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Article Excerpt
A sequence of bids in Internet auctions can be viewed as record-breaking events in which only those data points that break the current record are observed. We investigate stochastic versions of the classical record-breaking problem for which we apply Bayesian estimation to predict observed bids and bid times in Internet auctions. Our approach to addressing this type of data is through data augmentation in which we assume that participants (bidders) have dynamically changing valuations for the auctioned item, but the latent number of bidders "competing" in those events is unseen.
We use data from notebook auctions provided by one of the largest Internet auction sites in Korea. We find significant variation in the number of latent bidders across auctions. Our other primary findings are as follows: (1) the latent bidders are significant in number relative to observed bidders, (2) the latent number of remaining bidders is considerably smaller than that of new entrants to the auction after a given bid, and (3) larger bid and time increments significantly influence the bidding participation behavior of the remaining bidders. As part of our substantive contribution, we highlight the model's ability to understand brand equity in an Internet auction context through a brand's ability to simultaneously bring in bidders, higher bid amounts, and faster bidding.
Key words: latent bidders; bidding dynamics; record-breaking events; Bayesian inference; data augmentation
1. Introduction
The growing importance of online auctions as exchange mechanisms is evident in the emerging auction literature from economists (e.g., Bajari and Hortacsu 2003, Roth and Ockenfels 2002) to behavioral researchers (e.g., Ariely and Simonson 2003, Greenleaf 2004). We present here a new approach to modeling auction data (the entire sequence of bids and bid times) that relies on merging (yet also modifying) an existing record-breaking literature in statistics (e.g., Carlin and Gelfand 1993) with Bayesian data augmentation methods (Albert and Chib 1993, Tanner and Wong 1987).
Record-breaking data, in which only those data points that break the current record are observed (among those accumulated sequentially over time), have been well-studied in a variety of practical situations such as World and Olympic sporting records (e.g., Carlin and Gelfand 1993, Robinson and Tawn 1995) and meteorological data (e.g., Brown and Katz 1995, Coles and Tawn 1996). Our link to this literature is to note that the arrival of a new bid for an auction item can be considered a "record-breaking event," that is, the current bid has broken the record of the last bid. We note that the record-breaking mechanisms are somewhat different in these two areas, that is, a sequence of bids in auctions are placed by thinking individual bidders, while record-breaking data in the previous literature are realized through stochastic independent events. We thus seek to present a modeling framework that makes these two data structures inherently identical.
While this link is tight, the existing record-breaking literature is deficient to examine auction data in a number of important ways. The literature has been concerned with independent events and a constant (stationary) mean (e.g., Tryfos and Blackmore 1985). In our application area, assuming stable bidder valuations, while commonly assumed in rational economic models (e.g., Guerre et al. 2000, Hendricks et al. 2003), has been questioned in a variety of empirical settings (e.g., Ariely and Simonson 2003, Park and Bradlow 2005). Furthermore, the literature has directly incorporated record-breaking opportunities wherein occurrence times of all failed record-breaking attempts are known (e.g., Carlin and Gelfand 1993). In auctions, however, the assumption of perfect knowledge about the "failures" (unobserved bidders) could be very restrictive, which represents the unique merging of the record-breaking and the data augmentation literature developed here.
We apply the proposed modeling framework of records with unseen intermittent events to auction data in which bid amounts and bid times are analogous to record-breaking events and the event times. Bid amounts (and bid times) are accumulated sequentially and are recorded as long as a bid amount exceeds the outstanding bid. That is, (observed) bid increments have to be greater than zero. Moreover, the number of latent competing bidders, i.e., record-breaking attempts, is not observed (or there exists an unseen competition set as in Bradlow and Fader 2001). Instead, we only observe the largest of the potential bids but not those by the latent bidders. We therefore investigate stochastic versions of the classical record-breaking problem for which we apply Bayesian estimation to predict observed bids and bid times. In this respect, our research appears to be a clear generalization of the research on record-breaking events. To the best of our knowledge, it is the first time the record-breaking paradigm has been applied to auction data.
We note that our stochastic modeling approach differs considerably from the empirical auction literature in economics. Specifically, our research is an attempt to add to the growing body of literature by providing a descriptive and exploratory look at auction data utilizing a flexible and parsimonious stochastic model. We note that our model does not rely on theoretical assumptions of utility maximization or strategic behaviors that have provided a significant path forward in this research area (e.g., Jofre-Bonet and Pesendorfer 2003, Pakes et al. 2005). Instead, our work is meant to extend empirical understanding of bidding behavior and provide a platform by which structural aspects can be incorporated into a stochastic approach. In this vein, the closest paper to ours is Park and Bradlow (2005); however, their work assumes that the competing set of bidders is known based upon similar auctions that are on sale concurrently. In contrast, we stochastically impute the latent competition set, decompose those bidders into new entrants at a given bid and remaining bidders from the previous bid, and derive the distribution of the largest-order statistic (Johnson et al. 1994, 1995) conditionally on having imputed the unseen attempts.
The remainder of the paper is organized as follows. Section 2 gives an overview of the data and describes exploratory analyses. In [section] 3, we provide a detailed specification of our Bayesian model. Section 4 has model results and inferences. Section 5 concludes and suggests future research directions.
2. Data Description
We obtained a database of notebook computer auctions from one of the largest Internet auction sites in Korea. The auction mechanism on this site uses an ascending first-price or English auction in which the highest bidder wins and pays the amount he bids and is essentially identical to the format used by Yahoo!Auctions. The database contains information regarding the complete history of bids, auction design features set by the seller, seller characteristics, and product specifications. The total number of notebook auctions considered here is 218 with 3,124 bids. Thus, on average, there are about 14.33 bids (standard deviation = 11.22), i.e., record-breaking events, per auction. The data set used in this research are a subset of the data used in Park and Bradlow (2005).
There are three auction design variables under the sellers' control: placement (yes or no) of product images on the listing page, minimum bid ("public" reserve price), and auction duration. These variables are used as descriptors and are treated as exogenous. (1) In addition, we utilize seller reputation ratings given by past successful bidders. The rating is in the form of a positive, negative, or neutral response after each transaction, which we operationalize by using log(positive ratings + 1) and log(negative and neutral ratings + 1).
The product specifications contain the following variables: (1) CPU type (Pentium or Celeron), (2) CPU speed, (3) memory, (4) hard disk, (5) screen size, (6) the number of months that the auction item has been used, and (7) brand name. There are two American (Compaq and IBM), two Japanese (Fujitsu and Sony), and two Korean brands (Sambo and Samsung) which account for about 31%, 11%, and 52% of the 218 items, respectively. All the rest of the brands were aggregated and grouped into a category "others." Table 1 reports detailed descriptions of auction design, seller reputation ratings, and product specifications. These variables, along with bid-specific (time-varying) variables to be described, will serve as covariates towards explaining the latent number of competing bidders, the magnitude of new record-breaking events (bid amounts), the bid times, and the variance (dispersion) of the underlying dynamic bidder valuations.
In Internet auctions, incremental bid amounts are of great importance since the key decision by potential bidders centers on how much more to bid. Thus,...
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