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Revenue-maximizing Dutch auctions with discrete bid levels

Author

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  • Li, Zhen
  • Kuo, Ching-Chung

Abstract

This paper is concerned with setting a predetermined number of bid levels in a Dutch auction to maximize the auctioneer's expected revenue. As a departure from the traditional methods used by applied economists and game-theorists, a novel approach is taken in this study to tackle the problem by formulating the auctioning process as a constrained nonlinear program and applying standard optimization techniques to solve it. Aside from proposing respective closed-form formulae for computing the optimal bid levels and the auctioneer's maximum expected revenue, we also show that the bid decrements should be increasing if there are two or more bidders in the Dutch auction. Additionally, the auctioneer's maximum expected revenue increases with the number of bidders as well as the number of bid levels. Finally, managerial implications of the key findings as well as limitations of this research work are discussed.

Suggested Citation

  • Li, Zhen & Kuo, Ching-Chung, 2011. "Revenue-maximizing Dutch auctions with discrete bid levels," European Journal of Operational Research, Elsevier, vol. 215(3), pages 721-729, December.
  • Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:721-729
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    References listed on IDEAS

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    1. Peter Cramton & Emel Filiz-Ozbay & Erkut Ozbay & Pacharasut Sujarittanonta, 2012. "Discrete clock auctions: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 15(2), pages 309-322, June.
    2. Aleksandar Saša Pekev{c} & Ilia Tsetlin, 2008. "Revenue Ranking of Discriminatory and Uniform Auctions with an Unknown Number of Bidders," Management Science, INFORMS, vol. 54(9), pages 1610-1623, September.
    3. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, April.
    4. Rothkopf, Michael H. & Harstad, Ronald M., 1994. "On the role of discrete bid levels in oral auctions," European Journal of Operational Research, Elsevier, vol. 74(3), pages 572-581, May.
    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. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
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    Cited by:

    1. Jiang, Zhong-Zhong & Fang, Shu-Cherng & Fan, Zhi-Ping & Wang, Dingwei, 2013. "Selecting optimal selling format of a product in B2C online auctions with boundedly rational customers," European Journal of Operational Research, Elsevier, vol. 226(1), pages 139-153.

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