A laboratory study of auctions with a buy price.

Durham, Yvonne ; Roelofs, Matthew R. ; Sorensen, Todd A. 等

I. INTRODUCTION

The rapid growth in the use of auction markets on the Internet has led to a number of innovations in auction design. One of these innovations is the development of the buy price. A buy price allows the seller, during the listing of his or her item, to indicate a price at which he or she would be willing to sell. If, during the course of the auction, the buy price is accepted by a buyer, then the usual auction procedure is halted and the item is sold to that buyer for the specified price.

The buy price has been implemented by different online auction sites using various rules. On eBay, the buy price is temporary and is only available to bidders until an initial bid (or, more precisely, a bid that exceeds the reservation value) is made. Yahoo!, which currently only has auction sites active in Hong Kong, Taiwan, and Japan, uses a permanent buy price that is available throughout the auction. Amazon also featured a permanent buy price when its auction site was active. Although both Yahoo! and Amazon closed their respective auction sites in the United States, apparently unable to successfully compete with eBay for a variety of reasons, the fact that the buy price took various forms on these different sites is an interesting phenomenon.

The buy price has proven to be quite popular. In a CNET News.corn article, Kane (2002) noted that 33% of eBay listings worldwide in the second quarter of 2002 featured eBay's version of a buy price (called Buy-It-Now) and that 19% of gross merchandise sales were accounted for by fixed-price sales (both Buy-It-Now prices in auctions and the eBay Stores format). Anderson et al. (2008) studied a sample of 1,177 auctions for a Palm brand personal digital assistant sold on eBay in the late summer of 2001. They found that 49.4% of auctions that ended in a sale were listed with a buy price. The use of a buy price was popular with both high and low volume sellers. Their two high volume sellers (accounting for 28.4% of the auctions) used a buy price 100% of the time. Of the remaining auctions listed by lower volume sellers, 29.4% used a buy price.

The popularity of the buy price raises several interesting questions. What does a seller gain by using a buy price? For example, does it increase revenue? Under what conditions would a buyer find a buy price attractive? How do buyers respond to different buy price types and levels? What incentive is there for an auction house to allow sellers to specify a buy price? Does the use of a buy price affect bid timing or auction efficiency? And finally, our primary question, why would different auction sites use different versions of a buy price? This article is an attempt to gain some insight into these issues through the use of laboratory markets.

The experiments discussed here make use of three types of auctions: auctions with no buy price, auctions with a temporary buy price that disappears once a bid is made, and auctions with a permanent buy price that is available throughout the entire auction. All three types of auctions are examined in the context of two institutions: an ascending-bid auction with proxy bidding, and an ascending-bid auction without proxy bidding. Both auction institutions are implemented with a hard close (a specific ending time for the auction). Finally, when a buy price is available in these markets, its effects are examined at three different levels.

The data from these experiments lead to results in four areas: revenue, bidder utilization, bid timing, and auction efficiency. First, seller revenue is higher in auctions with buy prices than in auctions without, and revenue is higher when the buy price is permanent rather than temporary. This difference between permanent and temporary buy price revenues is most pronounced in the auctions that do not use proxy bidding. Second, auctions that utilize a permanent buy price are slightly more likely to end with the buy price being exercised than those in which the buy price is temporary, and buyers respond to lower buy price levels in the manner one would expect (with lower buy prices being exercised more frequently). Third, we observe that overall, auctions with buy prices exhibit more early bids, and more specifically in the case of proxy bidding, a temporary buy price increases the number of early bids when compared with either no buy price or a permanent buy price. Finally, under certain conditions, auctions with a buy price, either temporary or permanent, lead to a larger percentage of auctions ending efficiently than those without. (1) In auctions with a hard close, with or without a buy price, inefficiency may result from sniping/late bidding. In auctions with a buy price, inefficiency may also arise from the possibility that if both bidders have values high enough to accept the buy price, the low-value bidder can accept it and win the auction. However, if only one bidder has a value high enough to accept the buy price, the inefficiency from sniping cannot occur if the bidder accepts it. The experimental results indicate that a substantial portion of the increase in the percentage of efficient auctions with buy prices is indeed driven by this last case. Furthermore, the outcomes we observe in auctions with the various combinations of permanent or temporary buy prices and the presence or absence of proxy bidding are consistent with the choices in auction design that we see on auction sites such as eBay and Yahoo!

II. LITERATURE

The experiments described here are an attempt to explore buy prices in institutions similar to those that have developed in naturally occurring markets, and are therefore not designed to strictly test any particular theoretical model. However, our study is related to two areas of research: the literature on buy prices and the research exploring the impact of late bidding on auction outcomes. In both cases, these literatures are comprised of theoretical and experimental studies.

A. Buy Prices

Mathews (2004) discusses (as originally described by LabX, a site for buying and selling of scientific equipment) four possible factors that might motivate a buyer to exercise a buy price when it is offered: time discounting, a reduction in price uncertainty, bidder risk aversion, and lower monitoring costs. While the first three of these have been explored in the literature, to our knowledge, the fourth has yet to be addressed. In addition, the theoretical literature on buy prices essentially explores three key factors that might motivate a seller to specify a buy price: buyer and/or seller risk aversion, buyer and/or seller time sensitivity, and the presence of multiple units in sequential auctions. (2) Welfare and revenue implications vary from model to model, as does the type of buy price (permanent or temporary) and the way in which the auction is modeled.

Although seller risk aversion or time sensitivity and the presence of multiple units in sequential auctions are not factors in our experimental environment, many of our bidders did exhibit some degree of risk aversion on a risk questionnaire that was administered during the experiment. This questionnaire will be discussed further in the next section. Additionally, it is possible that time discounting may be present in some form for our bidders, but the fact that subjects are purchasing a fictitious product in auctions that are short in length probably minimizes this effect.

The presence of bidder risk aversion as a motivation for the use of a buy price has been explored theoretically by Budish and Takeyama (2001), Hidvegi et al. (2006), Ivanova-Stenzel and Kroger (2008), and Reynolds and Wooders (2009). In a model of two buyers with independent private valuations drawn from one of two possible values, Budish and Takeyama (2001) find that a risk neutral seller can increase his or her expected revenue by using a permanent buy price when the buyers are risk averse. Both Reynolds and Wooders (2009) and Hidvegi et al. (2006) extend this model to an arbitrary number of bidders and continuous valuation distributions, and find similar results.

Shahriar and Wooders (2007) present the results of an experiment that examines a temporary buy price in auctions with both private and common values. In the private values case, which is the most relevant to this study, the authors find that revenues are higher when a buy price is used, the standard deviation of revenue is lower (especially low and especially high prices happen less often), and efficiency, while slightly lower in the buy price auctions, is not statistically different from the ascending-clock auction.

Ivanova-Stenzel and Kroger (2008) explore a temporary buy price both theoretically and experimentally. An experimental test of their theory reveals that sellers offer buy prices that are below risk neutral predictions and buyers accept buy prices that are too high, resulting in unpredicted sales during the buy price stage. The authors find that incorporating risk aversion into the model can explain bidder behavior, but can only partially explain seller behavior. In a follow-up study, Grebe, Ivanova-Stenzel, and Kroger (2006) find similar behavior when students who have eBay experience participate in auctions set up by the experimenters on the eBay Web site.

