An Experimental Investigation of Procurement Auctions with Asymmetric Sellers Abstract Electronic reverse auctions are a commonly used procurement mechanism. Research to date has focused on suppliers who are ex ante symmetric in that their costs are drawn from a common distribution. However, in many cases a seller’s range of potential costs depends on their own operations, location, or economies of scale and scope. Thus, understanding how different bidder types impact auction outcomes is key when designing an auction. This paper reports the results of the first controlled laboratory experiment designed to compare prices between first-­‐price and second-­‐price procurement auctions for homogeneous goods when seller cost types are asymmetric and the number of bidders varies. The results indicate that first-­‐price auctions generate lower prices regardless of market composition. The results also reveal that first-­‐price auctions are either equally or more efficient than second-­‐price auctions despite the theoretical prediction that the reverse should hold in asymmetric auctions. The behavioral effect on market outcomes of adding a third bidder depends on the market composition and the specific auction format, but could lead to nominally higher prices. We list implications for managers who qualify suppliers to participate in online reverse auctions. Keywords: Procurement, Reverse Auction, Asymmetric Auctions, Laboratory Experiment. Introduction Electronic reverse auctions are now a ubiquitous method for procurement.1 Because they open up the process to a larger number of potential bidders and reduce the cost and effort of participation, the hope is that this will lead to more competitive bidding. It is common for firms to qualify suppliers based on product and service quality before conducting the auction (Kumar 2013). Kostamis et al. (2009) however, pose the question of whether the buyer wants to choose a different auction format depending on whether an additional supplier is qualified to bid. The evidence that electronic reverse auctions generate a greater number of bidders is mixed – Wyld (2012) finds that over time the number of bidders decreases rather than increases. However, there is a recent move toward attracting greater diversity of bidders by large firms such as General Electric, GlaxoSmithKline, Hewlett Packard, Dell, and Sun Microsystems with increased engagement from smaller firms as suppliers. The share of federal contracting dollars awarded to small businesses between 2006 and 2011 ranged from 20.5% to 22.8% annually (Wyld 2013).2 The overall growth rate for small business awards by the federal government using reverse auctions was 181% over the time period 2008-­‐2012 (Wyld 2013). Technology and globalization are also enabling firms from around the world to participate in auctions. Thus, the variations in operations, economies of scope and scale, and geographic locations could lead to vastly different production costs, regulatory compliance costs, and transportation costs to the delivery point (Baldwin and Lopez-­‐Gonzalez 2014). For these reasons, the typical academic assumption that firms have costs drawn from a common distribution even when supplying a homogeneous good may not be applicable in many real world settings. The evidence that a greater number of bidders result in lower prices is also mixed. Mithas and Jones (2007) find some evidence that the number of bidders has no effect on buyer surplus. They call for more research on this issue, and point to the need to explore alternative explanations. In practice however, many procurement auctions require only two or three bidders. States such as New York and North Carolina have such policies as do many firms (see Kulp and Randall 2005). 1
The term reverse auction is used as the roles of buyers and sellers are reversed from regular forward auctions in which buyers bid for a product offered by a seller. In a reverse auction, regardless of the auction rules, sellers bid for the right to supply a product to a buyer who proffers the contract with the product specifications. 2
