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e-Sourcing in Procurement: Theory and Behavior in Reverse Auctions with Non-Competitive Contracts Richard Engelbrecht-Wiggans

Elena Katok

College of Business University of Illinois Champaign, IL 61820 [email protected]

Smeal College of Business Penn State University University Park, PA, 16802 [email protected] October 22 2004

Abstract One of the goals of procurement is to establish a fair price while affording the buyer some flexibility in selecting the suppliers to deal with. Reverse auctions do not have this flexibility, because it is the auction rules and not the buyer that determine the winner. But an important advantage of having this flexibility is that it allows buyers and suppliers to establish long-term relationships. This is one of the reasons that buyers often combine non-competitive purchasing with auctions. We find that in theory such hybrid mechanisms that remove some suppliers and a corresponding amount of demand from the auction market increase competition and make buyers better off as long as suppliers are willing to accept non-competitive contracts. And it turns out that suppliers often do because under a wide variety of conditions these contracts have a positive expected profit. Our theory relies on two behavioral assumptions: (1) bidders in a multi-unit uniform-price reverse auction will follow the dominant strategy of bidding truthfully, and (2) the suppliers who have been removed from the market will accept non-competitive contracts that have a positive expected profit. Our experiment demonstrates that bidders in the auction behave very close to following the dominant strategy regardless of whether this auction is a stand-alone or a part of a hybrid mechanism. We also find that suppliers accept non-competitive contracts sufficiently often (although not always) to make the hybrid mechanism outperform the reverse auction in the laboratory as well as in theory.

JEL Classification Numbers: C72, D83, D44, C91 Keywords: Multi-Unit Auctions, Experimental Economics, Strategic Procurement The authors gratefully acknowledge the support from the National Science Foundation

1. Introduction With the growth of the internet, e-Sourcing, has become an important tool for procurement. E-Sourcing is a catch-all term that refers to the use of internet-enabled applications and decision support tools that facilitate competitive and collaborative interactions among buyers and suppliers through the use of online negotiations, reverse (decreasing bid) auctions, and other related tools. According to a September 2002 report by the Aberdeen Group (Aberdeen Group, 2002), e-Sourcing revenues increased from $820 million in 2001 to $1.14 billion in 2002, and are projected to increase to $3.13 billion by 2005. The use of auctions in e-Sourcing may save buyers considerable amounts of money. Such on-line auctions received much attention in the press when General Electric (GE) claimed savings of over $600 million and net savings of over 8% in 2001 by using SourceBid, a reverse auction tool and a part of GE’s Global Exchange Network (GEN)1. The U.S. General Services Administration attributed savings of 12% to 48% to the use of auctions (Sawhney 2003), and FreeMarkets, one of the leading on-line auction software providers, reported that its customers saved approximately 20% on over $30 billion in purchases between 1995 and 2001. However, auctions may not be delivering quite as much savings as hoped. The Aberdeen Group 2002 reports that 60% of end-users were unable to realize fully the savings that they had negotiated using e-Sourcing technologies, primarily due to the lack of effective communication of negotiated terms. Emiliani and Stec 2001 argue that not only do auctions rarely deliver savings as great as advertised, but also, they inflict damage on the long-term buyer-supplier relationships by inhibiting collaboration2. The importance of long-term relationships in procurement has been well established (see for example Monczka, Trent and Handfield 2005), and auctions as such are not conducive to promoting long-term relationships. But we should not be too quick to dismiss auctions—they

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According to a case study written by GE’s Global Exchange Services (Global Exchange Services 2003), GE’s Global Exchange Network is used by about 35,000 suppliers and handles over 10,000 e-invoicing enquiries per day. Approximately 37,000 reverse auctions, worth about $28.6 billion, have been conducted between 2000 and the 2nd quarter of 2002, generating $680 million in savings in 2000-01 and additional $900 million in savings projected for 2002. 2 Another common criticism of auctions is that they “squeeze suppliers on price” thus putting small suppliers at a disadvantage. But, it should be noted that auctions also give small suppliers access to a large market that they may not have had access to otherwise.

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have many benefits. Because auctions are visible, structured, and have clear rules, they make the procurement process transparent and, at least in theory, they yield a fair market price. Without this, the procurement process can become disastrously flawed.

For example, one recent,

notorious illustration of what can happen without competitive bidding is the $7 billion no-bid contract awarded by the US Army to Kellogg, Brown & Root (KBR), a Halliburton subsidiary, in March of 20033. So, let us look at auctions a bit more closely. Auctions introduce market competition into the procurement process, and this competition does put a downward pressure on price. However, auctions also determine who wins versus loses. In the case of e-Sourcing, this second function of auctions seems to be the source of the problem. Specifically, if a buyer conducts a sequence of auctions over time, each auction may result in different suppliers winning. Such a turn-over in suppliers does not facilitate long term relationships between a buyer and that buyer’s suppliers. Our work is motivated by the desire to create mechanisms that preserve benefits of auctions but limit their detrimental effect on long-term relationships. We investigate a mechanism that combines auctions with non-competitive contracts; an auction among some of the suppliers sets the price and the buyer contracts “non-competitively” with other suppliers to provide goods at whatever price the auction sets. This hybrid mechanism retains the price setting benefits of auctions; the auction component of the mechanism provides a transparent process for injecting market competition into the procurement process. However, the buyer retains some control over deciding which suppliers to deal with (in other words, this decision is not part of the mechanism). The buyer could repeatedly contract with same non-competitive suppliers, thus retaining the long-term relationships with those suppliers. The understanding of mechanisms that combine auctions and negotiations—the type of mechanisms most often used in practice—is quite limited. Jap 2002 provides a review of issues

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This contract, know as “Restore Iraqi Oil” (RIO), was a 2 year cost plus contract worth up to $7 billion to KBR for rebuilding Iraq’s oil infrastructure and extinguishing oil well fires. The no-bid contract caused such outrage in Congress and directed spotlight on Halliburton and the Vice President Dick Cheney, who served as the Halliburton CEO from 1995 through 2001, that the contract was subsequently cancelled and opened up for bid. Ultimately, the bulk of the contract was still awarded to KBR, and the balance to a joint venture of the California-based Parsons Corp. and the Australian firm Worley Group Ltd (Halliburton Watch 2004).

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in on-line reverse auctions used for procurement, including how these auctions differ from standard physical auctions (they typically have lower transaction costs and allow for bidder anonymity), and how they differ from auctions in the theoretical auction literature. There are two fundamental differences between on-line reverse auctions prevalent in practice and the models of auctions in the theory literature. The first difference is that in practice the value of products in procurement settings cannot be reduced to the single dimension of price. This leads to the second difference—the vast majority of auctions actually used in practice do not determine winners. In other words, the buyer (the auctioneer) does not commit to awarding the contract to the lowest bidder, but instead reserves the right to select the winner from a set of bidders. This type of mechanism has not been analyzed either theoretically or in the laboratory, but Jap 2002 reports on some empirical findings from interviewing buyers and sellers. Reverse auctions are usually a part of e-Sourcing tool kits, but they are not used exclusively, and although prevalent, they do not constitute the majority of e-Sourcing transactions. In addition to auctions, e-Sourcing applications typically provide platforms for online negotiations, such as request for quotes (FRQ), and request for proposals (RFP). The question of which is better (auctions or negotiations) is a complicated one.

