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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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    File URL: https://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp_832.pdf
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    References listed on IDEAS

    as
    1. Bikhchandani, Sushil & Riley, John G., 1991. "Equilibria in open common value auctions," Journal of Economic Theory, Elsevier, vol. 53(1), pages 101-130, February.
    2. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-943, June.
    3. Ilan Kremer, 2002. "Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 70(4), pages 1675-1682, July.
    4. McAdams, David, 2007. "Uniqueness in symmetric first-price auctions with affiliation," Journal of Economic Theory, Elsevier, vol. 136(1), pages 144-166, September.
    5. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    6. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. repec:eee:matsoc:v:87:y:2017:i:c:p:75-84 is not listed on IDEAS

    More about this item

    Keywords

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

    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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