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On the strictly descending multi-unit auction

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  • Gretschko, Vitali
  • Rasch, Alexander
  • Wambach, Achim

Abstract

We analyze the bidding behavior in a strictly descending multi-unit auction where the price decreases continuously without going back to the initial start price once an object is sold. We prove that any equilibrium in the multi-unit descending auction is inefficient. We derive a symmetric equilibrium for general distribution functions as well as an arbitrary number of bidders and objects. Moreover, equilibrium bidding is characterized by a set of initial value problems. Our analysis thus generalizes previous results in the literature.

Suggested Citation

  • Gretschko, Vitali & Rasch, Alexander & Wambach, Achim, 2014. "On the strictly descending multi-unit auction," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 79-85.
    • Handle: RePEc:eee:mateco:v:50:y:2014:i:c:p:79-85
    DOI: 10.1016/j.jmateco.2013.10.009
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    References listed on IDEAS

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    1. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
    2. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    3. Martínez-Pardina, Irene & Romeu, Andrés, 2011. "The case for multi-unit single-run descending-price auctions," Economics Letters, Elsevier, vol. 113(3), pages 310-313.
    4. Bulow, Jeremy & Klemperer, Paul, 1994. "Rational Frenzies and Crashes," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 1-23, February.
    5. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    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. Goeree, Jacob K. & Offerman, Theo & Schram, Arthur, 2006. "Using first-price auctions to sell heterogeneous licenses," International Journal of Industrial Organization, Elsevier, vol. 24(3), pages 555-581, May.
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    Cited by:

    1. Vitali Gretschko & Achim Wambach, 2014. "Information acquisition during a descending auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 731-751, April.
    2. Fabian Ocker & Karl‐Martin Ehrhart & Marion Ott, 2018. "Bidding strategies in Austrian and German balancing power auctions," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 7(6), November.
    3. Li, Zhen & Yue, Jinfeng & Kuo, Ching-Chung, 2018. "Design of discrete Dutch auctions with consideration of time," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1159-1171.

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