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Abstract
This study aims at contributing towards a theory of bidding dynamics in online reverse auctions.
It takes advantage of two recent developments, one methodological in the form of functional data analysis and one empirical in the form of the availability of detailed bidding data of high-stakes auctions. The availability of this data presents the possibility to ask new questions and test previously untested assumptions of existing theories.
One of these new questions to be investigated is the influence of bidding dynamics on the final outcome of the auctions. Classical auction theory assumes that people have a fixed valuation
(albeit drawn from some distribution) prior to the auction and place their bid based on maximizing their expected utility, given the assumptions about other bidders’ valuations (again drawn from some distribution) and the degree of bidder affiliation. In such a setup, the final outcome of the auction is determined by the a priori calculations of the bidders and there is little to no room for issues of bidding dynamics. Three such issues that remain underinvestigated in extant theory are issues related to when to bid, who bids when and the information that is revealed in placed bids respectively.
These are not just questions of theoretical importance, because some empirical literature has recently appeared that shows some of these aspects may indeed matter in explaining auction behavior in practice. For instance, studies on jump bidding in English auctions (i.e. placing a bid higher than what is necessary to become the current high bidder) have shown that jump bidding is both common as well as effective in winning the auction (Easley & Tenorio, 2004). Relatedly, studies on the role of the starting bid and the bid increment have shown that these have a significant impact on the final price of the auction (Bapna, Goes & Gupta, 2003; Ku, Galinsky &
Murnighan, 2006; Jones & Mithas, 2006). Also, the role of timing and entry into auctions has recently come under scrutiny, particularly the phenomenon of sniping and the general conclusion has been that the timing of bids matters a great deal in explaining auction outcome (Roth &
Ockenfels, 2002; Ariely & Simonson, 2003; Park & Bradlow, 2005; Borle, Boatwright &
Kadane, 2006). Finally, there is experimental evidence that the information revealed during the auction has an influence on the auction outcome (Koppius, 2002; Chen-Ritzo et al., 2006).
Together, these findings are difficult to explain without appealing to some aspect of the bidding process, yet a comprehensive theory of bidding dynamics is still missing.
Part of the reason for this may be the lack of statistical methods to analyze bidding processes.
This is where functional data analysis (FDA) becomes useful. Functional data analysis is a new statistical tool that has been gaining momentum in many application areas (Ramsay & Silverman,
2002; Jank & Shmueli, 2006). FDA is a powerful new tool since it looks at data in a completely new way and thus has the capability to extract new insight from it. FDA operates on functional objects such as curves or shapes rather than on the classical data vectors. In our context, we think of a functional object as the price process between the start and end of an auction. One particular property of these functional objects is their smoothness which allows the researcher to define new data characteristics such as a process' dynamics and associated dynamic models.
In this paper we will take a step towards a theory of bidding dynamics by analyzing a set of 770 reverse auctions conducted in the automotive industry for a wide variety of products and services.
This represents and improvement over previous online auction analyses that have mostly relied on C2C auctions, which, due to the lower stakes and the intrinsic value of ‘playing’ in an auction, a
University of Maryland, b
University of South Florida, c
RSM / Erasmus University

may not exhibit the fully rational behavior postulated by auction theory. In contrast, in these reverse auctions we investigate, the stakes are high, participants are industry experts and considerable effort has been put into preparing for the auction and thus this setting is likely to engender rational behavior (List, 2004) and thus present a stringent test of auction theory.
Our analysis proceeds in three phases. In the first phase, we propose several metrics of auction dynamics that capture various aspects of the competitiveness of the auction. The metrics proposed are: the percentage of jump bids, the number of bidders that at some point in time had the lowest bid, the number of times any bidder was being outbid (an indicator of the endowment effect
(Kahneman, Knetsch & Thaler, 1990) and the concentration of instances of being outbid among a small set of bidders (indication of a bidding war). In the second phase, we use standard econometric techniques to show that these metrics explain the outcome of the auction over and above models that only focus on the auction design parameters. The third phase consists of a more data-driven approach in which we use FDA to investigate the price paths in more detail, for instance the ‘burstiness’ of auctions. We show that different types of price paths exist in these reverse auctions and although a full theoretical explanation of these paths is beyond the scope of this paper, they offer significant potential for expanding our knowledge of auction theory and practice.
References
Ariely, D. and I. Simonson (2003), “Buying, Bidding, Playing, or Competing? Value Assessment and Decision Dynamics in Online Auctions,” Journal of Consumer Psychology, No.13, 113-123.
Bapna, R, Goes, P., Gupta, A., 2003, "Analysis and Design of Business-to-Consumer Online
Auctions ," Management Science, 49: (1), 85-101.
Chen-Ritzo, C., T. P. Harrison, A. M. Kwasnica, D. J. Thomas. 2005. Better, Faster, Cheaper: An
Experimental Analysis of a Multiattribute Reverse Auction Mechanism with Restricted
Information Feedback. Management Science 51(12). Pp. 1753-1762
Borle, S., P. Boatwright and J. B. Kadane. 2006. "The Timing of Bid Placement and Extent of
Multiple Bidding: An Empirical Investigation Using eBay Online Auctions." Statistical Science
(forthcoming)
Easley, RF and R. Tenorio, 2004, "Jump Bidding Strategies in Internet Auctions," Management
Science, October, 50:10, 1407-1419.
Jank W., and Shmueli, G., forthcoming 2006, “Functional Data Analysis in Electronic Commerce
Research”, Statistical Science.
Kahneman, D., Knetsch, J., & Thaler, R., 1990, “ Experimental tests of the endowment effect and the Coase theorem”. Journal of Political Economy, 98(6), 1325-1348.
O. Koppius, 2002, “Information Architecture and Electronic Market Performance,” Ph.D.
Thesis, RSM / Erasmus University.
Ku, G., Galinsky, A. D., & Murnighan, J. K. (in press, 2006). “Starting low but ending high: A reversal of the anchoring effect in auctions”. Journal of Personality and Social Psychology.
List, John A. 2004, "Neoclassical Theory Versus Prospect Theory: Evidence from the
Marketplace," Econometrica, 72(2): pp. 615-625.
Mithas, S. and Jones, J.L. (in press, 2006), "Do Auction Parameters Affect Buyer Surplus in E-
Auctions for Procurement?," Production and Operations Management.
Park, Young-Hoon and Eric T. Bradlow (2005), “An Integrated Model for Bidding Behavior in
Internet Auctions: Whether, Who, When, and How Much," Journal of Marketing Research, 42
(4), 470-482.
JO Ramsay, BW Silverman (2002), Applied functional data analysis : methods and case studies.
Publisher : New York : Springer.
Roth, Alvin E., and Axel Ockenfels., 2002, "Last-Minute Bidding and the Rules for Ending
Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet." American
Economic Review, 92(4), 1093-1103.