Reynolds and Wooders (2009) examine bidder risk aversion in both auctions with permanent buy prices and auctions with temporary buy prices. The auction portion of the game is modeled as an ascending-clock auction in which the highest-valued bidder wins and pays the second-highest value. When bidders are risk neutral, a temporary buy price raises strictly less revenue than the same auction run without a buy price. However, once bidder risk aversion is introduced, expected seller revenue in the auction with a buy price exceeds expected seller revenue in the auction without a buy price for a wide range of buy prices. With a permanent buy price, they find similar results, with risk neutral participants generating the same or lower expected seller revenue in an auction with a buy price, and buyer risk aversion generating an increase in expected seller revenue with a buy price option. In the presence of bidder risk aversion, both types of auctions raise seller revenue for a wide range of buy prices, but when bidders have either constant absolute risk aversion (CARA) or decreasing absolute risk aversion (DARA), the permanent buy price format raises more revenue than the temporary format. In addition, the buy price is accepted with higher total probability in the permanent case.

Finally, while buyer time sensitivity is not directly manipulated in our experiments, it is possible that the participants may have had some preference for shorter auction times as the faster the auctions finished, the sooner subjects would be able to collect their earnings, leave the laboratory, and go on to other things. We do not know the degree to which this may have entered into the subjects' decision-making processes. However, to the extent that it did, it may have implications for auction behavior. (3) Mathews (2004) examines a temporary buy price theoretically and finds that when the seller and/or the bidders are time impatient, a seller can be motivated to choose a buy price that is exercised with positive probability by the bidders. Gallien and Gupta (2007) examine the impact of buyer time sensitivity on auctions with both a temporary and permanent buy price. They find that a seller may increase his or her utility by introducing a buy price option, and that permanent buy prices yield higher predicted revenue than temporary options, but that they also provide additional incentives for late bidding and may therefore not always be more desirable.

B. Late Bidding

In the theoretical literature examining buy prices, the auction has typically been modeled either as an English auction, an ascending-bid auction with proxy bidding, or a sealed-bid second-price auction. Theoretically, these should be strategically and revenue equivalent with risk neutral bidders, as well as 100% efficient. However, experimental results have shown a tendency for bidding to occur above the dominant strategy in second-price auctions, while prices in English auctions tend to converge to the dominant strategy price. (4) In addition, the closing rules of an auction may have an important effect in terms of the amount of late bidding that occurs. In an article examining late bidding in the laboratory, Ariely, Ockenfels, and Roth (2005) find that auctions with a soft close are more efficient than those with a hard close. Given the experimental results, the choices of institution and closing rules for the auction are potentially very important ones.

An interest in the effects of auction closing rules on bidding behavior and auction outcomes has resulted in several empirical papers examining these issues. Roth and Ockenfels (2002) and Ockenfels and Roth (2006) use data from auctions on both eBay and Amazon to examine the effects of the different closing rules. They assert that the difference in closing rules gives bidders more reason to bid late on eBay (hard close) than on Amazon (soft close). Late bidding (sniping) can be a best response to a variety of strategies in an auction with a hard close. For example, a last-minute bid might be a best response to an incremental bidder (someone who continually raises their bid to maintain the status of high bidder) by giving that bidder insufficient time to respond at the end of an auction. This could, of course, result in an inefficient outcome if the losing incremental bidder has a higher value. The authors find that late bidding is substantially more prevalent on eBay than on Amazon. They also find that more experienced bidders bid later than less experienced bidders on eBay, while the opposite is true on Amazon.

The experimental analysis of late bidding and auction closing rules performed by Ariely, Ockenfels, and Roth (2005) finds that under controlled laboratory conditions, the difference in auction ending rules is sufficient to produce the differences in late bidding observed in the field data. They find that the experimental data is consistent with the field data, in that more late bidding occurs with a hard close and experience increases late bidding in hard close conditions and decreases late bidding in soft close conditions. And as discussed earlier, the data also indicate that the soft close auctions are more efficient than the hard close auctions (85% as opposed to approximately 70%). Using field experiments, Ely and Hossain (2007) and Gray and Reiley (2007) find little or no significant benefit to buyers from sniping/late bidding. Houser and Wooders (2005) find that soft close auctions yield significantly more seller revenue. Given that our auctions are all hard close, we expect late bidding to play a significant role.

III. METHODOLOGY AND EXPERIMENTAL DESIGN

A. Methodology

This study is an exploration into the revenue, utilization, bid timing, and efficiency differences that arise when using a permanent or temporary buy price and how these differences are affected by the presence or absence of proxy bidding in a controlled laboratory setting. The study was originally motivated by the question of why two of the most popular Internet auction sites in the United States at the time, eBay and Yahoo!, had introduced two different versions of a buy price, eBay's buy price is temporary, available only until a first bid is made, while Yahoo!'s was permanent, available until the auction ended. Why did both auction sites introduce a buy price, and why were they of different forms?

In an attempt to explore these questions, the laboratory auctions reported here were run in two different institutional settings. A simple English auction was used in the first set of experiments. In the second set of experiments, a version of proxy bidding, similar to that used on eBay, was introduced. In this setting, bidders privately submit a "highest bid" to the system. The computer then bids for the buyer by increasing the current bid by the given bid increment as long as it is less than the buyer's "highest bid." The unit is sold to the highest bidder. If the bidder submits her value as her "highest bid," this proxy bidding institution essentially becomes a second-price auction. Both types of auctions were run with a hard close. The first institution was chosen because the initial goal was to explore the difference between a temporary

ABBREVIATIONS

BPE: Buy Price Eligible

CARA: Constant Absolute Risk Aversion

DARA: Decreasing Absolute Risk Aversion

doi: 10.1111/j.1465-7295.2011.00423.x

Durham: Department of Economics, Western Washington University, Bellingham, WA 98225. Phone 360-650-7947, Fax 360-650-6315, E-mail vonne.durham@ wwu.edu

Roelofs: Associate Professor, Department of Economics, Western Washington University, Bellingham, WA 98225. Phone 1-360-650-7947, Fax 1-360-650-6315, E-mail matthew.roelofs @ wwu.edu

Sorensen: Department of Economics, University of California Riverside, Riverside, CA 92521. Phone 520-204-5017, Fax 951-827-5685, E-mail todd.sorensen@ucr.edu

Standifird: Schroeder Family School of Business Administration, University of Evansville, Evansville, IN 47722. Phone 812-488-2866, Fax 812-488-2872, E-mail ss500@ evansville.edu

and permanent buy price in a single institution that captured many of the characteristics of both eBay and Yahoo!. While an English auction with a hard close does not replicate exactly the auction characteristics of either site, it captures many of the characteristics that were common to both. A hard close was used as both auction sites had hard closes as a default (a Yahoo! seller could opt for a soft close if desired). Although the choice of a hard close may have a significant effect on the experimental results, particularly given the empirical evidence on late bidding when a hard close is used, it was a deliberate choice made in order to better reflect the institutions used on these sites. We chose not to use proxy bidding initially because although eBay auctions are run with proxy bidding, Yahoo!'s site gave the buyer a choice between using a proxy bidder and simply bidding for themselves. This, in addition to the argument made by many that most bidders do not use eBay's proxy bidding as instructed, instead bidding "'tit-for-tat' throughout the term of the auction" (Eglinton 2006), caused us to forego proxy bidding in our first set of experiments. Steiglitz (2007) also provides anecdotal support for bidder misunderstanding of the rules of eBay (and what proxy bidding entails), indicating that he has personally encountered several eBay participants who believe that the posted price is the current highest bid. If there are a significant number of bidders who have this basic misunderstanding of eBay's rules, it may well be that the behavior of subjects participating in an English auction with a hard close can give us some important insights into the behavior of actual eBay bidders.