Bulow and

Klemperer 1996, for example, show that if the seller is able to attract just one more serious bidder to the auction, then he can make higher expected revenue from an auction than from a negotiation. The Bulow and Klemperer model is stylized, and the example they used is selling a company. Although a company is a complex object, the contract for selling it can be easily reduced to a single dimension—price per share—a setting most conducive to auctions. Bajari et al. 2003 compare auctions and negotiations in a context of contracts that cannot be easily reduced to a single dimension. They examine private sector building contracts awarded in Northern California between 1995 and 2000 and find that auctions perform poorly when contracts are complex, specifications are incomplete, or the number of bidders is small. They also find that auctions tend to suppress communication between buyers and sellers. Salmon and Wilson 2004 investigate a setting with two units in which the seller starts out by auctioning off one unit using an ascending-price auction, and then negotiating with the pricesetting bidder for the remaining unit. The negotiation process is modeled as the Ultimatum

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game4. Salmon and Wilson 2004 find that since the losing bidder does not wish to reveal his true value, truthful bidding is not an equilibrium for the auction, and actually the only equilibria that exist are in mixed strategies. The authors find that the hybrid auction/negotiation mechanism is able to raise more money than the benchmark mechanism that consists of two sequential ascending-bid auctions. Mechanisms that most closely resemble those used by e-Sourcing applications are ones that combine auctions with some form of negotiations. Jap 2002 reports that suppliers generally do not like reverse auctions because they feel the “…visibility of their prices to competitors erodes their bargaining power.” (pg. 521). They feel that the computer interface prevents them from informing buyers about non-price attributes of their products, and thus causes their products to become “commoditized.” And they also fear losing control and bidding too low in the heat of the moment. In fact, according to Jap 2002, suppliers take the use of on-line reverse auctions by the buyers as a signal about the nature of their relationship, and they respond to this signal: If suppliers believe that the use of on-line reverse auctions signals a movement towards market-oriented, armslength relations, then suppliers will act accordingly. As suppliers believe that buyers are increasingly shortterm oriented and concerned about their own gains, then they too may respond in kind. However, if the buyer signals that the on-line auctions are a rare occurrence, used as a stepping stone to a long-term, mutually beneficial financial arrangement, then suppliers will be more motivated to become mutually oriented and may respond more competitively in light of the long-term gains. (pg. 521).

In other words, an occasional use of an auction by the buyer is (correctly) interpreted by suppliers as a way to “keep them honest” rather than as a signal that the buyer is ready to abandon the relationship. Therefore, suppliers are more likely to bid aggressively in such auctions, as a signal of good faith (see Goeree 2003 for a model of auctions with an aftermarket) because their own low bid signals a commitment to the relationship. But if buyers use auctions all the time, then suppliers lose the incentive to signal their commitment, and simply compete on price (or choose to not participate in the auctions and take their business elsewhere). The work most closely related to ours is Engelbrecht-Wiggans 1996, who presents a model of a mechanism that combines a multi-unit auction with some non-competitive contracts. In this model, suppliers have the option to commit to supply the units at a price to be determined by the auction. Doing so saves the supplier some auction participation fee (but typically results in a less desirable price.) Under a variety of conditions, even when bidders are homogeneous, at

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In the Ultimatum game the proposer makes a take-it-or-leave-it offer to the responder. If the responder rejects the offer, then both players earn zero (or their outside option).

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equilibrium some will voluntarily choose the non-competitive contract while others will choose to bid in the auction and the auctioneer benefits from having allowed non-competitive sales. Our study is a step towards gaining analytical and empirical insight into hybrid mechanisms that combine auctions with non-competitive contracts. We develop a model of a simple hybrid environment that combines an English auction with non-competitive contracts. We find that in theory this mechanism yields lowers costs to the buyer than a pure auction mechanism while still generating positive profits for suppliers. We then proceed to compare the two mechanisms in the laboratory, and find our theoretical benchmarks to be quite accurate. In section 2 we present our model and theoretical benchmarks. We describe the experimental design and related hypothesis in section 3, present results in section 4, and offer conclusions, managerial insights, and directions for future research in section 5.

2. Theory In this section we develop the basic model and derive key theoretical results. We will start by describing the general structure of the model, and then precisely define the two mechanisms of interest. We then examine implications for the buyer, for the suppliers and for efficiency. These theoretical predictions serve as benchmarks for the laboratory experiment. Imagine a “buyer” who needs to procure Q units of some commodity. There are N suppliers from whom the buyer can try to obtain units. Each supplier i (i = 1, 2, … N) can provide a single unit, knows his cost Ci of doing so, and has some say in whether or not he supplies a unit. If too few suppliers agree to provide units, then the buyer incurs some fixed cost Co ≥ Ci ∀ i for each of the remaining units; this cost may be interpreted in a variety of ways, including as the cost to the buyer of unsatisfied demand, as the cost of units from some unlimited backup supply source, or as the cost to the buyer of manufacturing the units in-house. One mechanism for determining which suppliers will provide units is a descending-bid (reverse) uniform-price auction. Consider the following stylized version of this auction: the buyer starts by offering a price of Co per unit and then reduces the price continuously; let Pt denote the price at time t. At any point in time a buyer can drop out of the auction, and once out

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cannot bid again. The price continues to decrease until there are exactly Q suppliers left willing to provide a unit5. Suppliers have the dominant strategy of dropping out of the auction at a point where Pt = Ci. At this point, the auction price is exactly the supplier’s cost, and the final auction price will be exactly equal to cost to the losing supplier who was the last to drop out. Our theory presumes that suppliers use this dominant bidding strategy. The idea behind using an auction is that it establishes a “competitive” price. In order for there to be any competition in the auction, there must be at least one supplier who “loses” in the sense of not supplying a unit to the buyer. Therefore, let us assume that N ≥ 2 and that 1 ≤ Q ≤ N1.6 Furthermore, intuitively, the more suppliers that must lose—i.e., the greater the excess supply—the greater the competition will be, and the lower the expected cost will be to the buyer. So, let us examine how the buyer might increase competition. One possibility is for the buyer to find additional potential suppliers, thereby increasing N and the excess supply; we presume that the buyer has already done so and that N can not be increased any further. Another possibility is for the buyer to reduce the number of units to be procured through the auction. This also increases the excess supply in the auction, but leaves the buyer with fewer than Q units. Our model already allows the buyer to make up for any shortfall at a cost of C0 per unit. But can the buyer do better than this? Consider the following extension to the auction. Suppose that prior to the auction the buyer approaches some of the supplier and offers them an opportunity to commit to providing the units at a price to be established later, by the auction7. More specifically, let M denote the number of suppliers to whom the buyer makes this offer. Those who turn down this offer are not allowed to participate in the auction; the auction will have the other N-M suppliers competing for 5

If the price decreases in discrete steps and/or suppliers have positive probability of having exactly the same cost, then there will be a positive probability that more than one supplier drops out at the same time. Our theory approximates reality by assuming a continuous price decrease and continuous value distributions. This assures that there is zero probability of two or more suppliers dropping out at the same time. In practice, if multiple suppliers drop out simultaneously, and this causes the supply to become strictly less than demand, the units could be allocated to all the suppliers who stayed in and randomly among the suppliers who dropped out last. 6 These, and subsequent, technical restrictions will hold in our experimental settings. 7 In the Engelbrecht-Wiggans, 1996,model, there is a cost to participate in the auction and individuals could decide whether or not to compete in the auction or take the non-competitive route; the number of non-competitive sales was endogenously determined. In contrast, in the proposed model, there is no cost of participating in the auction. As a result, suppliers would prefer to participate in the auction rather than take the non-competitive route. So the model assumes that the buyer can exogenously set the number of non-competitive sales M, and these M suppliers have option of turning down the non-competitive offer but do not have the option of participating in the auction.

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Q-M units.8

If any of the M selected suppliers turns down the offer, then buyer will have to

make up the resulting shortfall at a cost of C0 per unit. Since, in any case, the buyer acquires M units outside of the auction itself, we refer to M as the number of non-competitive units. Intuitively, we might argue as follows: Increasing M increases the fraction of suppliers in the auction who will lose; in other words, it increases the amount of excess supply relative to the total supply in the auction. This may increase competition and decrease the expected auction price. If so, and if the non-competitive suppliers accept the non-competitive offer, then the buyer benefits from having made the non-competitive offers. Furthermore, if there is little enough excess supply, then the expected auction price may well be high enough that non-competitive suppliers would be willing to accept it rather than be left entirely out of the process. We will show that increasing M does decrease the expected auction price, and that if the excess supply is small enough, then there will be a positive number M of non-competitive suppliers such that the non-competitive suppliers obtain a greater expected profit from accepting the offer than from declining it. In short, in theory, there is a range of cases in which the seller can decrease cost by making some non-competitive offers. Before deriving our results, we need to pin down a few more details. For one, the analysis will differ depending on when the buyer makes the non-competitive offer. We assume that the offer is made before the suppliers know precisely what their costs will be for this particular product. At this point, the suppliers are stochastically identical. Therefore it doesn’t much matter how the M non-competitive suppliers get selected, and for our purposes, we can (and will) think of them as being selected randomly. However, in practice non-competitive suppliers might be selected based on some non-monetary attributes, such as a good record for quality or delivery reliability. Committing to a supplier prior to the auction may be used as a signal by the buyer that he is committed to a long-term relationship. As we already argued above, under truthful bidding, the price will be equal to the lowest cost of any losing supplier. Specifically, this gives the following proposition:

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Note that the above restrictions on N, Q and M imply that N-M ≥ 2 and that N-M ≤ Q-M-1; in words, there will still be at least two bidders and more units than bidders, thereby assuring that there will be competition in the auction.

