Essays on applied economics


Bidding behavior with competing auctions in eBay



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4. Bidding behavior with competing auctions in eBay


Since we have very detailed bidding history for each auction, we can use it to study how bidders bid in face of competing auctions.

The most interesting result we observe is that bidders, even with single unit demand, bid across competing auctions.

In table 3 we report the statistics of the bidders and cross bidders in each sample. For each group of competing auctions, we use a Java program to get all different bidders and all bidders that bid on more than one auction.

We only consider the group of competing auctions with positive bid for at least one auction. In the daily sample, there are 458 such groups of competing auctions. On average, there are 2.28 auctions in each group and the maximum number of auctions in a group is 9. On average, there are 6.56 bidders for each group and 1.53 bidders bid across auctions in the group. On average, 23% of them bid across competing auctions in the group they bid.

In the hourly sample, there are 258 groups of competing auctions with positive bids for at least one auction. The number of different bidders per group is almost the same as that in the daily sample, and slightly few numbers of bidders who bid across auctions in a given group. 21% of the bidders bid across auctions in the group they bid.

In the minute sample, there are only 101 groups of competing auctions with positive bids for at least one auction. On average, there are fewer bidders in each group, with an average of 4.868. And there are 1.48 bidders who bid across auctions in a given group. The proportion of bidders who cross bid is higher than the other two samples, but it is not statistically significant. (The t-statistics for hourly sample and minute sample is 1.33 and the t-statistics for daily sample and minute sample is 1.14).

The data shows that a significant proportion of bidders bid across auctions in a competing group. For auctions with all most the same ending time, significantly higher proportion of bidders bid across competing auctions. The proportion of bidders who bid across competing auctions is not very different for daily sample and hourly sample (with a t-statistics of 0.54).

For competing auctions ending at all most the same time, the strategy for bidders to bid across auction is more effective in avoiding in trapping in highly competitive auctions. However, if there is a significant time difference in ending time, bidders cannot effectively coordinate bidding across auctions.

As documented at Roth and Ockenfels (2000) and Bajari and Hortacsu (2000), bids are clustered at the ending period of the auction. This is also true for our competing auction data. We have information about all the bids and the time the bids are submitted. Figure 3 shows the bid submission time for all auctions in the daily sample.

Bids are clustered at the ending period. Almost all auctions received their last bid in the last several hours. In addition, 28% of the samples receive their last bid within the last 60 seconds.

In Roth and Ockenfels (2000) the reason for delaying bids is that eBay auction has a fixed ending time. If the bids are submitted at the last minute, there is some probability that bids may not be submitted successfully. This can explain the very last minute bidding, but cannot explain late bidding. Roth and Ockenfels (2000) also find that even in auctions like Amazon auctions that have no fixed ending time, there are significant late biddings. Simply bidding late does not have effect that bids might not be submitted successfully. Bajari and Hortacsu (2000) argue that in a common value environment, bidders refrain from bidding earlier to avoid revealing their private information.9

Therefore, it is sometimes argued that early biddings are not serious, and only late biddings are serious. We look at the data of the last day of each auction, with all different bidders in the last day and the different bidders who bid across competing auctions. We use the sample consisting of the groups with at least one auction receiving positive bids in the last day. We find that for all bidders bidding in the last day of the auctions, significantly more bidders bid across competing auctions when the difference in ending time is less than 1 minute. (See Table 4.) For the minute sample, on average, 27% of the bidders in the last day bid across competing auctions, compared to the percentage of 0.20 in the hourly sample and 0.17 in the sample. For the hypothesis of having the same percentage of bidders who bid across competing auctions, the t-test for the minute data and the hourly data is 1.65 and the t-test for the minute data and daily data is 2.52, which is significant at the 0.01 level. And though there is slightly higher percentage of bidders who bid across competing auctions for hourly data than for daily data, the result is not statistically significant, with t-test 1.23.

We may wonder if the cross bidding observed here is only because of the existence of bidders who want more than one item at the same time. There is not a simple way to check directly if a bidder wants more than one item. We use the following methodology: bidders who need more than one item is very likely to be the highest bidders of more than one competing auction. In the first case, we define true cross bidders as all those bidders who bid across competing auctions and who are never the highest bidder of more than one auction at any time (type I). In the second case, we consider true cross bidders as all those bidders who bid across competing auctions and who are not the highest bidders of more than one competing auction in the last day (type II).

The first criterion for true cross bidder is stricter than the second criterion. The second criterion has already excluded all bidders who win more than one competing auctions. Some bidders excluded by the first criterion may still be true cross bidders, since at the early stage of the auctions, bidders may feel safe to be high bidders of more than auction even if they only need one item.

