Optimal design of the online auction channel: Analytical, empirical, and computational insights

Decision Sciences, Fall 2002 by Bapna, Ravi, Goes, Paulo, Gupta, Alok, Karuga, Gilbert

From the expected revenue expression in equations 1-3, it is clear that the bid increment k = a key determinant of the auction revenue. In this paper we seek to establish calibration mechanisms for the bid increment that optimize the expected auction revenue. A critical parameter necessary to optimize the bid increment is the value of the probability p that a bidder will be able to bid at the next higher bid level above B^sub 0^. To estimate p the auctioneer needs some information on the bidders valuation, a non-trivial task. Using such information, for any given bidding level, the auctioneers can infer the number of bidders who may have valuations for the product that are equal to or higher than the next feasible bid level.

Before we describe the empirical estimation tools, we would like to provide further intuition into the optimization of the expected revenue by setting the optimal bid increment using a numerical example:

Numerical Example 2. Suppose an auction has five items on sale, and the valuations for the highest six bidders are as follows:

Let B^sub 0^ = $110. Without knowing the actual valuation of each bidder, it would be sufficient if the auctioneer knew the number of bidders with a valuation above a certain bidding level. With the set of bidders above, the following table summarizes the relevant information for the auctioneer.

From the table above, it is clear that setting the bid increment at $11 would yield the optimal expected revenue.

The above example assumes that the auctioneer knows the distribution of bidders' valuations a priori. It is common in auction theory to assume some known continuous distribution to which consumer valuations are said to belong. In this study we make use of automated software data collecting agents to track real online auctions, and in doing so build historical repositories of bid patterns that permit the empirical estimation of p values, as well as for making informed distributional assumptions regarding the bidders' valuations. In the next section we explain how we collect data from real online auctions and use it for deriving empirical distributions of the p values. We are also able to fit uniform distributions to the critical fractile of bidders' valuations obtained from the empirical observations. This, in turn, allows us to analytically obtain the optimal bid increment and revenue.

APPLYING ANALYTICAL RESULTS TO REAL AUCTIONS

Data Collection

An automatic agent was programmed to capture, directly from the website, the html document containing a particular auction's product description, minimum required bid, lot size and current high bidders at frequent intervals of 5-15 minutes. A parsing module developed in Visual Basic was utilized to condense all the information pertinent to a single auction, including all the submitted bids, into a single spreadsheet. We tracked over 150 auctions; however, complete bidding data was available for 65 auctions. The screening process was designed to ensure: (1) that there was no sampling loss (due to occasional server breakdowns), and (2) that there was sufficient interest in the auction itself, given that some auctions did not attract any bidders. Data collection lasted over a period of 6 months so as to guarantee a large enough sample-size (> 20) for each of the levels of bid increment chosen ($10 and $20). From the data collected we can construct the bidding history of each bidder who participated in each of the 65 auctions.

Obtaining Empirical Valuation Data

Based on the final bid of each bidder, a valuation is generated for that bidder by adding a random number drawn from U(O, k). For the losing bidders using a pedestrian bidding strategy, this is a rational estimate because the final bid offer can be considered a tight lower bound on the consumer's valuation. If the consumer's real valuation is greater than one bid increment above the final bid, then the bidder should have been able to constitute a new bid and either be in the winners' list or propel the auction to a higher bidding level. For the winners of the auction, these estimates are conservative, because as we saw in section 3, that auction can stop with the N winners not necessarily bidding all the way to close to their real valuation: However, for the purpose of estimating the effect on auctioneers' revenue they may be adequate. Table 2 gives a list of bids on one of the auctions that we observed and the consumer valuations inferred from these bids.