In the most recent fiscal year there were 24,880 awards made through Fedbid (the online marketplace of the federal government) totaling over a billion dollars to small businesses (Wyld 2013). While there is a large academic literature examining reverse auctions (see Katok 2011), there is limited work relaxing the symmetry assumption, much less considering how the number and composition of bidder types affects behavior. Maskin and Riley (2000) consider a two bidder auction where one bidder is from a high value distribution and the second bidder is from a low value distribution. The only difference between the two types is a shift in the respective distributions: formally one bidder has a cost drawn from [a,b] while the other has a cost drawn from [a+c,b+c].3 Maskin and Riley (2000) show that the first-­‐price auction dominates the second-­‐price auction under some stringent assumptions (that the distributions are convex and log-­‐concave). Kirkegaard (2012) relaxes these strong assumptions and shows that the primary result – that the first-­‐price auction is better for the party holding the auction – holds more generally. Given the complexity in such problems, the extant theoretical work studies no more than two asymmetric bidders and also assumes rational, risk neutral bidders (see also Kaplan and Zimir 2012). Recent experimental work by Elmaghraby et al. (2012) incorporates asymmetric nominal seller costs into a model with heterogeneous quality. In their setting however, sellers are symmetric with respect to quality adjusted costs. Another recent experimental study by Saini and Suter (2013) investigates the bidding behavior of two shifted asymmetric sellers in a first-­‐price auction. However, we are unaware of any previous work that evaluates the behavioral performance across first-­‐ and second-­‐ price auction mechanisms or that considers more than two sellers when there are shift asymmetries. Hence, this study aims to fill a gap in the existing procurement auction literature with a laboratory experiment that manipulates (1) the market institution (first-­‐price vs. second-­‐price auctions), (2) the number of suppliers in the market (two vs. three suppliers), and (3) the distribution of types (percentage of low-­‐cost suppliers) participating in the auction. Related Literature There is a growing literature on bidding behavior in reverse auctions. Elmaghraby et al. (2012) compare rank-­‐based feedback, full-­‐price feedback, and no feedback to buyers in open-­‐bid auctions. While they consider asymmetric supports for seller cost structures, our research enhances theirs in two ways: (1) In their research setting the firms with higher costs also supply goods with higher quality so that the quality adjusted distribution of costs are in fact symmetric between firms. (2) They consider dyadic auctions and do not consider the competitive effect of a third firm. In contrast to commonly held 3
This work was done in the context of a standard auction, but one can switch between the two settings in a straight forward manner (see Ausubel 2003). beliefs in practice that full-­‐price feedback should result in more competition due to bid visibility, rank-­‐
only feedback resulted in lower prices than full-­‐price feedback. While Elmaghraby et al. (2012) do not study sealed bid auctions in the laboratory, Jap (2003) found no significant difference in buyer costs between sealed bid and open bid reverse auctions in the field. In the current research we consider sealed bid auctions using two market institutions: first-­‐price and second-­‐price auctions. When the same set of suppliers bid against each other repeatedly, both revelation of the winners’ bid and the revelation of all bids at the end of successive auctions has been shown to lead to higher bid prices (Kannan 2012). Greenwald et al. (2010) point out that electronic marketplaces typically feature two types of uncertainties: cost-­‐structure uncertainty, which is uncertainty about supplier costs, and market structure uncertainty, that geographically distributed suppliers face about the number of competitors. In buyer-­‐determined auctions sellers supply higher quality leading to higher market efficiencies, and buyers who can consider reputation effects prefer buyer-­‐determined auctions over price-­‐based auctions (Brosig-­‐Koch and Heinrich 2014). In our sealed-­‐bid studies sellers are anonymous in a stranger design so that there are no reputational effects. There are a few experimental studies that investigate behavior in asymmetric auctions. In their theoretical work, Maskin and Riley (2000) make a distinction between a shift, where both ends of a common support are shifted by a constant amount for one of the two bidders and a stretch, where only one end of the support is shifted. Güth, Ivanova-­‐Stenzel, and Wolfstetter (2005) compare standard two bidder first-­‐price and second-­‐price auctions with a stretch asymmetry. They observe bidders being more aggressive in the first-­‐price auction than predicted and they find prices being more favorable to the party holding the auction with a first-­‐price auction. Saini and Suter (2013) study a procurement auction with a shift in which one seller’s cost is drawn from the high distribution and the other’s is drawn from the low distribution. In their one shot auctions, the theoretical predictions are generally supported although bidders are more aggressive than predicted. Our research setting differs from theirs as they do not consider the competitive effects of more than two sellers or compare auction mechanisms for two bidders. Pagnozzi and Saral (2013) also consider two asymmetric cost sellers in their experimental investigation, but their setting is a multi-­‐object auction with resale. In addition, there is also a literature on procurement auctions in which products are differentiated on non-­‐price attributes (Engelbrecht-­‐
