Annals of Applied Statistics

The BARISTA: A model for bid arrivals in online auctions

Galit Shmueli, Ralph P. Russo, and Wolfgang Jank

Full-text: Open access

Abstract

The arrival process of bidders and bids in online auctions is important for studying and modeling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson bidder arrival process is a reasonable approximation. This approximation underlies theoretical derivations, statistical models and simulations used in field studies. However, when it comes to the bid arrivals, empirical research has shown that the process is far from Poisson, with early bidding and last-moment bids taking place. An additional feature that has been reported by various authors is an apparent self-similarity in the bid arrival process. Despite the wide evidence for the changing bidding intensities and the self-similarity, there has been no rigorous attempt at developing a model that adequately approximates bid arrivals and accounts for these features. The goal of this paper is to introduce a family of distributions that well-approximate the bid time distribution in hard-close auctions. We call this the BARISTA process (Bid ARrivals In STAges) because of its ability to generate different intensities at different stages. We describe the properties of this model, show how to simulate bid arrivals from it, and how to use it for estimation and inference. We illustrate its power and usefulness by fitting simulated and real data from eBay.com. Finally, we show how a Poisson bidder arrival process relates to a BARISTA bid arrival process.

Article information

Source
Ann. Appl. Stat., Volume 1, Number 2 (2007), 412-441.

Dates
First available in Project Euclid: 30 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1196438025

Digital Object Identifier
doi:10.1214/07-AOAS117

Mathematical Reviews number (MathSciNet)
MR2415742

Zentralblatt MATH identifier
05226940

Keywords
Nonhomogenous Poisson process bidding frequency self-similarity bidding dynamics sniping

Citation

Shmueli, Galit; Russo, Ralph P.; Jank, Wolfgang. The BARISTA: A model for bid arrivals in online auctions. Ann. Appl. Stat. 1 (2007), no. 2, 412--441. doi:10.1214/07-AOAS117. https://projecteuclid.org/euclid.aoas/1196438025