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Proposition 1: In our auction with N-M suppliers competing for Q-M units, N-Q suppliers will lose, and the per unit price established by the auction will be the N-Qth largest of the N-M competing suppliers’ costs. Proof: This follows immediately from truthful bidding being the dominant strategy.

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In addition, assume that the suppliers’ privately-known costs are independent draws from some known, continuous, cumulative distribution F(.). Except for the fact that our bidders are providing rather than acquiring goods, this is the Vickrey 1961 model with independently drawn, privately-known values, and we henceforth refer to it as the case of IPV. As a result, there is zero probability that two or more suppliers have exactly the same cost, and therefore truthful bidding results in there being zero probability that more than Q suppliers are willing to provide a unit at the final price. Now we are ready to derive our main results. We start by noting that what really matters is how the expected values of certain order statistics compare. Specifically, let C(i,k) (with 1≤i≤k) denote the i-th largest out of k independent samples9 and E(i,k) the expected value E[C(i,k)]. As we observed before, the expected price established by the auction is the N-Qth largest of N-M suppliers’ costs. Therefore, the expected auction price may be written as E(N-Q, N-M). And if the buyer offers few enough—“few enough” may be zero—non-competitive units so that all non-competitive offers will be accepted, then the buyer’s expected price per unit may also be written as E(N-Q, N-M). So, the buyer cares about how E(N-Q, N-M) varies with M. Furthermore, a non-competitive supplier has a greater expected profit from accepting rather than declining the offer whenever E(N-Q, N-M) exceeds the supplier’s expected cost. A non-competitive supplier’s expected cost is equal to the mean of the distribution. Note that the mean of a distribution can be viewed as the expected value of the largest of one sample from that distribution, which may be written as E(1,1). So an expected profit maximizing non-competitive supplier cares about how E(1,1) compares to E(N-Q, N-M). Our results follow from the following three basic properties of order statistics (see, for example, Arnold, et al. 1992): 9

Actually, these results on order statistics—and their corollaries—hold more generally. For example, let θ denote some (unknown) underlying state of Nature and assume that the Ci’s are independent draws from some conditional distribution F(c|θ). Then our results hold for each possible θ, and since we are interested in averages, they also hold unconditionally for such conditionally independent costs Ci.

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Property 1: E(i,k) increases as k increases. Property 2: E(i,k) decreases as i increases. Property 3: If F(.) is such that E ( median) ≥ mean , then E ( ⎢⎣ k / 2 ⎦⎥ , k ) > E (1,1) . For example, if the distribution F is symmetric, then E ( ⎢⎣ k / 2 ⎥⎦ , k ) > E (1,1) .

Now we can show that the buyer benefits when suppliers provide units non-competitively. Specifically, we have the following proposition: Proposition 2 (Corollary to Property 1): The bigger M, the lower the expected price established by the auction, and therefore, the lower the buyer’s expected cost per unit so long as all M noncompetitive suppliers accept the non-competitive offer. Proof: Property 1 implies that E(N-Q, N-(M-1)) > E(N-Q, N-M), and therefore that the buyer’s expected cost E(N-Q, N-M) decreases as M increases.

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So, the buyer benefits from procuring units non-competitively IF suppliers are willing to accept non-competitive offers. But under what conditions might the suppliers be willing to provide units non-competitively? The following two propositions address this question: Proposition 3 (Corollary to Property 1): If N ≥ 3, Q is close enough to N, and M = 1, then the non-competitive contract has positive expected value, and an expected profit maximizing supplier may be presumed to accept the contract. Proof: Consider Q = N-1. Then up to N-2 contracts can be offered non-competitively and N-2 ≥ 1. For Q = N-1, we have that N-Q = 1, and therefore E(N-Q, N-M) = E(1, N-M). By Property 1, E(1, N-M) > E(1,1), and therefore E(N-Q, N-M) – E(1,1) > 0.

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This proposition assures that if there is little enough excess supply, then a single non-competitive contract has positive expected value regardless of the suppliers’ cost distribution. But what if the buyer wants substantially less than almost all of the available supply? Or what if the buyer wants to offer more than one non-competitive contract? In general, the non-competitive contract may no longer have positive expected profit to the supplier. However, the next proposition shows that there are many distributions for which non-competitive contracts will have positive value -9-

even if the buyer wants substantially less than almost all of the available supply and/or offers more than one non-competitive contract. Proposition 4 (Corollary to Properties 2 and 3): A) If the mean cost is at most equal to the expected median cost and 0 < M ≤ 2Q-N, then the M non-competitive contracts have positive expected value, and expected profit maximizing suppliers may be presumed to accept the contracts. B) If the mean cost is equal to the expected median cost and M = 2Q-N+1 then the M non-competitive contracts have zero expected value. C) If the mean cost is at least equal to the expected median cost and 2Q-N+2 ≤ M < N, then the M non-competitive contracts have negative expected value, and expected profit maximizing suppliers may be presumed to decline the contracts. Proof: A) First, the hypothesized condition M ≤ 2Q–N implies that 2Q-2N ≥ M-N, and therefore that N-Q ≤ ⎢⎣( N − M ) / 2 ⎥⎦ . Second, the condition N-Q ≤ ⎢⎣( N − M ) / 2 ⎥⎦ together with Property 2

(

)

implies that E(N-Q, N-M) ≥ E ⎢⎣( N − M ) / 2 ⎥⎦ , N − M .

(

Finally, Property 3 implies that

)

E ⎢⎣( N − M ) / 2 ⎥⎦ , N − M > E(1,1). Therefore E(N-Q, N-M) – E(1,1) > 0. B)

This

follows

directly from the fact that in this case, the price setting bid in the auction is the median bid. C) This proof is simply the mirror image of that for part A).

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Note that the condition 0 < M ≤ 2Q-N implies that Q > N/2. So, if the mean cost is less than or equal to the expected median cost and the buyer wants just over half the available supply, then a single non-competitive contract will have positive expected value to the supplier. And the more that the buyer’s demand exceeds half of the available supply, the greater the number of non-competitive contracts that can be offered without them becoming unprofitable to the suppliers. In particular, if there is only one unit of excess supply, (ie Q = N-1) then the noncompetitive contracts will have positive expected value to the suppliers so long as M < Q, i.e. so long as the buyer auctions at least one unit.