After observing the results from the first set of experiments, we decided to further explore the effects of a buy price in a setting that more closely matches that of the institution used by eBay, the current market leader in the United States. To achieve this goal, our second set of laboratory auctions were run as ascending-bid auctions with proxy bidding and a hard close. As discussed in the previous section, the use of a hard close in these Internet auctions has some important implications. Steiglitz (2007) posits that the use of a hard close in Internet auctions is the natural result of an attempt to modify the typical English auction to an Internet auction setting in which all buyers are not present at the same time and are, instead, able to visit the site and bid at their leisure. This necessitates a specific beginning and ending time of the auction. Lucking-Reiley (2000) argues that a hard close poses an incentive problem for the bidders and destroys one of the important features of the English auction--that of a dominant strategy by the bidders to bid their value. He suggests that submitting a bid just before an auction ends dominates submitting the same bid early in an ascending auction with a hard close, and that if all bidders were to recognize this and follow this strategy, the game would be equivalent to a first-price, sealed-bid auction. He discusses two possible solutions for this problem--the introduction of proxy bidding and the implementation of a soft close by allowing small time extensions to the auction deadline until bidding stops. While we do not know what the true motivations were for their decisions, both eBay and Yahoo! introduced one or both of these solutions into their auctions, eBay implemented the proxy bidding solution, while Yahoo! provided each of these as options in its auctions.

Steiglitz (2007) also provides a discussion of a different possible motivation for eBay's combined use of proxy bidding and a temporary buy price. He maintains that eBay's use of proxy bidding as well as a temporary buy price are both efforts to attract more buyers (and in turn more sellers) to the site by encouraging early bidding. He claims that there is a much stronger disincentive against early bidding in a first-price auction than in eBay's proxy bidding auction, and that with a temporary buy price, an interested bidder may meet the opening bid more quickly simply to remove the possibility that the item is snatched up at the buy price by another bidder. He maintains that because it is more fun for bidders if they bid early, these two characteristics attract more buyers to the site and are an important part of eBay's success. "The driving force behind eBay, despite the prevalence of sniping, is the excitement and competition stimulated by early bidding. Otherwise it might as well be run as an ideal second-price, sealed-bid sale" (Steiglitz, 2007, 78).

B. Experimental Design

A total of 48 subjects participated in eight experimental sessions. The sessions were run during a series of summer quarters at Western Washington University between May 2005 and October 2009. Subjects were students recruited from various economics courses. Each session lasted approximately 90 minutes, and the average payment was $22.23. Instructions (including screen shots) are available upon request from the authors.

During each session, six subjects participated as buyers in auctions conducted in four 10-period blocks, for a total of 40 auctions during each session. As indicated above, the auctions were one-sided, ascending-bid auctions with a hard close. Each experimental session consisted of two auction stages, first a Baseline Stage and then a Treatment Stage. The Baseline Stage consisted of a set of auctions in which no buy prices were offered, while the Treatment Stage was made up of auctions in which buy prices were offered at various levels. (5) All auctions in each experimental session were run under a single institution, either an ascending-bid auction with proxy bidding (PROXY) or an ascending-bid auction without proxy bidding (NOPROXY). (6) Upon completion of the two auction stages, the subjects completed a risk questionnaire similar to Murnighan, Roth, and Schoumaker (1988), designed to gain some insight into their risk preferences. (7) The subjects were paid for one randomly determined decision on the questionnaire. A description of the two auction stages follows.

The Baseline Stage consisted of a block of 10 auctions in which no buy prices (NO) were offered. In this stage, the six subjects were randomly assigned values from a uniform distribution [1,100] and were randomly assigned to one of three auctions. There were three auctions running each period, each with two subjects. Each period (auction) lasted 60 seconds, and the unit was sold to the highest bidder in each auction. Subjects were not allowed to bid above their assigned value.

The Treatment Stage of each session consisted of three 10-period blocks that were run in the same manner as the Baseline Stage auctions, except for the addition of a buy price. In four of the sessions, the buy price was permanent (PERM) and remained available throughout each auction. In the other four sessions, the buy price disappeared (TEMP) as soon as one of the two participating buyers made a bid. We will refer to PERM and TEMP as "Buy Price Types." In addition to these different buy price types, the level of the buy price was also varied as a sub-treatment. The buy price was either "high," "medium," or "low" (75, 50, or 25). The order in which each of these blocks appeared was randomized. We will refer to these as "Buy Price Levels." As we did not have information on risk preferences prior to the auctions, no attempt was made to calculate optimal buy prices.

The auctions were run in 10-period blocks in order to make comparisons across treatments consistent. To achieve this consistency, the subject values and matchings were randomly generated during the 10-period block in the Baseline Stage. (8) In each of the Treatment Stage blocks, the randomly chosen buyer values and matchings were repeated, but were assigned to different subjects. Therefore, the same buyer values/matchings were used for each period across blocks, but the subjects who were assigned these values and matchings were different. (9) The pairing of buyers to one of three automated sellers was also adjusted to keep the value pairings consistent.

The three 10-period blocks used in the Treatment Stage allow the high, medium, and low buy price to be offered to each value pairing. (10) Therefore, each pair of values, although assigned to different subjects, can be observed for each session without a buy price and then with the buy price set at high, medium, and low levels. Table 1 summarizes the experimental design. Note that there are 30 observations per session in the Baseline Stage and 90 observations per session in the Treatment Stage. (11)

IV. RESULTS

A. Revenue

The effects of a buy price on revenue will certainly be important to sellers, and therefore to an auction house that wishes to attract more sellers. Table 2 gives summary statistics on revenue across institutions (the POOLED category combines PROXY and NOPROXY) and treatments (PERM and TEMP), presented in deviations from the baseline auctions without a buy price. We present the data in deviation form because there is evidence of significant variation across sessions in our data, and as we have a common set of auctions without a buy price that exists in every session, we can use that baseline to control for session-level differences. (12) These results show that in most cases average revenue is higher with buy prices than without, the exception being NOPROXY auctions with a temporary buy price. As one might expect, the low buy price of 25 results in lower revenue across all institutions and treatments. Finally, Table 2 also shows that PERM auctions generally have higher deviations from the baseline than do TEMP auctions, indicating that a permanent buy price results in higher prices than does a temporary one, though it should be noted that this result is driven by the NOPROXY auctions and reverses (though the magnitude is smaller) in the PROXY case.