Table 3B reports the result of such considerations. When we exclude those possible bidders with more than one demand, we still observe high percentage of bidders who bid across competing auctions. For the minute data, 28 bidders are high bidders for more than one competing auction in some point of time of auction process and 21 are high bidder for more than one competing auction in some pint of the last day of the auctions. The bidders who truly bid across auctions are 25% in the first criterion and 26% in the second criterion. Similarly, for the hourly data, we observe that among all bidders, 21% of them bid across competing auctions. Apart from those who need more than one item, the percentage of true cross bidder is 18% (first criterion) and 19% (second criterion). For the daily data, we observe 23% of bidders who bid across competing auctions. The percentage of true cross bidders is 21% (under the first criterion) and 22% (under the second criterion).

Another feature of bidding with competing auctions is that bidders tend to bid on the auction with the lowest standing bid. This strategy not only guarantee that a bidder never wins two auctions, it also let bidders to avoid being trapped in very competitive auction. (This also makes the price of the auction become uniform.) We report the result on whether bidders bid on the auction with the lowest standing bid in table 6. 10

When all auctions in a competing auction group are ended except the last one, bids submitted on this last auction thereafter are considered as bidding on auction with the lowest standing bid. This way of calculation tend to increase the number of bids submitted on the auction with the lowest standing bid for group of auctions with big difference in ending time, such as in the daily and hourly sample.

In the daily sample, the average number of bids a group of competing auctions received is 13.29 and the maximum number of bids a group received is 79. The average number of bids submitted on auctions with the lowest standing bid is 8.95 and the maximum number of such bids is 37. For the hourly sample, the average number of bid in a competing group and the average number of bids on auction with the lowest standing bid is roughly the same. The proportion of the bids submitted on the auction with the lowest standing bid is also roughly the same, representing 79% for daily sample and 77% for hourly sample (the t-test for the proportion for daily and hourly sample is 1.10).

For the minute sample, the average number of bids a group receives is relatively less, with a value of 10.89, and the maximum number of bids that a group receives is 7.86. The proportion of the bids submitted on the auction of the lowest standing bid is significant higher, with an average of 87%. The t-test for the minute data and the hourly data is 4.49 and the t-test for the minute data and the daily data is 4.33.

Bidder who bid across competing auctions are more likely to bid on the one with the lowest standing bid. In table 6, we report the result about the proportion of bids submitted by bidders who bid across competing auctions.

In all three samples, there are groups in which some auctions do not receive any bids while others receive positive number of bids. It happens usually that if there is any auction does not receive bids, then other competing auctions either receive no bids or receive only one bid. For same items, there is no reason that bidders bid on auctions with positive bids and not bid on auctions with zero bids. It is interesting to see how often it happens that in a group of competing auctions, some auctions receive no bids while other auctions receive more than one bid. Table 7 reports the result for three samples.

In the daily sample, there are 74 groups of competing auctions with positive bids and with zero bid auctions. 30% of them with auctions receiving more than 1 bid. In the minute sample, there are 20 groups of competing auctions with positive bids and with zero bid auctions. However, only 15% of them have auctions receiving more than 1 bid.

It is obvious from the above analysis that bidders are not following the strategy as in independent second price auction: bid once and bid the true valuation. Bidders are not following the advice form eBay to submit the true valuation and let the proxy to bid for them. The proxy bid mechanism in eBay is believed to save bidders from revising their bid. eBay’s help page about proxy bid explains the proxy bid as the following:
A proxy bid and a maximum bid are the same thing. To place a proxy bid, just enter the maximum amount you are willing to pay. eBay will then automatically bid up to your maximum amount for you. (http://pages.ebay.com/help/basics/e_item1.html)
In table 8, we report the result of the average number of bids a bidder submitted in each group. We only consider the sample consisting of groups with bidders who bid across competing auctions. With competing auctions, bidders do not bid on one auction, but rather on a group of competing auctions. We calculate the bids each bidder submitted on each competing group. There is a tendency that bidders bid more frequently with competing auctions with almost the same time. In the minute sample, on average, each bidder submit 2.24 bids on a group of competing auctions (On average, there are 2.6 auctions in each group. Each bidder bid less than 1 bid on each auction of a group). However, for bidders bidding cross auctions, the average number of bids they submitted on a group is significantly higher. For the minute sample, each bidder who bid across auctions submits 3.97 bids on a given group of competing auctions.

Bid revising can be a consequence of the existence of competing auctions. If there is no bidding cost, bidders should bid with the minimum increment and bid many times. If bidders bid true valuation and bid only once, they may be trapped in very competitive auctions and do not have opportunity to switch to other less competitive auctions. Even if with bidding cost, bidders still revise their bids very often if the cost is not too high compared to the risk of bidding with another high bidding bidder. (They may not always bid the minimum increment, which is too costly).



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