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For symmetric distributions, the expected value of the median equals the mean and therefore the relationship holds in each of the three parts to Proposition 4. This gives the following result: Proposition 5 (Corollary to Proposition 4): For any symmetric distribution F, the expected value of the contract will be positive if and only if and M < 2Q-N+1, zero if and only if M = 2Q-N+1, and negative if and only if M > 2Q-N+1. In short, the expected value of the contract will have the same sign as M – (2Q-N+1). Unlike Proposition 3, Proposition 4 does require that the distribution F satisfies certain restrictions. In particular, Part A of Proposition 4 requires that the mean cost is less than the expected median cost. However, many distributions satisfy this condition (such as all symmetric distributions; in general, more than half of all theoretically possible cost distributions satisfy the condition). Furthermore, the condition may well be satisfied by real suppliers’ actual cost distributions. In particular, imagine that there is some standard source or technology that puts an upper limit on suppliers’ costs. Than suppliers usually can’t do much better than this limit, but occasionally a supplier may discover a superior technology, that would lower this supplier’s costs. In this case, most of the probability is concentrated near the upper end of the distribution, with the rest scattered at lower values, and the necessary condition will hold. In this case, since the buyer wants to have as many non-competitive sales as possible, we know exactly the number of non-competitive contracts that should be offered. Indeed, combining propositions 2 and 4 immediately gives the following result: Proposition 6 (Corollary to Propositions 2 and 4): If the mean cost is at most equal to the expected median cost, the hybrid mechanism that minimizes the buyer’s cost is with M = 2Q-N non-competitive sales. As with “optimal” reservation prices (see for example Myerson, 1981), non-competitive purchases destroy efficiency. There are several different ways to define efficiency. We calculate how efficient our mechanism with non-competitive sales is in terms of the probability of an -11-

efficient allocation. Specifically, define PM = probability that the mechanism with M noncompetitively priced units yields an efficient allocation, and define the relative efficiency for mechanisms with M1 and M2 non-competitive sales by PM1 / M 2 . The auction always allocates its units efficiently. Therefore, P0 = 1. And when M > 1, the question becomes “How likely is it that the M non-competitive suppliers are all from the set of suppliers with the Q lowest costs (assuming that the non-competitive suppliers are chosen at random)?” This is a straight forward combinatorial question.10 In particular, the number of ways to chose M out of Q is Q! / (M! (Q-M)!) and the number of ways to chose M out of N is N! / (M! (N-M)!). Therefore, PM = Q! (N-M)! / (N! (Q-M)!). (Note that if M=0, then this expression equals 1, as it should.) 3. Design of the Experiment Our design compares the performance of the non-competitive sales mechanism (NC) and a uniform-price descending-bid “oral” auction mechanism (AU) in the procurement setting. The bidders play the roles of suppliers, and the auctioneer is the buyer who wishes to minimize the total cost of procuring two units. Three suppliers (who together have the capacity to produce three units) compete for the right to supply the commodity to the buyer. So in our experimental setting, N = 3, Q = 2, and M = 1. Suppliers have costs that are drawn randomly from a uniform distribution from zero to 100 tokens (rounded up to the nearest integer), so F is U(0,100). The buyer also has an outside option of purchasing units at a cost of 100 tokens (the highest possible cost). In the AU treatment the price starts at 100 tokens and goes down by one token every second. When the price becomes too low and a bidder wishes to stop bidding he clicks the “Stop” button. As soon as one of the bidders stops bidding, the total supply falls from three to two units, and the auction ends at the price at which the bidder dropped out. The two remaining bidders each supply one unit and earn the difference between the auction price and their own cost. In the NC treatment one of the three bidders is randomly selected and given an option to supply one unit at the price to be determined by the auction in which the other two bidders compete. The bidder has to make a decision before he learns his cost in this round; he can 10

Under our assumptions, there is zero probability of two (or more) suppliers having exactly the same cost, and therefore there is only one set of suppliers that is efficient.

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decline this option, in which case he earns zero for the round, or he can accept the option, in which case he earns the difference between the price that will be determined by the auction and his own cost for the round that he will learn after he decides whether or not to supply a unit. If the non-competitive supplier declines the option to supply the unit, the buyer purchases one unit at his outside option cost of 100, and the right to supply the second unit is still auctioned off.

Session 1 2 3 4 5 6 7 8 9 10 11 12

Draw Number 1 2 3 4 5 6 1 2 3 4 5 6

Number of Treatment Participants Date and Time AU 6 6/1/2004, 4 PM AU 6 6/1/2004, 4 PM AU 6 6/1/2004, 4 PM AU 6 6/2/2004, 3:30PM AU 6 6/2/2004, 3:30PM AU 6 6/2/2004, 3:30PM NC 6 6/1/2004, 2:30 PM NC 6 6/1/2004, 2:30 PM NC 6 6/1/2004, 2:30 PM NC 6 6/2/2004, 1:30 PM NC 6 6/2/2004, 1:30 PM NC 6 6/2/2004, 1:30 PM Table 1. Experimental sessions

Average Earnings $25 $25 $25 $25 $25 $25 $24 $24 $24 $24 $24 $24

We conducted six sessions for each treatment, with six participants in each session. Each round the participants were randomly re-matched in groups of three. The costs and matching were randomly drawn in each session within a treatment (we designate a random cost and matching draw with a “draw number” one through six), but were identical in the two treatments. So, in total, our study consists of six independent observations for each of the two mechanisms, and the mechanisms performance can be compared pair-wise across sessions. We summarize the design in Table 1. Each session started with 10 practice rounds. In the NC treatment, the practice rounds included 2-bidder auctions for one unit, and in the AU treatment the practice rounds included three bidder auctions for two units. The values and matching for the ten practice rounds were identical in all twelve sessions. At the end of each round bidders saw a history of the costs and prices in the session so far that included: • • • •

Actual costs of all six suppliers Average cost of each supplier Average cost in each period Average cost across all suppliers and periods. -13-

They also saw similar information about auction prices that included: • • • •

Auction prices that resulted in each market Average price in each market Average price each period Average price across all markets and all periods.

Figure 1 displays the actual information that participants in the non-competitive treatment saw at the end of the ten practice rounds.

Figure 1. Summary information shown to participants at the end of the ten practice periods in the non-competitive sales treatment.

We used a random number generator in Microsoft Excel to draw the costs, and for the practice rounds we selected a sample of draws that resulted in overall average cost of close to 50 (51.07 in actuality) and an overall average auction price, assuming that all bidders follow the dominant bidding strategy, of close to 66.7 (the actual prices varied slightly by session, since participants deviated slightly from the dominant bidding strategy, especially in early rounds). The purpose of providing this summary information was to promote faster understanding on the part of the participants in the NC treatment about what the average costs and auction prices are likely to be. The practice rounds were also conducted in the AU treatment for the purpose of keeping the experimental protocol as similar as possible in the two treatments. Starting in period 11, the participants played the 30 rounds of the game. Each round in both treatments started with the summary information similar to Figure 1 (but also including information for all previous rounds). In the NC treatment one of the three suppliers was also asked to decide whether to accept or decline the option to supply one unit at the end of the auction at the auction price. The other two suppliers in the NC treatment, as well as all three -14-

suppliers in the AU treatment, simply had a “Continue” button on their screen. The round then proceeded to the auction. After the auction all suppliers learned the outcome of the current round that included: • • • •

A reminder of what they did in this round (either bid in the auction, supplied a unit after the auction, or did not participate) Cost this round Auction price Profit.

Additionally, in the NC treatment the non-competitive supplier was told what his profit would have been had he made a decision that was different from the one he actually made. So if the supplier opted to not supply the unit, he was told the profit or loss he would have made had he decided to supply it, and if the supplier opted to supply the unit, he was told that had he decided not to supply the unit he would have earned zero. See the Appendix for complete instructions. All sessions were conducted at Penn State’s Smeal College of Business Laboratory for Economic Management and Auctions (LEMA) on June 1 and 2, 2004. Participants, mostly undergraduate students from diverse fields of study, were recruited using the on-line recruitment system. Cash was the only incentive offered. Participants were paid their total individual earnings from all 40 rounds (ten practice rounds and 30 actual rounds) plus a $5 show-up fee at the end of the session. The software was built using the zTree system (Fischbacher 1999). Each session lasted about 90 minutes and average earnings were approximately $25 in the AU treatment and $24 in the NC treatment. 4. Results 4.1 Non-competitive Suppliers’ Decisions The critical assumption of our theory is that the non-competitive supplier should decide to accept the option to supply one unit after the auction at the price determined by the auction. Expected profit from accepting the option is positive, so if the suppliers’ objective is simply to maximize their expected profit, then they should always accept the option. Figure 2 shows the actual average acceptance rates over time in all six sessions.

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100.00% 90.00% 80.00%

Percentagee IN

70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Period

(a) Proportion of suppliers opting in of all six sessions over time 100% 90% 80% Proportion In

70% 60% 50% 40% 30% 20% 10% 0% 11 - 20

21 - 30

31 - 40

Periods Session 1

Session 2

Session 3

Session 4

Session 5

Session 6

(b) Proportion of suppliers opting in, grouped in blocks of ten periods broken out by session. Figure 2. Actual average Proportion of suppliers opting in for all six sessions over time.

