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On the Lowest-Winning-Bid and the Highest-Losing-Bid Auctions

Author

Listed:
  • Mezzetti, Claudio

    (University of Warwick, Department of Economics,)

  • Tsetlin, Ilia

    (INSEAD)

Abstract

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n - k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner.

Suggested Citation

  • Mezzetti, Claudio & Tsetlin, Ilia, 2007. "On the Lowest-Winning-Bid and the Highest-Losing-Bid Auctions," The Warwick Economics Research Paper Series (TWERPS) 832, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:832
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    References listed on IDEAS

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    1. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1997. "The Loser's Curse and Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 65(6), pages 1247-1282, November.
    2. Mezzetti, Claudio & Pekec, Aleksandar Sasa & Tsetlin, Ilia, 2008. "Sequential vs. single-round uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 62(2), pages 591-609, March.
    3. Jackson, Matthew O. & Kremer, Ilan, 2004. "The relationship between the allocation of goods and a seller's revenue," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 371-392, June.
    4. Matthew O. Jackson & Ilan Kremer, 2006. "The Relevance of a Choice of Auction Format in a Competitive Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 961-981.
    5. McAdams, David, 2007. "Uniqueness in symmetric first-price auctions with affiliation," Journal of Economic Theory, Elsevier, vol. 136(1), pages 144-166, September.
    6. Marc S. Robinson, 1985. "Collusion and the Choice of Auction," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 141-145, Spring.
    7. Jeroen M. Swinkels & Wolfgang Pesendorfer, 2000. "Efficiency and Information Aggregation in Auctions," American Economic Review, American Economic Association, vol. 90(3), pages 499-525, June.
    8. Bikhchandani, Sushil & Riley, John G., 1991. "Equilibria in open common value auctions," Journal of Economic Theory, Elsevier, vol. 53(1), pages 101-130, February.
    9. Ilan Kremer, 2002. "Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 70(4), pages 1675-1682, July.
    10. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-943, June.
    11. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    Cited by:

    1. Han Hong & Harry J. Paarsch & Pai Xu, 2013. "On the asymptotic distribution of the transaction price in a clock model of a multi-unit, oral, ascending-price auction within the common-value paradigm," RAND Journal of Economics, RAND Corporation, vol. 44(4), pages 664-685, December.
    2. Mezzetti, Claudio & Pekec, Aleksandar Sasa & Tsetlin, Ilia, 2008. "Sequential vs. single-round uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 62(2), pages 591-609, March.
    3. Muto, Nozomu & Shirata, Yasuhiro, 2017. "Manipulation via endowments in auctions with multiple goods," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 75-84.

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    More about this item

    Keywords

    Auctions; Lowest-Winning Bid; Highest-Losing Bid; k-th Price Auction; (k+1)-st; Price Auction;
    All these keywords.

    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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