Figures 1 and 2 present empirical density functions of all the revenue data for all buy price types, levels, and institutions. The figures again make use of our experimental design by showing deviations of revenue obtained in the treatment (PERM or TEMP) from the average revenue obtained in the baseline (NO) in the same session. In Figure 1, the vertical axis is the density of prices at each deviation level as measured on the horizontal axis. Results are reported in the top row for all buy prices combined (360 observations per treatment), and in the other three rows, for buy prices of 25, 50, and 75 individually (120 observations each for PERM and TEMP). Note that in most cases PERM generates larger positive deviations than TEMP (as evidenced by more and taller bars to the fight of zero). This implies that when controlling for differences across sessions, prices are higher under PERM than TEMP (as reported in Table 2 and tested formally in Table 3 below). (13)

In Figure 2 we report price deviations across institutions. The primary result here is that while the difference between the PERM and the TEMP treatment is the same as in Figure 1, if we break that comparison down by institution, we see that while in the NOPROXY auctions PERM generates larger deviations than TEMP, in the PROXY auctions there appears to be little difference. Again, we report formal tests of these relationships in Table 3. (14)

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Table 3 reports six fixed-effects regressions (each row in the table is a separate regression) with comparisons of each of the buy price types to the baseline case, as well as a comparison of the two buy price types. (15) This analysis is conducted for the pooled data as well as for PROXY and NOPROXY individually. In the table, the PERM and TEMP columns show

estimates of the [[beta].sub.i]s and their associated p values from a regression of the form:

(1) [P.sub.ij] = [[beta].sub.0] + [[beta].sub.PERM] x [PERM.sub.ij] + [[beta].sub.TEMP] x [TEMP.sub.ij] + [Session.sub.j] + [[epsilon].sub.ij]

where [P.sub.ij] is the price in the ith auction in session j, and PERM and TEMP represent the two different buy price types. We model the price as being determined by the buy price type, a set of session unobservables that are controlled for with fixed-effects estimation, and an auction-specific error term. The "PERM versus TEMP" column reports the difference between the estimates of [[beta].sub.PERM] and [[beta].sub.TEMP] and gives the significance for a test that the two are equal. The "Data" column indicates which set of data is being analyzed. "All Auctions" includes every auction, regardless of the buy price level (25, 50, or 75). The row labeled BP = 50 or BP = 75 eliminates the suboptimal buy price of 25. (16) In all cases, the auctions without a buy price are included in order to identify the fixed effect of each session. Finally, the "Institution" column indicates whether the regressions were run for data pooled across institutions (POOLED) or broken down by institution (PROXY or NOPROXY).

The results vary depending on the subsets of the data examined, but there are some general patterns worth mentioning. First, as noted in the summary statistics and figures above, PERM generates higher revenue than NO (see estimates of [[beta].sub.P]). This is true in every case for all data subsets and is strongly significant in all cases. Second, if we ignore the auctions with a buy price of 25 and use the "BP = 50 or BP = 75" subset, the TEMP auctions also generate higher revenue than NO auctions (though significant at only 12.5% in the PROXY institution). (17) Most importantly, the third column in Table 3 presents the results of an F-test that compares the PERM and TEMP coefficients and tests whether the difference between the two is statistically different from zero. In the pooled data, this test indicates that PERM generates higher prices than TEMP, though the difference is not statistically significant at the 10% level. If we break the results down by institution, the data show that in PROXY auctions, PERM and TEMP are equally effective at raising revenue (p values on the difference between PERM and TEMP of .998 for "All Auctions" and .756 for "BP = 50 or BP = 75"). In NOPROXY auctions, however, PERM is clearly a better choice as the sign of the difference is positive and highly significant with estimates of 9.78 and 8.89 and p values around 1%. (18) Taken together, these results are interesting as eBay's auctions combine proxy bidding with a temporary buy price while Yahoo!'s approach was auctions without proxy bidding (although it was an option) combined with a permanent buy price. (19)

B. Bidder Utilization of a Buy Price

In discussing a bidder's utilization of a buy price, it is important to distinguish between bidders whose use of the buy price is precluded by a low-value draw and those whose use is not. Because buyer values in these auctions were randomly generated, it is possible that one, or even both bidders in an auction may not have been able to take advantage of a buy price. If a bidder's value is greater than the buy price, we will call that bidder "Buy Price Eligible" or BPE. Table 4 gives the breakdown of numbers of BPE bidders in a given treatment across buy price levels. The notation 0, 1, or 2 refers to the number of BPE bidders (e.g., TEMP 1 includes only those auctions in TEMP with exactly one BPE bidder). (20)

In considering how often buy prices are utilized by the bidders, there are three related questions: (1) does buy price utilization vary between buy price types, (2) does buy price utilization vary across institutions, and (3) how does buy price utilization vary with buy price level? Table 5 shows the percentage of auctions in which the buy price was used by the buyer in both the aggregate (across all categories of eligibility), as well as broken down into subsets by the number of BPE bidders and buy price level.

These summary data generate three results. First, buy prices are used more frequently as the number of BPE bidders increases in every case except for TEMP/NOPROXY with a buy price of 25. Second, with only one exception (PERM 2 under NOPROXY with a buy price of 75), low buy prices are used more frequently than higher ones. Finally, at least for the column in which we group all three buy prices together (OVERALL), we see that permanent buy prices are used slightly more often than temporary ones regardless of institution. It is also interesting to note that, again for the OVERALL statistics at least, buy prices are used more often in NOPROXY than in PROXY.

To further quantify these effects, Table 6 presents the results of three probit regressions in which the dependent variable is 1 if an auction ended with the buy price being accepted by the winning bidder and 0 otherwise. The explanatory variables are an indicator that is equal to one if the auction has a permanent buy price (PERM), an indicator that is equal to one if the number of BPE bidders is 2 (BPE = 2), and indicators for buy price levels of 25 and 75. The omitted group, therefore, is TEMP 1 with a buy price of 50.

From these regressions, it can be observed that buy price type is not particularly important in determining buy price utilization (the coefficient on PERM does have the expected positive sign, but is not statistically significant), that utilization is more likely in those auctions with more competition in the form of two BPE bidders, and that utilization is highest for a buy price of 25 and lowest for a buy price of 75, when compared to the reference group of 50. (21)

C. Bid Timing and Efficiency

Issues of bid timing may be important to an auction house wishing to attract more buyers, which in turn attracts more sellers, to its site. It may very well be the case, as Steiglitz (2007) asserts, that buyers enjoy the auction experience and are attracted to sites where there is more early bidding instead of ones in which there are mainly a rush of bids at the end of the auction. In addition, bid timing may impact whether auctions are efficient (i.e., whether the high-value bidder wins the item). While auction efficiency may not be the primary concern for either buyers or sellers, it seems reasonable that both would prefer to use an auction site that is fair and predictable (i.e., one where auctions are likely to end efficiently). Therefore, an auction house that wishes to attract more buyers and sellers would have an incentive to encourage auction efficiency. For both of these reasons, an examination of bid timing, efficiency, and any links between the two is important.