Wiggans and Katok 2006; 2007; Fugger et al. 2013; Shachat and Swarthout 2010; Haruvy and Katok 2013) All of these studies feature bidders with symmetric costs (i.e., seller costs are drawn from a common distribution). Experimental Design and Procedures To explore behavior in shift asymmetry procurement auctions we conduct an incentivized experiment in a controlled laboratory setting. In each experimental auction, a computerized buyer solicits offers for a fictitious item. Seller output is assumed to be homogeneous so that the buyer only cares about the price and not the identity of the supplier. Subject sellers observe their own induced cost for providing the item, as well as the number of other sellers and the distribution from which those suppliers’ induced costs were drawn. In the experiment there are two types of sellers: low-­‐cost types and high-­‐cost types. Low-­‐cost types have induced costs that are distributed Uniform[0,20] while high-­‐cost types have induced costs that are distributed Uniform[10,30]. Note that a “high-­‐cost” type may actually have a lower cost than a low-­‐cost type in any given realization. The experiment varies three factors: Factor 1: The auction mechanism is either first-­‐price or second-­‐price. Subject sellers earn a profit from winning the auction and receiving a price greater than their own cost. The lowest offer always wins (with ties broken randomly), while the price received by the winner depends on the auction mechanism. In a first-­‐price sealed-­‐bid auction the price equals the lowest bid and in a second-­‐price sealed-­‐bid auction the price equals the second lowest bid. Factor 2: The number of bidders in the auction is either two or three. Factor 3: The percentage of bidders who are low-­‐cost types varies between 0$% and 100%. The possible percentages of low-­‐cost types is dependent on the number of bidders. The auction mechanism is varied between sessions while the other two factors are varied within a session. For a discussion of theoretical price predictions, see Appendix A. In each session, a group of 8 subjects, each at a private computer station, read auction format-­‐
specific instructions. Subjects then answer a series of comprehension questions and participated in three practice auction periods followed by 36 paid auction periods. Copies of the directions and the comprehension questions are provided in Appendix B. Subjects do not know how many total periods there will be in the study, but do know that they will be paid their cumulative earnings in cash at the end of the session. All costs and prices in the experiment are denoted in terms of Lab Dollars (valued at the pre-­‐specified rate of 5 Lab Dollars = 1 $US). In each auction period the 8 subjects are randomly and anonymously assigned to different markets of two or three sellers. The subjects learn their type and realized cost for the period as well as the number and types of the other sellers in the auction. Let H denote a high-­‐cost type seller and let L denote a low-­‐cost type seller. There are seven possible market compositions involving two or three sellers: LL, LH, HH, LLL, LLH, LHH, and HHH.4 A session involves 16 repetitions of each of the 7 market compositions. The periods in which the different combinations of market compositions occur are randomized over the course of the session. After each auction, subjects receive feedback regarding the price in their auction and their own profit. To reduce variation between sessions and auction mechanisms, one set of groupings, types, and cost realizations is drawn and used in all 12 sessions. Subjects were recruited from a database of over 3000 study volunteers at the behavioral laboratory of a large state university. While some of the subjects had participated in other studies, none had participated in any related auction experiments. In addition to their salient earnings, subjects received an initial endowment of $10, including the lab’s standard participation payment. The average total payment for the 60 minute experiment was $19.22. A total