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Session 1

2

3

4

5

6

Subject 1 2 3 4

Periods in 1 - 10 1 - 10 1,2,6,9 1 - 6,8,10

Periods out none none 3,4,5,7,8,10 7,9

5 6

1,2,3,5 - 10 1,2,10

4 3-9

1

1,3,4,7,8

2,5,6,9,10

2 3

1,2,5,7,8,10 1-7

3,4,6,9 8 - 10

4 5

1,2,6,8 1 - 6, 8 - 10

2,4,5,7,9,10 7

6 1 2 3 4 5 6 1

1 - 4, 7 1 - 10 1 - 10 1 - 10 1 - 10 1 - 10 1-3,5-10 1 - 4,8 - 10

5,6,8 - 10 none none none none none 4 5,6,7

2

1,4,5,7 - 10

2,3,6

3 4

1 - 5,7 - 9 1 - 10

6,10 none

5 6 1 2

1,4,5,10 1 - 5,7,9,20 1 - 7, 9,10 2

2,3,6 - 9 6,8 8 1, 3 - 10

3

1,2,5,7,8,9

3,4,6,10

4 5 6 1 2 3 4 5 6

1,3 - 6,9,10 1-8 1 - 4,7 - 10 1 - 6, 8 - 10 1 - 10 1 - 10 1 - 10 1 - 10 1 - 10

2,7,8 9,10 5,6 7 none none none none none

Comments always in (A) always in (A) First out after a large profit (59), subsequent outs after a loss (M) First out after first loss, second out after a large win (76) (M) One out after a small win (3) that followed a large loss (71). Subsequently all wins (A) Out following 2 losses in a row. No gain experience (L) First out following a large loss (-66); second out following a large loss (-80) followed by a large gain (91), subsequent outs following a small gain (13) that followed a small loss (-17) (M) First out following 2 losses, next out following a loss, last out following a large (86) gain (M) Out following a small gain (9) that followed a small loss (-4) First 2 outs followed a large gain (60 and 56) and last followed a medium gain (26) (G) Out followed a loss (-19) (A) First out followed a gain of 0 that followed a large loss (-62); second out followed a large gain (55) (M) always in (A) always in (A) always in (A) always in (A) always in (A) Out followed a loss (32) (A) out followed a large gain (41) (G) Out in period 1, next 2 outs followed a medium (22) and a large (47) gain (G) Out followed a large gain (74), out last time following a small gain (15) always in (A) First out followed a small loss (-9) and second out followed a large gain (97) (M) Outs followed a loss (L) no reason (A) out in period 1 and following a loss. No gain experience (L) First out followed a loss (-33), second after a gain of 0, last in period 10 First out followed a small loss (-6) and second followed a large gain (33) (M) Out followed a large gain (56) (G) Out following a small gain (14) that followed a large gain (64) One out followed a large gain (A) always in (A) always in (A) always in (A) always in (A) always in (A)

Table 2. Summary of individual behavior of non-competitive suppliers

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Acceptance rates start out at 100% decrease over the first 10 periods, and then settle down at about 70%. The actual average acceptance rate in periods 11 – 20 is 89%, in period 21 – 30 it is 71.6% (the decrease from 89.1% to 71.7% is statistically significant; one-sided matched-pair ttest p-value is 0.0106). The average acceptance rate in periods 31 – 40 is 70% (the decrease from 71.7% to 70% is not statistically significant; one-sided matched-pair t-test p-value is 0.3856).

Note some heterogeneity among the sessions: acceptance rate is nearly 100%

throughout in sessions 3 and 6, is only 60% in session 2, and close to 70% in the other three sessions. The initial high acceptance rate and the initial fall is not surprising: Recall that in periods 1 – 10 participants experience the outcomes of an ascending auction with two bidders and one object, and observe information about costs and prices. By the end of period 10 the average actual costs are close to the theoretical average of 50, and the average actual auction price is close to the theoretical average of 66.7. The fact that acceptance rates are close to 100% early on is evidence that participants are able to process the average cost and price information correctly, and determine that accepting the non-competitive contract is profitable on average. To obtain a clearer picture of how individuals make decisions to accept or to decline non-competitive contracts, we summarize individual decisions in Table 2. Of the 36 subjects, 18 (50%) either always accept the contract, or reject it one time only one time (we classify them as “A” in Table 2). Of the remaining 18 subjects, 14 (78%) reject the contract either following a loss of following a large gain (for the purpose of this analysis, we conservatively classify a gain as being large when it is over 20—the average expected gain from accepting the contract is 66.7 – 50 = 16.7). Rejecting the contract after a loss can be explained by loss aversion, while rejecting it after a large gain is the common “quit while ahead” strategy. There appears to be a fairly common pattern, marked “M” in Table 2, that involves rejecting the contract after either a loss or a large gain, and often the same participant does both (subjects 3 and 4 in session 1, subjects 1, 2 and 6 in session 2, subject 5 in session 4, and subject 4 in session 5—seven subjects in total). The rest of the subjects, marked “L”(oss) and “G”(ain) in Table 2, reject the contract either only after a loss (subject 6 in session 1, subject 6 in session 4, subject 2 in session 5—three subjects) or only after a large gain (subject 4 in session 2, subjects 1 and 2 in session 4, and subject 5 in session 5—four subjects). The remaining four subjects reject the contract after a small or medium gain: subject 3 in session 2 opted out after a small gain that -18-

followed a loss, subject 3 in session 2 opted one time after a large gain of 74 and the second time after a gain of 15, subject 3 in session 5 opted out one time after a loss, then again after a gain of zero, and last time in period 10, and subject 6 in session 5 opted out the first time after a gain of 14, and the second time after a large gain of 64. The main point is that the acceptance rate, after the initial decrease, settles down and stays fairly constant at about 70% in the last 20 rounds of the game (or after the initial ten rounds). Therefore, we will confine the rest of our analysis to the last 20 rounds of the game—a period where acceptance rates have reached a constant level. 4.2 Bidding Behavior The second presumption of the theory is that bidders follow the dominant bidding strategy in the auction. It has been well-established that participants are able to learn to bid close to the dominant strategy in ascending auctions (see Kagel 1995 and references therein).

Our

experiment differs from the standard setting because we use the reverse auction frame, and in that (in the AU treatment) two units are auctioned off. We plot bids as a function of cost in Figure 3. 100 90 80 70

Bid

60 50 40 30 20 10 0 0

10

20

30

40

50

60

70

80

90

100

Cost

Figure 3. Bid as a function of cost

Despite the differences between our setting and the standard experimental setting, the bidding behavior is very close the dominant strategy in both treatments. Overall, 66% of the bids exactly equal cost (68% in the AU treatment and 65 in the NC treatment), and 89% of the bids are within five tokens of cost (87% in the AU treatment and 90% in the NC treatment). About 9.5% of the bids are more than five tokens above cost (10.9% in the AU treatment and 8% in the -19-

NC treatment) and about 2% of the bids are more than five tokens below cost (1.7% in the AU treatment and 2.3% in the NC treatment). Since a bid that is below cost might result in a loss, bids below cost are clearly errors, and we see very few of them (only 2%). Bids that are slightly above cost indicate that a bidder dropped out before the price reached the cost, so those bids can potentially result in foregoing an opportunity to win the auction, and might indicate an attempt on the part of some of the bidders to collude by driving the overall price level down. This tendency indicates that actual auction prices are slightly above those predicted by the theory. However, since the tendency to drop out early is small, and is approximately the same in both treatments, it should not have a significant effect on the differences in total costs between the two treatments. 4.3 Efficiency Comparisons In theory the AU mechanism is 100% efficient, and the NC mechanism is only 67% efficient, because when the high cost supplier is selected for the noncompetitive contract, the mechanism must result in an inefficient allocation. In the experiment, about 91% of the auctions resulted in the efficient allocation in the AU treatment, but only 48% in the NC treatment.