Bid Timing. Data on bid timing is presented in Figure 3. This figure shows the number of bids made during each of 20 equal-length intervals during the auctions, both by institution and buy price type.

It is clear in the figure that there is more early bidding in auctions with buy prices, regardless of the type, than those without (note the greater number and taller bars to the left). This result is stronger for TEMP than PERM in the pooled data and when looking only at PROXY, the difference is quite dramatic, with TEMP generating roughly 2.5 times more early bidding than PERM. (22) This may be one of the reasons why eBay combines a temporary rather than a permanent buy price with its proxy bidding institution. In the case of NOPROXY, the difference between the amount of early bidding with TEMP versus PERM is much smaller. (23) So Yahoo!'s choice of a permanent buy price likely resulted in a smaller decrease in early bidding than if it had used the proxy bidding institution.

In addition to the early bidding evident in auctions with a buy price, there is also a large amount of late bidding that occurs in all auctions, even those without buy prices. In general, once past the first few seconds of an auction, a typical 3-second block contains roughly 2-3% of bids in any given auction. This is quite small when compared to the amount of bid activity in the final 3 seconds where, in the pooled data, 20% of NO, 15% of TEMP, and 20% of PERM bids occur. This is an important observation as increased late bidding has been associated with decreased efficiency in previous studies.

Efficiency. Table 7 presents the percentage of auctions that are efficient across treatments and institutions, both in the aggregate and also broken down by buy price eligibility and buy price level. It is clear from this summary data that the number of BPE bidders is an important determinant of auction efficiency. In all cases, auctions with one BPE bidder are the most efficient and those with two BPE bidders are the least efficient. Efficiency results across buy price levels show no discernible pattern. (24)

[FIGURE 3 OMITTED]

The efficiency percentages in Table 7 may well be driven by the choice of closing rule in these auctions. As discussed earlier, a hard close may lead to an increase in the incidence of sniping or late bidding behavior, and previous research (Ariely, Ockenfels, and Roth 2005) has shown that soft close auctions tend to be more efficient than hard close auctions. Because the auctions in this set of experiments were all hard close auctions, the presence of sniping or late bidding is not unexpected. Note that in the NO auctions, approximately 70% of the auctions are efficient, which is nearly identical to what Ariely, Ockenfels, and Roth (2005) find in their hard close auctions. (25)

To examine the possible connection between late bidding/sniping and efficiency, the presence of sniping was defined, albeit somewhat arbitrarily, as a winning bid that was submitted in the last 3 seconds of an auction (including auctions that ended with a buy price acceptance). (26) With this definition, the incidence of sniping in the pooled data is 56% for NO, 24% in TEMP, and 31% in PERM. There is, however, significant variation between PROXY and NOPROXY, with dramatically less late bidding in PROXY. For NOPROXY, the percentages of auctions with a winning bid in the final 3 seconds are 81% in NO, 40% in TEMP, and 38% in PERM, while in PROXY, the same percentages are 33, 8, and 23%. (27) Finally, in the pooled data, NO auctions are efficient 73.1% of the time when sniping is not present and only 66.9% of the time for auctions that end with sniping, though this difference is not statistically significant. (28) If we examine the relationship between efficiency and late bidding in the individual institutions, we find that sniping does, in fact, lead to less efficient outcomes in NOPROXY, but has no significant effect on efficiency in PROXY. (29)

Given the evidence of widespread and highly variable late bidding across institutions, Table 8 presents a final set of probit regressions that explore the role of buy price type, as well as the number of BPE bidders with regards to efficiency. Each estimation is run for three subsamples of the data, based on the number of BPE bidders. In each estimate, we include fixed effects for both session and value pairing to control for unobservable effects in these two dimensions. (30) The inclusion of the number of BPE bidders is necessary as there are two possible ways in which an auction with a buy price can be inefficient--either the low-value bidder can win the auction (usually via sniping) in normal bidding or the low-value bidder can win the auction by using a buy price. In the auctions with two BPE bidders, either of these effects is possible, while in the auctions with zero or one BPE bidder, only the sniping effect can happen. In addition, in the case of one BPE bidder, if that bidder uses the buy price to end the auction early, the result will certainly be efficient as she is the high-value bidder, and the potential for distortionary sniping at the end of the auction is removed.

As usual, the NO auctions serve as the control group. It is unclear whether a given NO auction should correspond to the case of 0, 1, or 2 buy price eligible bidders, as there is no buy price for comparison. To address this issue, we use all NO observations in the estimation and then include fixed effects for each value pairing, even though in some cases there is no corresponding value pair in the treatment. (31) Thus, our estimate of the treatment effect for a given number of

BPE bidders is identified by within variation for each value pairing.

The potential effects of buy price eligibility suggested above hold true in all three sets of regressions, though they vary in strength across institutions depending on the type of buy price used. In the case of the pooled data, of the four estimates with 0 or 2 buy price eligible bidders, three show no statistically significant effect on efficiency when compared to the baseline auctions without a buy price. The exception is PERM with 0 BPE bidders where efficiency is 5.3% more likely. Most importantly, in the cases with one BPE bidder, auctions are 11.6% more likely to be efficient under PERM and 15.1% more likely to be efficient under TEMP, when compared to NO.

When making the same comparisons individually for PROXY and NOPROXY, the results are not quite as clean, but they do show that the best results in terms of increased probability of an auction ending efficiently come when TEMP is combined with PROXY (a 25.0% increase) and in the case where PERM is used with NOPROXY (an 18.7% increase). These combinations are, of course, the ones that have been observed in actual online auctions on eBay and Yahoo! (32)

The differences seen in the percentage of efficient auctions across treatments, and especially across variations in buy price eligibility, suggest an interesting alternative explanation for the presence and popularity of the buy price option. The theoretical literature has offered a number of possible explanations for the presence of a buy price, including time discounting, risk aversion, etc. One shortcoming of the theory, however, is that it typically assumes that auctions without a buy price are efficient. This is a result that, although easy to show theoretically, does not hold in the data here. The most likely culprit for the reduced efficiency in auctions without a buy price is sniping, and although sniping can still occur in auctions with a buy price, in some settings, a bidder's acceptance of a buy price could mitigate the sniping effect to some degree. This is especially true if the buy price is set such that only a few of the highest value bidders would be buy price eligible. So, it is possible that the development of a buy price option in online auctions with a hard close is, in part, a desire to improve efficiency in the face of sniping behavior.

Both the additional early bidding and improved efficiency that may accompany the use of a buy price may be important motivating factors for the introduction of buy prices in online auctions. Most notably, the combinations of institutions and buy price types that we find to be most effective in promoting early bidding and/or efficiency in the data are the same as those observed in actual online auctions.

V. CONCLUSION

This article is an attempt to gain some insight into why different auction sites would use different versions of a buy price. The experiments discussed here make use of three types of auctions: auctions with no buy price, auctions with a temporary buy price, and auctions with a permanent buy price. All three types of auctions are examined in the context of two institutions: an ascending-bid auction with proxy bidding, and an ascending-bid auction without proxy bidding.