of 96 subjects participated in the experiment. Half of these were assigned to first-­‐price sealed bid markets and the other half were assigned to second-­‐price sealed bid markets. Each subject participated in only one session in one of the two auction conditions. However, subjects experienced markets of all 7 compositions as both a high-­‐cost and a low-­‐cost type. Behavioral Results The results are organized in two subsections: market outcomes and individual bidding behaviors. First, we evaluate how price and efficiency change across different auction institutions and various market compositions of bidder types. Then, we estimate individual bidding strategies in order to shed further light on market-­‐level results. Market outcomes are analyzed using OLS regressions with robust standard errors clustered at the session level to account for potential serial correlation within the 4
Given the homogeneity of the supplied items HL is isomorphic to LH. HLH and HHL are isomorphic to LHH, and HLL and LHL are isomorphic to LLH. For consistency, we always list the low-­‐cost types first when referring to a market composition. session. Individual bidding strategies are estimated via random effects models at the subject level, in addition to robust standard errors clustered at the session level. While theoretical work on auctions is typically concerned with a priori expected prices; in the laboratory, however, observed prices are ex post in relation to cost realizations. Thus, empirical investigation not controlling for realized costs is prone to misleading inferences, as differences in outcome variables such as prices and efficiencies might be caused by variations in costs, rather than differences in institutions or market compositions. For this reason, we include realized costs in all our regression analyses.5 The data for the findings are from 1,344 laboratory auctions as summarized in Table 1. Table 1: Number of Auctions (N = 1,344) Symmetric Auctions Asymmetric Auctions Total Market Composition LLL LL HHH HH LLH LHH LH First-­‐Price (6 sessions) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 672 Second-­‐Price (6 sessions) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 96 (16/session) 672 Market Outcomes: Auction Price and Efficiency The left panel of Table 2 reports regression analyses of auction prices across institutions and bidder compositions in the market. Model (1) includes all auctions, while Model (2) and Model (3) examine the subset of first-­‐ and second-­‐ price auctions, respectively. The first regressor “First-­‐Price Auction” = 1 if the auction is a first-­‐price auction, and 0 if a second-­‐price auction. Hence, this variable is not used in Models (2) and (3). The next two regressors are the lowest and second lowest costs in the market. Then we 5
Because the same set of cost realizations are used in each session, one can conduct non-­‐parametric analysis to compare prices and efficiencies between first-­‐ and second-­‐price auctions. We perform such rank-­‐sum tests in Table C1 and C2 in Appendix C. One should keep in mind that such tests are always conditional on the costs realizations. For completeness, we also conduct sign rank tests comparing market compositions for each auction type in Tables C3 and C4 in Appendix C. However, it is impossible to fix cost realizations between certain different market compositions for example when the fraction of high-­‐cost types differs (i.e., LL vs LH) or when a third bidder is added (i.e., LL and LLH), or both. Rank sum test are used in Tables C1 and C2 because the treatment effect is measured between observational units (sessions) whereas a sign rank test is used in Tables C3 and C4 where the treatment effect is measured within an observational unit (session). include indicator variables for the six of the seven market compositions, leaving LH market out as the base group. The coefficients of these indicator variables thus show the direct comparison of the corresponding market against the LH market. The right panel of Table 2 is constructed in an identical fashion to the left panel, except that the dependent variable is auction efficiency instead of auction price. Table 2: Auction Price and Efficiency (OLS Regression with robust standard errors clustered at the session level) (LH markets are used as the base group in all models) Price Efficiency (1) (2) (3) (4) (5) all 1st-­‐price 2nd-­‐price all 1st-­‐price auctions auctions auctions auctions auctions First-­‐Price Auction Lowest Cost Second Lowest Cost LL LLL LLH LHH HH HHH Constant N. of Observations N. of Clusters R2 -­‐3.417*** (0.159) 0.396*** (0.097) 0.441*** (0.118) -­‐1.284*** (0.265) -­‐1.599*** (0.362) -­‐1.286*** (0.387) -­‐0.565 (0.370) 0.962** (0.361) 0.503 (0.403) 5.413*** (1.005) 1344 12 0.794 -­‐ -­‐ 0.713*** (0.018) 0.057* (0.025) -­‐1.286* (0.521) -­‐1.669* (0.682) -­‐1.130 (0.750) 0.072 (0.462) 1.697*** (0.271) 0.460 (0.440) 4.998*** (0.862) 672 6 0.894 -­‐ -­‐ 0.079** (0.030) 0.824*** (0.036) -­‐1.281*** (0.195) -­‐1.530*** (0.337) -­‐1.441*** (0.300) -­‐1.201* (0.478) 0.228 (0.532) 0.546 (0.723) 2.411*** (0.394) 672 6 0.855 0.086*** (0.023) -­‐0.013*** (0.002) 0.016*** (0.002) 0.086** (0.033) 0.023 (0.061) 0.001 (0.042) -­‐0.004 (0.039) 0.015 (0.036) 0.063** (0.022) 0.664*** (0.067) 1320 12 0.0751 -­‐ -­‐ -­‐0.010*** (0.002) 0.016*** (0.003) 0.102** (0.029) 0.117 (0.076) 0.053 (0.062) 0.016 (0.049) 0.018 (0.032) 0.055** (0.018) 0.686*** (0.085) 660 6 0.0582 (6) 2nd-­‐price auctions -­‐ -­‐ -­‐0.016*** (0.004) 0.015** (0.004) 0.069 (0.062) -­‐0.071 (0.085) -­‐0.051 (0.052) -­‐0.025 (0.066) 0.012 (0.068) 0.071 (0.042) 0.729*** (0.107) 660 6 0.0749 Notes: In parenthesis are fully robust standard errors clustered at the session level, taking into account potential correlations within sessions. *** indicates significance at 1% level, ** at 5%, and * at 10%. Our first finding concerns price comparison between first-­‐ and second-­‐ price auctions. Finding 1 (first-­‐ vs second-­‐ price auctions): First-­‐price auctions generate significantly lower procurement prices than second-­‐price auctions. Evidence: Figure 3 reports the average of the six session-­‐average market prices (and the standard error of the average) in first-­‐ and second-­‐ price auctions within each market composition. Regardless of the market compositions, first-­‐price auctions always generate significantly lower procurement prices than second-­‐price auctions. A more thorough analysis in Model (1) in Table 2 suggests that, holding lowest costs and market composition constant, procurement prices using first-­‐price auctions are $3.42 lower than those using second-­‐price auctions (p-­‐value < 0.01). This difference is economically significant; by using first-­‐price auctions instead of second-­‐price auctions, the buyer can expect a reduction in procurement price by 17% of the range of the cost distributions ($3.42 out of $20), on average. The price difference between auction institutions is also revealed in Figure 3. Figure 3: Market Price Comparison between First-­‐ and Second-­‐ Price Auctions First-­‐price Aucrons Second-­‐price Aucrons Price 25 20 15 10 5 0 LL LH HH LLL LLH Market ComposiNon LHH HHH Note: There are six sessions in first-­‐price auctions and another six sessions in second-­‐price auctions, in each of the seven market compositions. The six session-­‐average market prices are used to obtain the overall average price and standard error in each of the 14 types of markets in the figure. We report nonparametric rank sum tests for difference between auction institutions in Table C1 in Appendix C. Our finding is consistent with previous experimental results in symmetric cost settings, where first-­‐
price auctions generate lower procurement prices, which is largely attributed to bidders’ risk aversion (see e.g., Davis and Holt 1993 and Kagel and Roth 1995). The next set of findings investigates how auction prices are affected when the market composition changes with the presence of an additional bidder. Finding 2a (LL vs. LLL and LL vs. LLH markets): Regardless of the third bidder’s type, prices in first-­‐ and second-­‐ price auctions are the same as in LL markets, controlling for costs. Evidence: Controlling for the two lowest costs in the market, we first compare the prices in (coefficients of) LL and LLL markets in Models (2) and (3), and the difference is statistically identical to 0, in both first-­‐ and second-­‐ price auctions: p-­‐value is 0.295 and 0.186, respectively. Next, we compare prices in LL and LLH market, and find no difference in either first-­‐ or second-­‐ price auctions: p-­‐value is 0.749 and 0.616, respectively. Finding 2b (HH vs. LHH and HH vs. HHH markets): LHH markets have significantly lower prices in both first-­‐ and second-­‐ price auctions as compared to HH markets; HHH markets have significantly lower prices than HH markets only in first-­‐price auctions. Evidence: Controlling for the two lowest costs in the market, we compare prices in HH and LHH markets, and find LHH markets generate significantly lower prices in first-­‐price auctions ($1.62 lower; p-­‐value = 0.017), as well as in second-­‐ price auctions ($1.43 lower; p-­‐value = 0.010). We then compare prices in HH and HHH markets, and find that HHH markets generate significantly lower prices in first-­‐price auctions ($1.24 lower, with