Export citation

References

  • Ariely. D., Ockenfels, A. and Roth, A. E. (2005). An experimental analysis of ending rules in internet auctions. RAND Journal of Economics 36 890–907.
  • Aurell, E. and Hemmingsson, J. (1997). Bid frequency analysis in liquid Markets. TRITA-PDC Report. ISRN KTH/PDC/R–97/3–SE. ISSN 1401-2731. Available at http://www.pdc.kth.se/~payam/pub/AurellHemmingsson970208.ps.
  • Avery, C. N., Jolls, C., Posner, R. A. and Roth, A. E. (2001). The Market for Federal Judicial Law Clerks. Univ. Chicago Law Rev. 68 793–902.
  • Bajari, P. and Hortacsu, A. (2000). Winner's curse, reserve price and endogenous entry: Empirical insights from eBay auctions. Working paper. Dept. Economics, Stanford Univ.
  • Bapna R., Goes, P. and Gupta, A. (2003). Analysis and design of business-to-consumer online auctions. Management Sci. 49 85–101.
  • Bapna R., Goes, P., Gupta, A. and Karuga, G. (2002). Optimal design of the online auction channel: Analytical, empirical and computational insights. Decision Sci. 33 557–577.
  • Beam, C., Segev, A. and Shanthikumar, J. G. (1996). Electronic negotiation through internet-based auctions. CITM Working Paper 96 WP-1019.
  • Borle S., Boatwright, P. and Kadane, J. B. (2006). The timing of bid placement and extent of multiple bidding: An empirical investigation using eBay online auctions. Statist. Sci. 21 194–205.
  • Bruschi, D., Poletti, G. and Rosti, E. (2002). E-vote and PKI's: a need, a bliss or a curse? In Secure Electronic Voting (D. Gritzalis, ed.). Kluwer Academic Publishers.
  • Croson, R. T. A. (1996). Partners and strangers revisited. Economics Lett. 53 25–32.
  • Dennis, J. E. and Schnabel, R. B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall, Englewood Cliffs, NJ.
  • Efron, B. and Tibshirani, R. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
  • Etzion, H., Pinker, E. and Seidmann, A. (2003). Analyzing the simultaneous use of auctions and posted prices for on-line selling. Working Paper CIS-03-01, Simon School, Univ. Rochester.
  • Gwebu, K., Wang, J. and Shanker, M. (2005). A simulation study of online auctions: Analysis of bidders' and bid-takers' Strategies. In Proceedings of the Decision Science Institute.
  • Haubl, G. and Popkowski Leszczyc, P. T. L. (2003). Minimum prices and product valuations in auctions. Marketing Science Institute Reports 3 115–141.
  • Hlasny, V. (2006). Testing for the occurrence of Shill-bidding (in internet auctions). Graduate J. Social Sci. 3 61–81.
  • Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. Univ. Michigan Press, Ann Arbor, MI.
  • Huberman, B. A. and Adamic, L. A. (1999). Growth dynamics of the World Wide Web. Nature 401 131.
  • Jank, W. and Shmueli, G. (2007). Studying heterogeneity of price evolution in eBay auctions via functional clustering. In Handbook on Information Series: Business Computing (G. Adomavicius and A. Gupta, eds.) North-Holland, Amsterdam. To appear.
  • Kauffman, R. J. and Wood, C. A. (2000). Running up the bid: Modeling seller opportunism in Internet auctions. In Proceedings of the 2000 Americas Conference on Information Systems.
  • Ku, G., Malhorta, D. and Murnighan, J. D. (2004). Competitive arousal in live and Internet auctions. Working paper, Northwestern Univ.
  • Liebovitch, L. S. and Schwartz, I. B. (2003). Information flow dynamics and timing patterns in the arrival of email viruses. Physic. Rev. E 68 017101-1–017101-4.
  • McAfee, R. P. and McMillan, J. (1987). Auctions with stochastic number of bidders. J. Econom. Theory 43 1–19.
  • Menasce, D. A. and Akula, V. (2004). Improving the performance of online auction sites through closing time rescheduling. In The First International Conference on Quantitative Evaluation of Systems (QEST'04) 186–194.
  • Pinker, E., Seidmann, A. and Vakrat, Y. (2003). The design of online auctions: Business issues and current research. Management Sci. 49 1457–1484.
  • Ross S. M. (1995). Stochastic Processes, 2nd ed. Wiley, New York.
  • Roth A. E., Murninghan, J. K. and Schoumaker, F. (1998). The deadline effect in bargaining: Some experimental evidence. American Economic Review 78 806–823.
  • Roth A. E. and Ockenfels, A. (2000). Last minute bidding and the rules for ending second-price auctions: Theory and evidence from a natural experiment on the Internet. NBER Working Paper #7729.
  • Roth, A. E. and Xing, X. (1994). Jumping the gun: Imperfections and institutions related to the timing of market transactions. American Economic Review 84 992–1044.
  • Shmueli, G., Russo, R. P. and Jank, W. (2004). Modeling bid arrivals in online auctions. Robert H. Smith School Research Paper No. RHS-06-001. Available at: http://ssrn.com/abstract=902868.
  • Vakrat Y. and Seidmann, A. (2000). Implications of the bidders arrival process on the design of online auctions. In Proceedings of the 33rd Hawaii International Conference on System Sciences 1–10.
  • Wang, S., Jank, W. and Shmueli, G. (2007). Explaining and forecasting online auction prices and their dynamics using functional data analysis. J. Business and Economic Statistics. To appear.
  • Wilcox, R. T. (2000). Experts and amateurs: The role of experience in Internet auctions. Marketing Letters 11 363–374.
  • Yang, I., Jeong, H., Kahng, B. and Barabasi, A.-L. (2003). Emerging behavior in electronic bidding. Phys. Rev. E 68 016102.
  • Zhang, A., Beyer, D., Ward, J., Liu, T., Karp, A., Guler, K., Jain, S. and Tang, H. K. (2002). Modeling the price-demand relationship using auction bid data. Hewlett-Packard Labs Technical Report HPL-2002-202. Available at http://www.hpl.hp.com/techreports/2002/HPL-2002-202.pdf.

Supplemental materials