The data from these experiments lead to four basic results. First, the introduction of a buy price may be an attempt to increase seller revenue as revenue is higher in auctions with buy prices than in auctions without. When the auctions are run without the use of proxy bidding, more revenue is generated using a permanent buy price rather than a temporary one. However, in auctions run with proxy bidding, permanent and temporary buy prices are equally effective at increasing revenue. Second, auctions that utilize a permanent buy price are slightly more likely to end with the buy price being exercised than those in which the buy price is temporary. As would be expected, there is a negative relationship between the buy price level and the frequency with which buyers exercise it. Third, we observe that overall, auctions with buy prices exhibit more early bids, and specifically, in the case of proxy bidding, a temporary buy price increases the number of early bids when compared with either no buy price or a permanent buy price. We also find that there is a significant amount of sniping/late bidding in these auctions, with more sniping in the auctions without proxy bidding than those with proxy bidding. Finally, buy prices may also serve to increase auction efficiency. The experimental results indicate that a substantial portion of the increased efficiency of auctions with buy prices is driven by the case of auctions with one buy price eligible bidder in which the possible inefficiency caused by sniping can be mitigated by the acceptance of the buy price.

The results from these experiments indicate that auction houses may have the incentive to introduce a buy price option in order to increase seller revenue, the number of early bids, and auction efficiency, all of which may contribute to a more attractive site for both buyers and sellers. In addition, the specific combinations of institution and buy price types that are implemented may also have important implications. The results from this study indicate that with proxy bidding, temporary and permanent buy prices are equally effective at raising revenue, but temporary buy prices result in more early bidding. So eBay's choice of combining a temporary buy price with proxy bidding seems appropriate if it is concerned with both seller revenue and early bidding. Additionally, without proxy bidding, a permanent buy price generates more revenue than a temporary one, and while less early bidding occurs with the permanent buy price than with a temporary one, the difference is quite a bit smaller than it is with proxy bidding. In light of this, Yahoo!'s default combination of a permanent buy price without proxy bidding also seems reasonable.

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(1.) An auction is defined as efficient if the high-value bidder wins.

(2.) These motivations have been explored by Budish and Takeyama (2001), Mathews (2003, 2004), Kirkegaard and Overgaard (2004), Hidvegi et al. (2006), Mathews and Katzman (2006), Gallien and Gupta (2007), Caldentey and Vulcano (2007), Ivanova-Stenzel and Kroger (2008), and Reynolds and Wooders (2009), to name a few.

(3.) The impact here is likely minor. As each period was comprised of three concurrent auctions, a buy price had to be exercised in all of them for the period to end prematurely.

(4.) See Kagel and Roth (1995) for a summary of experimental results.

(5.) Four additional sessions were run in which the Treatment Stage occurred prior to the Baseline Stage (all without proxy bidding). The motivation behind these sessions was to determine if there were any ordering effects related to subjects participating in the auction without a buy price before moving on to the buy price case. The results indicate that there are indeed ordering effects. However, as our focus here is on different types of buy prices, and as auctions with buy prices are more complicated than those without (particularly in the case of proxy bidding), we have chosen to include only those sessions in which subjects were able to gain experience in a simpler environment before moving to a more complicated one with buy prices.

(6.) All auctions were run using the zTree software package (Fischbacher 2007).

(7.) The questionnaire consists of 15 choices between a sure payment of 10 experimental dollars and a lottery, with a consecutively increasing probability of earning 0 and decreasing probability of earning 20 experimental dollars. Subjects were paid for one randomly determined choice. The eighth choice on the questionnaire involves a fair gamble--a lottery with a 50/50 chance of earning 20 experimental dollars or 0 experimental dollars. Asking each subject to identify whether he or she would prefer the sure payment of 10 experimental dollars or participation in various lotteries allows us to classify participants as being more or less risk averse. We classify someone who would not accept the fair lottery as being risk averse. Someone who is willing to accept an even riskier gamble is more risk loving. Out of 45 subjects, 38 were not willing to accept the fair gamble. Four subjects were willing to accept the 50/50 lottery but were unwilling to accept the next (45/55) lottery. The remaining three subjects waited to switch to the sure thing at choice #11 (35/65) or higher.

(8.) The values are listed in material available upon request from the authors.

(9.) For example, in the first period of the Baseline Stage, Buyer 2 had a value of 77 and was paired with Buyer 5 who had a value of 58. During the first period of the first block in the Treatment Stage, Buyer 3 was assigned the value of 77 and was paired with Buyer 6 who had a value of 58. During the first period of the second block in the Treatment Stage, Buyer 4 was assigned a value of 77 and was paired with Buyer 1 who had a value of 58, and so on. This progression was continued for the second and third blocks of the Treatment Stage as well.

(10.) During each period of the first block in the Treatment Stage, the buy price was randomly drawn as either high, medium, or low. During each period of the second block in the Treatment Stage, the buy price was a random selection from the two possible remaining levels for that period, and during each period of the third block of the Treatment Stage, the buy price was the only possible remaining level for that period.

(11.) There was one instance in the TEMP treatment where a buy price was miscoded as 15 rather than 50. This observation was discarded leaving 359 auctions in the TEMP treatment.

(12.) The average prices for baseline (NO) auctions across the four NOPROXY sessions were 22.0, 30.3, 35.1. and 43.1. For the PROXY sessions, prices in the NO auctions averaged 22.6. 23.5. 26.0, and 27.8. The one case where it is not possible to control for these differences is when we are making cross-institutional (PROXY vs. NOPROXY) comparisons. As our design has a given set of subjects participating with multiple buy price types but in only one institution, our estimates of institution effects will necessarily be between session.

(13.) In addition to the regression analysis presented in Table 3 below, a series of Kolmogorov-Smirnov tests were used to determine which distributions of adjusted prices were different from others. These results largely agree with the parametric results in Table 3. In particular, we find that a comparison between the rows of Figure I (e.g.. between a buy price of 25 and 50 in PERM or between a buy price of 50 and 75 TEMP) results in significant differences in all cases (all tests are significant at better than 1%). When looking across the columns of Figure 1 (e.g., the comparison between TEMP and PERM overall and at various buy price levels), we find that adjusted prices are higher in PERM in all but the case where the buy price is equal to 75 (again all tests are significant at better than 1% except for the buy price of 75 where the p value is .306).

(14.) As before, we supplement our regression results with Kolmogorov-Smirnov tests to look for differences in these distributions. Most relevant to the results presented in Table 3, we find that the non-parametric tests that compare across columns in Figure 2 show that TEMP produces lower prices for the pooled data as well as for each institution individually (p values are .000 for the pooled data, .019 for PROXY, and .000 for NOPROXY). Also, we do find that the PROXY and NOPROXY distributions differ (comparing rows 2 and 3) for both buy price types (p values of .000 in each case).