Proportion of inefficient allocation

Figure 4 summarizes the causes of inefficiencies in the 2 treatments. 60% 50% 40% 30% 20% 10% 0% AU

NC Treatment

Auction outcome

Hich cost chosen

Low cost opt out

Figure 3. Causes of inefficiency

The auction outcome itself is not 100% efficient because bidders occasionally stop bidding short of their costs, and this causes 31 out of 360 auctions (about 9%) in the AU treatment to result in inefficient allocations. In the NC treatment, only ten out of 360 auctions -20-

result in inefficient auction allocations (about 3%), but the two major sources of inefficiency are (1) the high cost supplier being chosen for the non-competitive contract (which, by design, happened in 33% of the auctions), and (2) a low cost supplier was chosen for the noncompetitive contract, but rejected the contract (this happened in 57 out of 360 auctions—about 16%11). . 4.4 Buyer Cost Comparison We summarize the actual and predicted buyer costs grouped in ten period blocks in Table 3, and display this information for the last 20 periods graphically in Figure 4. Predicted Periods 21 - 30 Periods 31 – 40 All Periods Session AU NC AU NC AU NC 1 141.3 123.2 139.4 132.9 146.7 132.9 2 153.8 138.9 147.9 131.0 150.9 130.6 3 161.7 147.7 156.5 134.2 149.4 132.0 4 155.6 132.0 148.2 130.0 150.6 134.1 5 146.8 133.9 139.5 130.0 145.4 133.5 6 158.4 142.0 132.3 114.2 147.6 130.9 Average 152.9 136.3 144.0 128.7 148.4 132.3 Actual Periods 11 - 20 Periods 21 - 30 Periods 31 – 40 All Periods Session AU NC AU NC AU NC AU NC 1 170.4 147.5 144.5 135.0 141.1 138.4 152.0 140.3 2 155.2 128.6 161.9 148.8 155.9 148.7 157.7 142.0 3 132.2 115.3 168.4 148.9 159.2 133.8 153.3 132.7 4 149.9 141.8 161.2 150.6 154.0 146.8 155.0 146.4 5 157.0 144.4 152.8 146.0 144.9 149.2 151.6 146.5 6 157.2 142.4 159.9 148.6 137.4 134.7 151.5 141.9 Average 153.7 136.6 158.1 146.3 148.8 141.9 153.5 141.6 Table 3. Summary of the predicted and actual total buyer cost. Periods 11 - 20 AU NC 159.4 142.5 151.2 121.8 130.0 114.1 148.0 140.4 149.8 136.6 152.1 136.5 148.4 132.0

11

We count this latter case as an inefficiency, although in practice a supplier who rejected a non-competitive contract may have some more attractive outside options, and therefore the actual outcome may not be inefficient

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Average Costs AU: Predicted: 148.5 Actual: 153.4 Difference: 5.0 (3.25%) p-value: 0.2356

165.0 160.0

Average Cost

155.0 150.0

NC:

145.0

Predicted: Actual: Difference: p-value:

140.0 135.0 130.0 125.0 1

2

3

4

5

Session AU

6

144.1 132.5 11.6 (8.05%) 0.0041

Difference between AU and NC: Predicted: 16.0 (10.7%) p-value: 0.0026

NC

9.3 (6.1%) Actual: p-value: 0.0153 Figure 4. Actual and predicted average costs for all 30 periods (periods 21 – 40 in the study), broken out by sessions. The p-values refer to one-sided Mann-Whitney U test (Wilcoxon test) with the null hypothesis of MC < AU and Predicted < Actual.

We use the Mann-Whitney U test (also referred to as a Wilcoxon test, see Seigel ,1965, pg. 116) to compare the costs in the two treatments and the average predicted and actual costs in each treatment in the last 20 periods. The test reveals all the differences to be statistically significant, with the exception of the difference between the actual and the predicted costs in the AU treatment12. We note several regularities. •

Actual costs in both treatments are higher than the predicted costs. These differences are not very significant economically but are statistically significant for the last 20 periods in the NC treatment, as well as for all 30 periods in the AU treatment (Mann-Whitney pvalue is 0.0026). These differences are caused by the tendency of about 10% of the bids to be more than 5 tokens above costs.

•

The actual differences in costs between the AU and the NC treatments are statistically significant, although slightly below predicted differences (actual difference in cost for the last 20 periods is 9.3 tokens, or 6.1%, which is slightly smaller than the predicted difference of 16 tokens, or 10.7%). The actual differences are below predicted differences primarily because not 100% of non-competitive suppliers accept the contract (see detailed discussion in the previous section). Since only 70% of the suppliers accept the contract (in the last 20 periods), buyer costs are calculated under the assumption that

12

Sign test yields the similar results, except that the difference between the actual and predicted costs in the AU treatment is also significant. The sign test p-values are 0 0156 in all cases.

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the buyer exercises his outside option to purchase one unit at 100 when the noncompetitive supplier rejects the contract. This happens in about 30% of the auctions, driving the actual costs above the predicted costs in the NC treatments. In short, consistent with our theory, the non-competitive sales mechanism reduces costs. The reduction is smaller than the theory suggests because non-competitive suppliers sometimes decide not to participate. 4.5 Supplier Profit Comparisons Next, we look at the actual and predicted supplier profit under the two mechanisms. Figure 5 shows the average profit in the last 20 periods, separated by session. The differences between the averages of actual and predicted profits from auctions are extremely small and not statistically significant (Mann-Whitney test one-sided p-values are 0.4364 for AU and 0.2609 for NC).

Actual profits of the non-competitive suppliers are lower than predicted and the

differences are weakly significant (Mann-Whitney test one-sided p-values is 0.0868), and are substantially more variable than the profit of auction participants. The differences are due to the fact that only 70% of suppliers accept non-competitive contracts, and suppliers who reject the contracts earn 0. The average profit in the last 20 periods for non-competitive suppliers who accept the contracts is 17.0—exactly matching the predicted profit. Profit differences between treatments are significant, both economically and statistically. Suppliers in the AU treatment make on average 35% more than the auction participants in the NC treatment and 53% higher gains than non-competitive suppliers in the NC treatment (the latter higher difference is again, due to the fact that only 70% of the non-competitive suppliers choose to participate).

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30

25.0

25

Average profit

Average profit

30.0

20.0 15.0 10.0 5.0

20 15 10 5

0.0

0

1

2

3

4

5

6

1

2

Session Actual

4

5

6

Session

Predicted

Actual

(a) NC treatment: suppliers in the auction

Predicted

(b) NC treatment: non-competitive suppliers Average Profits: NC (Non-competitive Suppliers) NC (Auction) Actual: 12.2 Actual: 17.1 Predicted: 17.0 Predicted: 17.7 p-value: 0. 0868 p-value: 0.2609

30.0 25.0

Average profit

3

20.0 15.0 10.0 5.0 0.0 1

2

3

4

5

Session Actual

Predicted

6

AU Actual: Predicted: p-value:

25.9 25.4 0.4364

(c) AU treatment Figure 5. Profit comparisons in the last 20 periods

5. Summary and Discussion In practice, reverse auctions are often combined with non-competitive mechanisms when used for procurement.