p-­‐value = 0.005), but no difference in second-­‐ price auctions (p-­‐value = 0.505). Finding 2c (LH vs. LLH and LH vs. LHH markets): In first-­‐price auctions, LLH and LHH markets have the same price as LH markets; however, both LLH and LHH markets have lower prices than LH markets in second-­‐price auctions. Evidence: Controlling for the two lowest costs in the market, the coefficients of LLH and LHH markets in first-­‐price auctions are both statistically identical to 0 (p-­‐value = 0.192 and 0.882, respectively). In contrast, in second-­‐price auctions, LLH markets generate significantly lower auction prices than LH markets ($1.44 lower, p-­‐value = 0.005), and LHH markets also generate lower auction prices than LH markets ($1.20 lower, p-­‐value = 0.054). Findings 2a, 2b, and 2c all examine what happens to market prices as the number of bidders changes ceteris paribus. Of course, if a third bidder is added to the market, such an assumption may not hold. In particular, the addition of a third bidder would change the expected lowest and second lowest cost. Thus, to identify how adding a bidder to a market is expected to impact price given the behavioral patterns we observe, one needs to jointly consider the change in the market composition dummy as well as the expected change in costs. For example, adding a low-­‐cost type bidder to an LL market reduces the expected lowest cost from 6.7 to 5 and reduces the expected second lowest cost from 13.3 to 10. Thus, the expected price change of going from an LL to an LLL market with a first-­‐price auction is (1.286 -­‐ 1.669) + .713 (5 – 6.7) + .057 (10 – 13.3) = -­‐$1.78 from Model (2) in Table 2. Table 3 summarizes the predicted price changes from adding a third bidder with each type of auction. In general, the price drop of adding a third bidder is large when the new bidder is a low-­‐cost type. When the new bidder is a high-­‐cost type the price reduction is generally small and actually (nominally) positive when adding a high-­‐cost type to an LL market with a first-­‐price auction. Table 3: Price Impact of Adding a Third Bidder by Auction Mechanism First-­‐Price Auction LLL LLH LHH HHH LL -­‐$1.78 +$0.05 LH -­‐$3.80 -­‐$0.32 HH -­‐$7.24 $-­‐2.64 LLL LLH LHH HHH LL -­‐$3.10 -­‐$0.66 LH -­‐$8.02 -­‐$3.78 HH -­‐$6.96 -­‐$2.54 Second-­‐Price Auction As a final point regarding the price analysis in Table 2, we consider how changes in the realized costs impact market outcomes. In second-­‐price auctions, if all bidders follow dominant strategies of reporting their true costs, then the market price would be solely determined by the second lowest cost. However, the coefficient on Second Lowest Cost is significantly lower than 1 (p-­‐value = 0.005) and the coefficient on Lowest Cost is significantly higher than 0 (p-­‐value = 0.045). This suggests that not all bidders are truthfully reveling their costs in the second-­‐price auctions, which is confirmed by our further analysis of bidding strategy at the individual level. In first-­‐price auctions, whether or not the second lowest cost should influence market prices depends on whether or not the auction is symmetric or asymmetric. Thus we leave exploration of this until later in the paper. We now turn to the question of efficiency in reverse auctions: did the lowest cost supplier sell the item? This is impossible to investigate in the field where private costs are not observable. We denote auction efficiency as 100% when the seller with the lowest cost wins the auction; otherwise the auction efficiency is 0%.6 Figure 4 reports the average of the six session-­‐average market efficiencies (and the standard error of the average) in first-­‐ and second-­‐ price auctions for each market composition. The figure suggests that first-­‐price auctions tend to be more efficient than second-­‐price auctions. This is formalized in Finding 3. Figure 4: Market Efficiency Comparison between First-­‐ and Second-­‐ Price Auctions First-­‐price Aucrons Second-­‐price Aucrons Efficiency 100% 80% 60% 40% 20% 0% LL LH HH LLL LLH Market ComposiNon LHH HHH Note: There are six sessions in first-­‐price auctions and another six sessions in second-­‐price auctions, for each of the seven market compositions. The six session-­‐average market efficiencies are used to obtain the overall average efficiencies and standard error in each of the 14 types of markets in the figure. We report nonparametric rank sum tests for difference between auction institutions in Table C2 in Appendix C. Finding 3: First-­‐price auctions are significantly more efficient than second-­‐price auctions. Evidence: As shown in Figure 4, first-­‐price auctions are more efficient than second-­‐price auctions, in every single market composition. Statistically, the finding is supported by regression analysis in Model (4) of Table 2. Controlling for lowest costs in the market, the efficiency of first-­‐price auctions is on average 8.6 percentage points higher than second-­‐price auctions (p-­‐value < 0.01). 6