(15.) The within-design used here means that observations within sessions may not be independent from one another. The fixed-effects specification controls for potential session-level variation in the first moment of prices and we account for any variation in the second moment by clustering our standard errors by session. Note that the standard errors become smaller after we cluster. While it is common for standard errors to obtain larger after clustering, they can go up or down. Furthermore, there is a potential concern about the validity of clustering with small numbers of clusters. We address this possibility by also testing our hypotheses using standard non-parametric tests to explore the robustness of our results. A two-sample Komolgorov-Smirnov test at the session level indicates that PERM and TEMP always produce prices that come from different distributions. This is true for both "All Auctions" and "BP = 50 or BP = 75" as well as the pooled, PROXY, and NOPROXY data.

(16.) Reynolds and Wooders (2009) calculate the certainty equivalent payment, [[delta].sub.0](v), for a bidder. This is the payment that would make a bidder with value v and index of risk aversion [alpha] indifferent between winning the auction (and making a random payment between the reserve price and the maximum of the other bidders values) and winning and paying the certain amount of [[delta].sub.0](v). When bidders are risk neutral, this certainty equivalent is determined by [[delta].sub.0](v) = E(max{r, y}|v [less than or equal to] y [less than or equal to] v), where r is the reserve price, y is the maximum value of the other bidders, and [v.bar] and [bar.v] are the minimum and maximum possible values, respectively. With the parameters used in these markets, [[delta].sub.0]([bar.v]) = 50. When bidders are risk averse, Reynolds and Wooders (2009) find that a sufficient condition for a buy price to increase expected revenue in TEMP is that the buy price be strictly greater than [[delta].sub.0]([bar.v]). In PERM, the buy price must be greater than or equal to [[delta].sub.0]([bar.v]). As a buy price of 25 does not satisfy either of these conditions, it is suboptimal from the perspective of the seller.

(17.) In addition, recall that we also ran a series of sessions under the NOPROXY institution in which the treatment (PERM or TEMP) was run first, followed by the baseline NO auctions. We can use these "backward" sessions to control for any possible order effect created by running the baseline first. When we control for order in this fashion and combine all the NOPROXY auctions together, we find the same qualitative results as reported here where we use only those auctions in which the baseline was conducted first. Finally, as our main locus is on the comparison of TEMP and PERM, we reel that it is more appropriate to make that comparison by giving our subjects experience first via the baseline auctions. We did not conduct any PROXY auctions with the order reversed.

(18.) The results from the risk questionnaire administered to the subjects indicate that the subjects who participated in these experimental sessions were overwhelmingly (84%) risk averse to varying degrees. Although not a direct test of Reynolds and Wooders (2009), the data on revenue are largely consistent with their predictions for risk-averse bidders. The introduction of a buy price (whether temporary or permanent) to risk-averse bidders increases revenue for a wide range of buy prices, and when bidders have either CARA or DARA, the optimal introduction of a permanent buy price results in higher revenue than that of a temporary buy price.

(19.) To test whether the combination of treatment and institution used by Yahoo! (a permanent buy price without [mandatory] proxy bidding) yields a higher or lower price in our data than the eBay combination (a temporary buy price with proxy bidding) we construct two indicator variables that define those two cells in our design and then run an ordinary least squares regression of price on the Yahoo! variable. In this regression the coefficient estimate on the Yahoo! dummy is 3.48 with a p value of .083, so the Yahoo! combination yields prices that are 3.48 units higher than the eBay combination.

(20.) Note that whether or not a given bidder is BPE is exogenous and determined by the random number drawn for that subject compared to the buy price in effect for that period. Furthermore, as the experimental design is identical across PROXY and NOPROXY, the number of BPE bidders in the different treatment categories is the same as well (with the exception of the one missing observation discussed earlier).

(21.) As in the analysis of revenue, we supplement the regression results in Table 6 with a series of Komolgnrov-Smirnov tests in which we compare utilization at the session level. What we find is that buy price type never makes a difference, that there is a strong and significant effect of having two BPE bidders, that there is always (across both institutions as well as in the pooled data) a difference for a buy price of 25 versus a buy price of 50, and that there is a difference for a buy price of 50 versus a buy price of 75 only in the pooled data.

(22.) Early bids are defined here as bids occurring in the first 4 seconds of the auction. With this definition, 44% of all bids in the TEMP treatment with proxy bidding are classified as early, while on 18% of bids in the PERM treatment are early. A Pearson chi-square test confirms these two values are statistically different with a p value of .000.

(23.) Without proxy bidding early bids account for 40% of all bids in TEMP and 31% of all bids in PERM. A Pearson chi-square test is significant with a p value of .004.

(24.) Note that in some cases the presence of a buy price appears to improve efficiency even in cases where there are no BPE bidders (e.g., PROXY/NO shows efficiency of 65.8% while the TEMP 0 auctions have efficiency of 86.5% on average). This is most likely due to an experience effect as the subjects participate in the baseline auctions first. As our primary interest is in the comparison of TEMP and PERM this is not a concern.

(25.) This provides some support that the increases in efficiency we observe in our buy price auctions are not merely driven by experimental design or subject pool differences between their study and ours.

(26.) Note that these calculations use only winning bids as opposed to the data presented in Figure 3 that showed all bids.

(27.) This result is quite sensitive to our definition of what constitutes a sniping bid. If instead of using the final 3 seconds as our benchmark, we extend the time out to the final 6 seconds, the two institutions look much more alike.

(28.) A Pearson chi-square test returns a p value of .304.

(29.) The relevant comparisons are 91.3% efficient auctions without sniping versus 69.1% efficient with sniping (Pearson chi-square p value = .030) for NOPROXY and 67.9% (without sniping) versus 61.5% (with sniping) (Pearson chi-square of 0.491) for PROXY.

(30.) Some pairs of values for the two bidders participating in the auction could result in instances where the number of BPE bidders depends upon the level of the buy price (25, 50, 75), while others are deterministic. For example, the value pairing 30-60 would have 0 BPE bidders if the buy price were 75, 1 BPE bidder if the buy price were 50, and 2 if it were 25. On the other hand, the value pairing 92-5 would always have 1 BPE bidder, regardless of the buy price.

(31.) It should be noted that including observations for NO that do not correspond to value pairings appearing in the treatment effect estimates does not add any identifying variation, and thus their inclusion does not affect the estimates.

(32.) Recall that in Yahoo! auctions, proxy bidding was an option for buyers.

