdf
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    References listed on IDEAS

    as
    1. Keith Waehrer & Ronald M. Harstad & Michael H. Rothkopf, 1998. "Auction Form Preferences of Risk-Averse Bid Takers," RAND Journal of Economics, The RAND Corporation, vol. 29(1), pages 179-192, Spring.
    2. Arieh Gavious & Benny Moldovanu & Aner Sela, 2002. "Bid Costs and Endogenous Bid Caps," RAND Journal of Economics, The RAND Corporation, vol. 33(4), pages 709-722, Winter.
    3. Zheng, Charles Z., 2001. "High Bids and Broke Winners," Journal of Economic Theory, Elsevier, vol. 100(1), pages 129-171, September.
    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.
    5. Inami, Yusuke, 2011. "The buy price in auctions with discrete type distributions," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 1-11, January.
    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. Nicolas Sahuguet, 2006. "Caps in asymmetric all-pay auctions with incomplete information," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    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. Simon Board, 2007. "Bidding into the Red: A Model of Post‐Auction Bankruptcy," Journal of Finance, American Finance Association, vol. 62(6), pages 2695-2723, December.
    10. Timothy Mathews, 2003. "A Risk Averse Seller in a Continuous Time Auction with a Buyout Option," Brazilian Electronic Journal of Economics, Department of Economics, Universidade Federal de Pernambuco, vol. 5(2), January.
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    More about this item

    Keywords

    Auction; Rejection prices; Non-monotonic utility;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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