Since auctions are often perceived as damaging to long-term

relationships, these combined (or hybrid) mechanisms are used as a way to capture the benefits of auctions (competition) while at the same time preserving the long-term relationships with existing suppliers. Our work is a first step towards gaining analytical and empirical insights into the performance of these hybrid mechanisms. We investigate a simple mechanism that combines an auction with a non-competitive sales contract. Specifically, we develop an analytical model of the new mechanism, and test this model in the laboratory. Our results show that using the hybrid mechanism decreases the buyers’ costs relative to a stand-alone auction, even without considering any benefits from long-term relationships. This finding is a critical first step in studying more complex and realistic procurement mechanisms. Our model, and the laboratory setting we use to test this model, is stylized relative to eSourcing settings observed in practice, and yet it helps us to draw useful conclusions for e-24-

Sourcing. In practice we observe that suppliers prefer hybrid mechanisms to pure auctions (Jap 2002). But it is up to the buyers to design the rules for these mechanisms. We demonstrate that it is possible to design hybrid mechanisms that generate costs that are as low, or lower, than reverse auctions. In practice, price is not the only dimension used to generate value for the buyer, and since hybrid mechanisms leave more room for communication, suppliers may perceive them as more attractive than stand-alone auctions. For example, a supplier who is offered a non-competitive contract might be a long-term supplier with a proven track record for quality and delivery reliability. The auction is used to establish a baseline price that could then be adjusted for the non-competitive supplier in order to properly account for the higher quality of this supplier’s product. A small part of the business could be auctioned off in order to establish the baseline price and also discover new potential suppliers. Auction winners get an opportunity to prove themselves in order to enter into a longer-term contract in the future. Finally, we suggest a direction for future research. A potentially fruitful direction that can bring our model closer to reality is to investigate how to combine non-competitive contracts with auctions in which a bidder may provide more than one unit. When bidders may supply multiple units, several new issues arise: the demand reduction, the exposure and the free riding problems13. It has been shown analytically that when bidders with linear preferences bid on multiple units, demand reduction may hinder competition14. Some of these analytical findings have also found support in the field15. 13

Demand reduction means that bidders bid below their true valuation on some of the units (in other words, they reduce the demand for the unit.) 14 Ausubel and Crampton 1998 showed that the sealed-bid uniform-price auction mechanism is vulnerable to the demand reduction problem. They also showed that the uniform price auction often does not perform as well as a mechanism that permits price discrimination. Engelbrecht-Wiggans and Kahn 1998a show that in pay-your-bid multi-unit auctions there is a tendency for bids on different units to be close even when valuations for these units are not the same. Of course there may be practical reasons to prefer a uniform price mechanism, since price discrimination is often viewed as being unfair. Engelbrecht-Wiggans and Kahn 1998b characterize equilibria that involve demand reduction for the uniform price multi-unit auctions when bidders have decreasing marginal values. Engelbrecht-Wiggans 1999 characterizes the equilibria to uniform price auctions when bidders have uniformly distributed flat demands. 15

List and Lucking-Reiley 2000 use a field experiment to study demand reduction in uniform price and Vickrey auctions for multiple units (see also Engelbrecht-Wiggans et al. (forthcoming)). Both mechanisms allow bidders to submit multiple sealed bids, but under the uniform price rule, when m units are for sale, the top m bids win, and all units are sold at the price equal to the highest rejected bid. Under the Vickrey rules, the top m bids win, but a winner’s price is the highest rejected bid made by other bidders (and therefore, different winners may well pay different prices). List and Lucking-Reiley sell pairs of sports cards (football, basketball and baseball) in 2-person markets where each bidder would like to purchase both cards and find that, consistent with the theory, demand reduction is higher in the uniform price auctions relatively to the Vickrey auctions. They also find that, contrary to

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When bidders have non-linear preferences (for example, when objects are either substitutes or compliments) two potential problems arise. The exposure problem happens when bidders with synergies are not guaranteed all the units they want, and therefore they risk losing money. The free riding problem happens when the efficient allocation requires bidders without synergies to combine in order to outbid a bidder with synergies (see Milgrom 2004 and references therein)16. Combining non-competitive sales with multi-unit auctions impact these problems. For example, bidders who have synergies may have an additional incentive to prefer non-competitive contracts, since those contracts remove the uncertainty associated with the production quantity. Buyers may have an additional incentive to offer non-competitive contracts to bidders with synergies because those bidders, fearing the exposure problem, may be unwilling to compete aggressively in auctions. Therefore, an area for future research is to investigate what happens if suppliers may provide multiple units, the impact that combining non-competitive contracts with auctions has on the free-rider and exposure problems, and the managerial question of, for example, if only some suppliers can provide multiple units, it is better to offer these suppliers the non-competitive contracts or to make them bid in the auction.

References Arnold, B. C., N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics, John Wiley and Sons, 1992, New York.

the theory, the bids on the first unit are higher in the uniform treatment than in the Vickrey treatment, and there are no significant differences in revenue between the two mechanisms. The field experiment setting does not provide a way for comparing efficiency. Kagel and Levin (2001) also find significant demand reduction in the laboratory, in both, sealed bid and ascending bid auctions. 16

Krishna and Rosenthal (1996) examine the simultaneous ascending auctions with synergies and heterogeneous bidders, and find that when bidders who exhibit economies of scale (synergies) are present, the bidding is less aggressive. Kagel and Levin (forthcoming) compare the performance of the sealed-bid uniform-price and the ascending-bid uniform-price multi-unit auctions when bidders have synergies and find that the ascending bid mechanism generally works better than the sealed bid mechanism, in terms of the frequency of the optimal bidding behavior, and participants’ profit, and consistently, the revenues are higher in the sealed bid auctions. A major finding is that subjects in ascending auctions tend to bid too timidly in response to the exposure problem, but this does not happen in sealed bid auctions. Bidders do learn to bid correctly in the environment without the exposure problem, and the learning is faster in ascending auctions than in the sealed bid. Katok and Roth (2004) compare the descending-bid Dutch auction and the ascending-bid uniform-price auction for homogeneous goods in an environment with synergies and find that descending auction generate higher revenues and more efficient allocations in a variety of environments.

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Aberdeen Group, Making e-Sourcing Strategic: From Tactical Technology to Core Business Strategy, September 2002, Boston, MA http://www.marketresearch.com. Ausubel, Lawrence M and Peter Cramton. Demand Reduction and Inefficiency in Multi-Unit Auctions, Working Paper No. 96-07, University of Maryland, July 1998. Bajari, P.L., McMillan, R.S. and Tadelis, S, Auctions versus Negotiations in procurement: an Empirical Analysis, NBER Working paper 9757, June 2003, http://www.nber.org/papers/w9757. Bulow, J. and Klemperer, P., Auctions versus Negotiations, American Economic Review 86(1), March 1996, pp. 180-194.

Emiliani, M.L. and D.J. Stec, Online Reverse Auction Purchasing Contracts, Supply Chain Management, 2001, Vol. 6, No. 3. Engelbrecht-Wiggans, Richard and Kahn, Charles. M. Multi-Unit Pay-Your-Bid Auctions with Variable Awards, Games and Economic Behavior, 1998a, 23, pp. 25-42. Engelbrecht-Wiggans, Richard and Kahn, Charles. M. Multi-Unit Auctions with Uniform Prices, Economic Theory, 1998b, 12 (2), pp. 227-258. Engelbrecht-Wiggans, R., "Sequential Auctions of Stochastically Equivalent Objects," Economics Letters, 1994, Vol. 44, pp. 87-90.) Engelbrecht-Wiggans, Richard, Auctions with Noncompetitive Sales, Games and Economic Behavior, 1996, 16, pp. 54-64. Engelbrecht-Wiggans, R., J. A. List, and D. Lucking-Reiley, Demand Reduction in Multi-unit Auctions with Varying Numbers of Bidders: Theory and Evidence from a Sports Card Field Experiment, International Economic Review, forthcoming. Engelmann, D. and Grimm, V, Bidding Behavior in Multi-Unit Auctions—an Experimental Investigation and Some Theoretical Insights, Working paper June 2003, http://www.cergeei.cz/pdf/wp/Wp210.pdf. Fischbacher, U., z-Tree - Zurich Toolbox for Readymade Economic Experiments Experimenter's Manual, Working Paper Nr. 21, Institute for Empirical Research in Economics, University of Zurich, 1999. Global Exchange Services, GE GSN, The World’s Largest Private Web Marketplace: case study, General Electric, Gaithersburg, MD, 2003 http://www.gxs.com/downloads/cs_gsnq202.pdf. Goeree, J.K., Bidding for the Future: Signaling in Auctions with an Aftermarket, Journal of Economic Theory 108, 2003, pp. 345-364. Halliburton Watch http://www.halliburtonwatch.org/, 2004. Jap, S.D., Online Reverse Auctions: Issues, Themes and prospects for the Future, Academy of Marketing Science Journal, Fall 2002, 30(4), pp. 506-525. -27-