TABLE 1
Experimental Design

Session Institution Buy Price Type

A NOPROXY TEMP
B NOPROXY TEMP
C PROXY TEMP
D PROXY TEMP
E NOPROXY PERM
F NOPROXY PERM
G PROXY PERM
H PROXY PERM

TABLE 2
Mean Revenue (SD) Relative to Corresponding NO Auction, by
Institution, Buy Price Type, and Buy Price Level

 Buy Price Level
 Buy Price
Institution Type OVERALL 25

POOLED PERM 5.83 (18.18) -1.73 (6.12)
 TEMP 0.91 (18.80) -9.09 (8.89)
PROXY PERM 4.37 (17.42) -0.48 (4.91)
 TEMP 4.31 (19.21) -3.72 (7.28)
NOPROXY PERM 7.29 (18.85) -2.98 (6.94)
 TEMP -2.50 (17.79) -14.47 (6.90)

 Buy Price Level
 Buy Price
Institution Type 50 75

POOLED PERM 9.50 (17.40) 9.73 (23.89)
 TEMP 5.17 (16.39) 6.70 (23.77)
PROXY PERM 7.75 (18.89) 5.85 (22.41)
 TEMP 8.13 (18.47) 8.52 (25.04)
NOPROXY PERM 11.25 (15.73) 13.60 (24.88)
 TEMP 2.15 (13.46) 4.88 (22.50)

TABLE 3
Comparison of Revenue across Buy Price Types (Standard Errors
Clustered on Session), Marginal Effects

 PERM

Institution Data N [[beta] p value
 .sub.P]

POOLED All Auctions 959 5.83 0.000
 BP = 50 or BP = 75 719 9.61 0.001
PROXY All Auctions 480 4.37 0.014
 BP = 50 or BP = 75 360 6.80 0.001
NOPROXY All Auctions 479 7.29 0.001
 BP = 50 or BP = 75 359 12.43 0.001

 PERM Versus
 TEMP TEMP

Institution Data [[beta] p Diff p
 .sub.T] value value

POOLED All Auctions 0.91 0.735 4.92 0.116
 BP = 50 or BP = 75 5.94 0.050 3.68 0.255
PROXY All Auctions 4.31 0.310 0.06 0.998
 BP = 50 or BP = 75 8.33 0.125 -1.53 0.756
NOPROXY All Auctions -2.49 0.253 9.78 0.013
 BP = 50 or BP = 75 3.54 0.081 8.89 0.011

TABLE 4
Number of Bidders for Each Category of Buy
Price Eligibility

 Buy Price Level
Buy Price No. of Bidders
Type All Observations 25 50 75

All TEMP 359 120 119 120
TEMP 0 103 8 27 68
TEMP 1 128 28 64 36
TEMP 2 103 84 28 16
All PERM 360 120 120 120
PERM 0 104 8 28 68
PERM 1 128 28 64 36
PERM 2 128 84 28 16

TABLE 5
Buy Price Utilization (Percentage) by Buy
Price Type, Buy Price Eligibility, and Buy
Price Level

 Buy Price Level
 Buy Price
Institution Type OVERALL 25 50 75

POOLED All TEMP 52.6 84.2 49.6 24.2
 TEMP 1 60.9 85.7 56.3 50.0
 TEMP 2 86.7 91.7 82.1 68.8
 All PERM 55.8 91.7 52.5 23.3
 PERM 1 62.5 96.4 59.4 41.7
 PERM 2 94.5 98.8 89.3 81.3

PROXY All TEMP 49.4 80.0 46.7 21.7
 TEMP 1 57.7 71.4 53.1 44.4
 TEMP 2 84.4 90.5 78.6 62.5
 All PERM 51.7 93.3 46.7 15.0
 PERM 1 53.1 100.0 50.0 22.2
 PERM 2 92.2 100.0 85.7 62.5

NOPROXY All TEMP 55.9 88.3 52.5 26.7
 TEMP 1 67.2 100.0 59.4 55.6
 TEMP 2 89.1 92.9 85.7 75.0
 All PERM 60.0 90.0 58.3 31.7
 PERM 1 71.9 92.9 68.8 61.1
 PERM 2 96.9 97.6 92.9 100.0

TABLE 6
Probit Regressions of Buy Price Utilization
(Standard Errors Clustered on Session),
Marginal Effects

Dependent Variable = 1 if Buy Price Accepted

 POOLED PROXY NOPROXY
Explanatory dF/dx dF/dx dF/dx
Variable (p value) (p value) (p value)

PERM 0.059 0.052 0.064
 (0.430) (0.578) (0.552)
BPE = 2 0.183 0.227 0.144
 (0.000) (0.000) (0.023)
Buy Price = 25 0.221 0.261 0.179
 (0.000) (0.002) (0.001)
Buy Price = 75 -0.091 -0.116 -0.031
 (0.011) (0.025) (0.000)
N 512 256 256
Observations/ 0.762/0.819 0.711/0.774 0.813/0.862
 Predictions

TABLE 7
Percentage of Efficient Auctions by Buy Price
Type, Buy Price Level, and Institution

 Buy Price Level
 Buy Price
Institution Type OVERALL 25 50 75

POOLED NO 69.6
 All TEMP 77.4 67.5 83.2 81.7
 TEMP 0 77.7 87.5 81.5 75.0
 TEMP 1 93.8 96.4 90.6 97.2
 TEMP 2 60.9 56.0 67.9 75.0
 All PERM 73.3 63.3 79.2 77.5
 PERM 0 77.9 62.5 82.1 77.9
 PERM 1 87.5 96.4 84.4 86.1
 PERM 2 55.5 52.4 64.3 56.3

PROXY NO 65.8
 All TEMP 80.0 70.0 81.7 88.3
 TEMP 0 86.5 100.0 85.7 85.3
 TEMP 1 90.6 92.9 84.4 100.0
 TEMP 2 64.1 59.5 71.4 75.0
 All PERM 72.2 63.3 76.7 76.7
 PERM 0 80.8 75.0 85.7 79.4
 PERM 1 84.4 100.0 81.3 77.8
 PERM 2 53.1 50.0 57.7 62.5

NOPROXY NO 73.3
 All TEMP 74.9 65.0 84.7 75.0
 TEMP 0 68.6 75.0 76.9 64.7
 TEMP 1 96.9 100.0 96.9 94.4
 TEMP 2 57.8 52.4 64.3 75.0
 All PERM 74.4 63.3 81.7 78.3
 PERM 0 75.0 50.0 78.6 76.5
 PERM 1 90.6 92.9 87.5 94.4
 PERM 2 57.8 54.8 71.4 50.0

TABLE 8

Probit of Auction Efficiency for Matched Samples
(Standard Errors Clustered on Session), Marginal
Effects

Dependent Variable = 1 if Number of BPE Bidders
Buy Price Accepted
 0 1 2
 Coefficient Coefficient Coefficient
Institution Treatment (p value) (p value) (p value)

POOLED TEMP -0.016 0.151 -0.032
 (0.908) (0.000) (0.781)
 PERM 0.053 0.116 -0.007
 (0.018) (0.002) (0.876)
 N 407 440 456
 Observations/ 0.708/0.757 0.780/0.869 0.605/0.647
 Predictions
PROXY TEMP 0.164 0.250 0.146
 (0.000) (0.000) (0.090)
 PERM 0.054 0.109 -0.085
 (0.000) (0.000) (0.000)
 N 176 196 224
 Observations/ 0.671/0.836 0.709/0.784 0.580/0.621
 Predictions
NOPROXY TEMP -0.368 0.136 -0.238
 (0.000) (0.061) (0.029)
 PERM 0.047 0.187 0.070
 (0.435) (0.008) (0.289)
 N 187 164 220
 Observations/ 0.674/0.723 0.756/0.863 0.609/0.657
 Predictions