Another measure of auction efficiency is the fraction of gains from trade that were realized over the maximum gains that could have been obtained from trade. The results are essentially the same with this measure. Our finding that first-­‐price auctions are more efficient than second-­‐price auctions is quite interesting. For symmetric market compositions, the two mechanisms are predicted to be equally efficient. However, as discussed in Appendix A, for asymmetric market compositions second-­‐price auctions are expected to be more efficient. Individual Behavior: Bidding Strategy Now we turn to analyzing the determinants of individual bidding strategies, as summarized in Table 4. The dependent variable is an individual bid; we include both “cost” and “cost squared” to allow for the possibility of nonlinear bidding as a function of private costs. We analyze Low-­‐cost and High-­‐cost bidders’ strategy, in first-­‐ and second-­‐ price auctions, separately. The regressions utilize random effects at the subject level, with fully robust standard errors clustered at the session level to account for correlations within the session. In Appendix D we estimate bid functions allowing the cost and cost squared terms to vary by market composition. We also plot the observed and estimated bids by bidder type, market composition and auction mechanism in Appendix D. Finding 4 (bidding in first-­‐price auctions): In first-­‐price auctions, both low-­‐cost types and high-­‐cost types adjust their bids based on their own costs and their opponents’ types. Evidence: Low-­‐cost types bid non-­‐linearly as evidenced by the significance of the coefficient on Cost Squared. It is not surprising that low-­‐cost types reduce their bids in LL, LLL, or LLH markets as compared to LH markets (the omitted group) as all of these are more competitive. However, low-­‐cost type bidders actually increase their bid when a high-­‐cost type is added to an LH market as indicated by the positive and significant coefficient on LHH in model (1). According to Model (2), high-­‐cost types bid linearly as indicated by the lack of significance on Cost Squared. Somewhat surprisingly, high-­‐cost type bidders do not distinguish among markets so long as there is a least one low-­‐cost type in it as evidence by the lack of significance for LLH and LHH. Finding 5 (bidding in second-­‐price auctions): In second-­‐price auctions, high-­‐cost type bidders generally follow the weakly dominant strategy of reporting true costs, while the low-­‐cost type bidders do not. Evidence: The dominant strategy in the second-­‐price auction is to bid exactly one’s private cost and this does not change based on the market composition or the bidder’s type. Model (4) suggests high-­‐cost types bidding strategies are generally consistent with this prediction. First, the coefficient on Cost for high-­‐cost types is not statistically different from 1 (p-­‐value = 0.162, two-­‐sided). Second, the coefficient on Cost Squared is not different from 0 (p-­‐value = 0.824). Finally, the various market indicator variables are not significant (with the exception of marginal significance in LLH markets). For low-­‐cost types in contrast, the coefficient of Cost is 0.71 in Model (3), significantly lower than 1 (p-­‐value = 0.028, two-­‐
sided). Moreover, low-­‐cost types employ significantly different bidding strategies across the four market compositions in which they participate. Table 4: Individuals’ Bidding Strategy: (Random effects at subject level; robust standard errors clustered at the session level) (Bidding in LH markets are used as the base group in all models) First-­‐Price Auctions Second-­‐Price Auctions (1) (2) (3) (4) Low-­‐cost type High-­‐cost type Low-­‐cost type High-­‐cost type Cost 0.489*** 0.725*** 0.714*** 0.889*** Cost Squared LL LLL LLH LHH HH HHH Constant (0.039) 0.016*** (0.002) -­‐1.481*** (0.346) -­‐1.784*** (0.443) -­‐1.415*** (0.397) 0.480** (0.244) -­‐ -­‐ -­‐ -­‐ 6.564*** (0.454) of Observations 864 N. N. of Clusters 6 (0.119) 0.004 (0.003) -­‐0.112 (0.311) -­‐0.026 (0.172) 1.064*** (0.148) 0.557*** (0.123) 5.033*** (1.251) (0.131) 0.006 (0.007) -­‐1.377*** (0.284) -­‐1.278*** (0.335) -­‐1.271*** (0.346) -­‐0.577** (0.288) -­‐ -­‐ -­‐ -­‐ 2.938*** (0.493) (0.079) 0.000 (0.002) -­‐ -­‐ -­‐ -­‐ -­‐0.843* (0.453) 0.182 (0.544) 0.245 (0.476) 0.555 (0.603) 