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Third- and higher-price auctions

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  • Wolfstetter, Elmar

Abstract

This paper solves the equilibrium bid functions of third- and higher-price auctions for a large class of distribution functions of bidders' valuations, assuming the symmetric independent private values framework, and risk neutrality. In all these auctions, equilibrium bids exceed bidders' valuations, and bidders raise their bids when one moves to a higher price auction, and lower bids when the number of bidders is increased.

Suggested Citation

  • Wolfstetter, Elmar, 1995. "Third- and higher-price auctions," SFB 373 Discussion Papers 1996,3, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:19963
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    References listed on IDEAS

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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    3. Wolfstetter, Elmar, 1996. "Auctions: An Introduction," Journal of Economic Surveys, Wiley Blackwell, vol. 10(4), pages 367-420, December.
    4. Kagel, John H & Levin, Dan, 1993. "Independent Private Value Auctions: Bidder Behaviour in First-, Second- and Third-Price Auctions with Varying Numbers of Bidders," Economic Journal, Royal Economic Society, vol. 103(419), pages 868-879, July.
    5. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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    Cited by:

    1. Mezzetti, Claudio & Tsetlin, Ilia, 2009. "Auctions in which losers set the price," Games and Economic Behavior, Elsevier, vol. 66(2), pages 855-864, July.
    2. Olga Gorelkina, 2014. "Bidder Collusion and the Auction with Target Bids," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2014_10, Max Planck Institute for Research on Collective Goods.
    3. Martin Mihelich & Yan Shu, 2018. "k-price auctions and Combination auctions," Papers 1810.03494, arXiv.org, revised Mar 2019.
    4. Gadi Fibich & Arieh Gavious, 2010. "Large auctions with risk-averse bidders," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 359-390, July.

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    More about this item

    Keywords

    auctions; procurement;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • H57 - Public Economics - - National Government Expenditures and Related Policies - - - Procurement
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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