Kagel, John H., and Levin, Dan, Behavior in Multi-Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions."Econometrica, 2001, 69(2), pp. 413-454. Kagel, John H., and Levin, Dan Common Value Auctions and the Winner’s Curse, Princeton University Press, 2002, Princeton, NJ. Kagel, John H., and Levin, Dan, Multi-Unit Demand Auctions with Synergies: Behavior in Sealed-Bid versus Ascending-Bid Uniform Price Auctions, Games and Economic Behavior, forthcoming. Katok, E. and Roth, A.E. Auctions of Homogeneous Goods with Increasing Returns: Experimental Comparison of Alternative “Dutch” Auctions, Management Science August 2004, 50(8), pp. 1-20. Krishna, Vijay, and Rosenthal, Robert W., Simultaneous Auctions with Synergies Games and Economic Behavior, 1996, 17, pp. 1-31. List, John and Lucking-Reiley, David H. Demand Reduction in Multi-Unit Auctions: Evidence from a Sportscard Field Experiment. American Economic Review, September 2000, 90(4), pp. 961-972. Milgrom, Paul, Putting Auction Theory to Work (Churchill Lectures in Economics), Cambridge University Press, 2004, Cambridge, UK. Monczka, R.M, Trent, R.J, and Handfield, R.B., Purchasing and Supply Chain Management 3rd edition, Thomson South-Western, 2005. Myerson, Roger B., 1981, Optimal Auction Design, Mathematics of Operations Research, 6(1), February 1981, pp. 58-73. Salmon, T.C. and Wilson, B.J., Second Chance Offers vs. Sequential Auctions: Theory and Behavior, Working Paper, May 2004, http://garnet.acns.fsu.edu/~tsalmon/SWaucbarg.pdf. Sawhney, M., Forward Thinking about Reverse Auctions, CIO Magazine, article number 060103, June 1 2003. Seigel, S. Nonparametric Statistics for the Behavioral Sciences, Wiley 1965, New York. van den Berg, Gerard J., van Ours, Jan C. and Pradhan, Menno P. The Declining Price Anomaly in Dutch Dutch Rose Auctions, American Economic Review, September 2001, 91(4), pp. 10551062. Vickrey, W., Counterspeculation, Auction, and Competitive Sealed Tenders,' Journal of Finance, 16, 1961, 8-37,.

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Appendix: experimental instructions The italicized text is for the NC treatment only, and the underlined text is for the AU treatment only. The rest of the text is common in the two treatments. Overview You are about to participate in an experiment in the economics of decision making. If you follow these instructions carefully and make good decisions you will earn a considerable amount of money that will be paid to you in cash at the end of the session. If you have a question at any time, please raise your hand and I will answer it. We ask that you not talk with one another for the duration of the experiment. In the main part of today’s session you will be randomly matched with 2 people in the room. You will be playing with different people during every round of today’s session. On your desks you should have a check-out form, a pen and two copies of the consent form. In each round of today’s session you will be playing a role of a supplier in a procurement setting. You will be competing against other suppliers for the right to provide one unit of a fictitious commodity. In total, there are two units of the fictitious commodity that are required.

How you make money NC Treatment only: The competition will take the form of a procurement auction. In the beginning of the round one of the three suppliers will be randomly selected to have an opportunity to supply one unit at a price to be determined by the auction. This supplier can either agree or decline this opportunity. After the one randomly-chosen supplier made his decision, all suppliers will find out their own costs for supplying one unit. AU Treatment only: The competition will take the form of a procurement auction. In the beginning of the round, each supplier will find out his own cost for supplying one unit. The costs for all participants and for all rounds have already been pre-determined, and they are integers from 1 to 100, with each integer being equally likely. Your cost in one round has no correlation with your cost in any other round or with the costs of any of the other suppliers (in other words, all costs have been drawn independently). If you are one of the two suppliers bidding in the auction, then you make money by winning the auction at a favorable price. If you win an auction at a price that is higher than your cost, then your profit is: Auction Price – Cost. For example, if your cost is 50 and you win the auction at a price of 60, then your profit in this auction is 60 – 50 = 10. Note: if you win the auction at an unfavorable price (at a price that is below your cost), you will lose money. Since you will know your cost prior to bidding you can avoid the possibility of losing any money in an auction by not bidding at unfavorable prices. If you do not win the auction, your profit for the round is 0. NC Treatment only: A supplier who agrees to supply one unit after the auction at the auction price, earns Auction Price – Cost for that round. Since the cost can be either above or below the auction price, this supplier can either make or lose money. A supplier who declines to supply one unit after the auction at the auction price, earns 0 for that round.

The mechanics of the auction The offer price will start at 100 tokens and will go down by 1 token every second. Your cost for the current round will be displayed on the screen next to the price. Every time the price changes, the computer will calculate and display on your screen the profit you could make at the current offered price. When the price falls below your cost

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the potential profit amount will become negative (giving you a way of knowing that the price has become unfavorable). As long as you wish to continue bidding at the price currently offered, you do not need to do anything. Once you decide to stop bidding, click the “Stop Bidding” button located on the bottom of your screen. Once you have clicked the button, you are assured of earning 0 for the current round. The auction ends when there is only one bidder remains in the auction. This remaining bidder wins one unit, and earns profit that equals to the amount of the auction price at the time the auction ended minus this bidder’s cost. Example NC Treatment only: Suppose there are 3 bidders in the auction (call them A, B and C). Suppose that bidder B has been randomly selected to supply one unit after the auction, and suppose bidder B accepted this opportunity. Suppose that later it turns out that the costs of three bidders in a round are 30, 50 and 70 respectively. AU Treatment only: Suppose the costs of three bidders (call them A, B and C) in a round are 30, 50 and 70 respectively. The price starts at 100 and decreases by 1 every second. When the price reaches 70 bidder C cannot make any money at this price, and therefore he clicks the “Stop Bidding” button. At this point only bidder A remains in the auction, so the auction ends. Bidder A earns 70 – 30 = 40 tokens, and bidder B earns 70 – 50 = 20 tokens NC Treatment only: by supplying one unit after the auction at the auction price. Had bidder B declined to supply one unit, he would have earned 0 instead of 20. Also note that had bidder B’s cost turned out to be above 70 (for example, 80), he would have had to supply one unit at a loss and earned 70 – 80 = -10. Summary information you will see in the beginning of each round In the beginning of each round you will see pertinent historical information on prices and costs for past rounds of the auction. You will see costs of six randomly-chosen people in this room (one of them will be yourself), including average costs for every person, average of the six costs for every period, and the overall average cost. You will also see prices that resulted in the auctions the six people participated in, including the average price for each of the auctions over all pervious periods, the average of the prices every period, and the overall average price. This information is there to give you a sense about average costs and prices that result from auctions NC Treatment only: and is especially useful for the randomly-selected supplier in his decision about whether to accept or decline the offer to supply one unit after the auction at the price determined by the auction. How the session will progress The session will include 40 rounds. We call the first 10 rounds of the session Phase 1, and the remaining 30 rounds Phase 2. NC Treatment only: In the first 10 rounds you will be competing in an auction against one other supplier for the right to supply one unit. In Phase 1 everyone will compete in auctions and nobody will be supplying a unit after the auction at the auction price. The purpose of Phase 1 is to give you a better understanding of the mechanics of the auction in which you are competing against one person, and to give you an opportunity to collect data about costs and auction prices that result. This information is pertinent for Phase 2. AU Treatment only: There is no difference in rules between Phase 1 and Phase 2. Your earnings from all rounds in both phases will contribute to your total earnings from the session. At the end of Phase 1 you will see a screen that will repeat all summary information about prices and costs thus far, and will inform you that Phase 1 is over and Phase 2 is about to start. Take a few minutes at this point to reflect on what you are doing. Remember that you will be playing with two randomly-chosen competitors in Phase 2 of the session. NC Treatment only: Two of the three will be bidding in the auction, and the third will be given an opportunity to supply one unit after the auction. How you will be paid At the end of the session, the computer will calculate the total profit you earned in all rounds and will convert it to US dollars at the rate of 3 cents per token. Your dollar earnings will be added to your $5 participation fee and displayed on your computer screen. Please use this information to fill out the check-out form on your desk. All earnings will be paid in cash at the end of the session.

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