Revenue and Duration of Oral Auction

Junmin SHI, Ai-Chih CHANG

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DOI: 10.4236/jssm.2009.24044                

Abstract

This paper investigates the revenue and duration of a well-known hybrid oral auction (English auction and Dutch auction) that is extensively adopted in practice, for instance the Christie’s. Unlike sealed bid auction, oral auction is featured by its complexity of dynamic process. The bidding price varies as a stochastic time series. Therefore, the duration of oral auction as well as its revenue performs randomly. From the seller’s perspective, both the revenue and the duration are so important that extra attention and effort should be put on auction design. One of the most important issues is how to choose the starting bid price to maximize its revenue or minimize its duration. In this paper, the bidding process is decomposed into two phases: English auction (descending-bid) phase and the Dutch auction (ascending-bid) phase. For each phase, with the aid of Markov method, we derive the expected revenue and duration as a function of the starting bid. For an oral auction with a large number of bidder and each bidder behaves independently, we provide the limit results of the expected revenue and duration. The results of the auction model can be easily implemented in auction design.

Keywords

Duration, Dutch Auction, English Auction, Oral Auction, Revenue

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. W. Smith, “Auctions: The social construction of value,” University of California Press, Berkeley, Los Angeles, 1990.
[2]	W. Vickrey, “Counter speculation, auctions, and competi-tive sealed tenders,” Journal of Finance, Vol. 16, pp. 8–37, 1961.
[3]	N. Buchbinder, K. Jain, and J. Naor, “Online primal-dual algorithms for maximizing ad-auctions revenue,” Lecture Notes in Computer Science, 4698, pp. 253–264, 2007.
[4]	G. Vulcano, G. V. Ryzin, and C. Maglaras, “Optimal dynamic auctions for revenue management,” Management Science, Vol. 48, No. 11, pp. 1388–1407, 2002.
[5]	E. J. Pinker, A. Seidmann, and Y. Vakrat, “Managing on- line auctions: Current business and research issues,” Manage-ment Science, Vol. 49, No. 11, pp. 1457–1484, 2003.
[6]	Z. J. Shen and X. Su, “Customer behavior modeling in revenue management and auctions: A review and new re-search opportunities,” Production and Operations Man-agement, Vol. 16, No. 6, pp. 713–728, 2009.
[7]	K. Hendricks and H. J. Paarsch, “A survey of recent em-pirical work concerning auctions,” Canadian Journal of Economics, Vol. 28, No. 2, pp. 403–426, 1995.
[8]	J. Laffont, “Game theory and empirical economics: The case of auction data,” European Economic Review, Vol. 41, No. 1, pp. 1–35, 1997.
[9]	R. L. Zhan and Z. J. Shen, “Optimality and efficiency in auctions design: A survey,” Working Paper, 2006.
[10]	S. M. Ross, Stochastic Processes, 2nd Edition, Wiley, 1995.
[11]	S. Park, E. H. Durfee, and W. P. Birmingham, “Use of Markov chains to design an agent bidding strategy for continuous double auctions,” Journal of Artificial Intelli-gence Research, Vol. 22, pp.175–214, 2004.
[12]	A. Segev, C. Beam, and J. Shanthikumar, “Optimal de-sign of internet-based auctions,” Information Technology and Management, Vol. 2, pp. 121–163, 2001.
[13]	D. Reiley, D. Bryanz, N. Prasad, and D. Reevesz, “Pen-nies from eBay: The determinants of price in online auc-tions,” The Journal of Industrial Economics, Vol. 55, pp. 223–233, 2007.
[14]	C. Mason, “The Art of the steal: Inside the Sotheby’s- Christie’s auction house scandal,” Berkley Trade, 2005.
[15]	S. Chou, C. S. Lin, C. Chen, T. R. Ho, and Y. C. Hsieh, “A simulation-based model for final price prediction in online auctions,” Journal of Economics and Management, Vol. 3 No. 1, pp. 1–16, 2007.