1.388* (0.840) 864 6 864 6 864 6 -­‐ -­‐ -­‐ -­‐ Notes: In parenthesis are fully robust standard errors clustered at the session level, taking into account potential correlations within sessions. *** indicates significance at 1% level; ** at 5%, and * at 10%, respectively. Concluding Remarks This paper reports the results of controlled laboratory experiments designed to investigate how the auction institution, as well as the number and type of bidders participating, impact market outcomes and bidding behavior in asymmetric procurement auctions. In addition to two-­‐bidder auctions where recent theoretical advances have been made, we study three-­‐bidder markets as this is sometimes specified as practical rule-­‐of-­‐thumb for the minimum number of bidders. This highlights one of the main advantages of laboratory techniques, namely that it is possible to explore behavior beyond where theory is well developed while avoiding potentially prohibitively costly field implementation. At the market level, our first main result indicates that first-­‐price auctions lead to significantly lower procurement prices -­‐ both statistically and economically -­‐ than second-­‐price auctions. Our second finding shows that the price impact from including a third bidder depends on the types of all bidders in the auction as well as the institution. For example, in a market with one low-­‐cost type and one high-­‐cost type, adding a third bidder lowers price for a second-­‐price auction but not for a first-­‐price auction. This finding reveals that benefit of increasing the raw number of bidders may be overstated, and contrary to conventional wisdom, policies that specify a minimum number of bidders could be overly restrictive. Our third result shows that first-­‐price auctions are no less and sometimes more efficient than second-­‐
price auctions, implying that first-­‐price auctions are preferred from a social perspective as they are more likely to lead to procurement by the seller with the lowest realized cost. This finding is particularly interesting given that second-­‐price auctions are expected to be more efficient than first-­‐price auctions when there are asymmetries. At the individual level our findings reveal several interesting patterns. In second-­‐price auctions where there is a dominant strategy, truthful bidding is generally observed for high-­‐cost types but not for low-­‐cost types. In first-­‐price auctions, both high-­‐ and low-­‐cost types adjust their bids based on their own costs and the types of opponents they face. High-­‐cost types bid linearly and do not distinguish among markets so long as a low-­‐cost type is present. Low-­‐cost types on the other had bid non-­‐linearly and sometimes increase their bid when an additional bidder enters the market. We hope that this paper helps spur a wide reexamination of procurement auctions allowing for asymmetries. In addition to considering other auction formats and more bidders in the framework used in this paper, future research should consider other asymmetries as well. For example, one could consider cases other than stretches or shifts such as where the cost distributions are non-­‐overlapping as in [a,b-­‐ε] and [b+ε,c] for ε > 0 or one is strictly contained in the other as in [a,b] and [a-­‐ε,b+ε] for ε > 0. The typical assumption of a uniform distribution over the support may also be overly restrictive and there is no particular reason not to allow each bidder to have their own unique distribution of costs. Once one allows for these types of changes then there is a need to explore robustness of other auction results such as the impact of feedback in open auctions or allowing for quality differentials. In the current research bidders knew how many other bidders were in the market and their types. Another potentially interesting extension would be to consider a setting in which bidders did not know the types or number of their competitors. Our contributions are as follows: (1) We extend prior experimental work by incorporating asymmetric potential seller costs which are a descriptive reality given variation in transportation and regulation costs for providers from different geographical locations as well as variation in economies of scale, expertise, or administrative overhead for firms of different size. (2) We provide some insight regarding the nature of competition that arises when additional firms with higher or lower costs participate in an auction. Specifically we provide evidence that knowing that the competitor is of a different type (cost structure) seems to affect behavior by causing a reaction to that different type. 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