supply and Demand

Seller Beware: Supply and Demand Reduction and Price Manipulation in Multiple-Unit Uniform Price Auctions Abel M. Winn,* Michael L. Parente, †and David Porter ‡ We experimentally compare under-revelation of supply and demand across alternative variations of ascending and descending two-sided price clock auctions. We find that buyers reduce demand more when the price is ascending but sellers behavior is consistent across clock directions. As a result, the clock price rule has empirical effects on efficiency even though it is theoretically neutral.

JEL Classification: D02, D03 1. Introduction “It is good for nothing,” cries the buyer; but when he has gone his way, then he boasts. -Proverbs 20:14 Auctions are popular tools for allocating scarce resources in a timely manner. Krishna (2009) notes that the most widespread auction rules are iteration (participants may revise their bids) and an ascending price. Cramton (1998) suggests two reasons why these rules might be so popular. First, iteration provides feedback to the bidders on their private valuation of winning compared with the valuations of their competitors. This assists the participants in the price discovery process. Second, the ascending price rule confers a sense of legitimacy on the outcome, because the losing bidders are given multiple opportunities to outbid the winner(s), but ultimately decline to do so. The strong track record of ascending price auctions has led economists to study them in multiple contexts, including the sale of treasury bills (Ausubel and Cramton 1998), carbon emission permits (Cramton and Kerr 1999), electromagnetic spectrum licenses (Banks et al. 2003), nitrous oxide emission per- mits (Porter et al. 2009), and even the provisionof public goods (Levati and Neugebauer 2004).

The ascending price rule is popular for “one-sided” auctions, in which supply is fixed exoge- nously and buyers are the only active participants. However, for “two-sided” auctions—in which supply is determined endogenously and both buyers and sellers are active—the Double Auction (DA) institution (Smith 1962) is usually deemed more appropriate, particularly for environments in which participants wish to buy or sell multiple units. The DA essentially consists of multiple single-unit auctions in which buyers call out successively higher bids and sellers successively lower offers until an agreed price is reached. Note that this process, like the one-sided ascending price * Argyros School of Business and Economics, Chapman University, One University Dr., Orange, CA 92866, USA; E-mail: [email protected]; corresponding author.

† Capital Habeus Unit of the Office of the Federal Public Defender, 321 E. 2nd St., Los Angeles, CA 90012, USA; E-mail: [email protected] ‡ Economic Science Institute, Chapman University, One University Dr., Orange, CA 92866, USA; E-mail:

[email protected] Received December 2013; accepted January 2015. 760 2015 by the Southern Economic Association Southern Economic Journal2016, 82(3), 760–780 DOI: 10.1002/soej.12086 auction, also provides feedback to buyers (sellers) and offers losing participants multiple opportu- nities to outbid (undersell) the winners.

A third salutary feature of the DA is that it discourages participants from strategically reducing the number of units they demand or supply in an effort to manipulate the market price. If all trades in an auction are executed at a uniform price it is profitable for buyers (sellers) to reduce their demand for (supply of) some units if doing so sufficiently lowers (raises) the price at which they buy (sell) the remaining units. 1Consequently, a uniform price auction is likely to be inefficient. Traders have the option of strategically reducing demand or supply to manipulate prices in a DA, but to do so profit- ably would require an overwhelming amount of coordination, because the price for each unit is deter- mined independently. As a result, DAs routinely exploit all of the available gains from trade.

The incentive to strategically reduce is strongest when there is some asymmetry in the partic- ipants message space and/or their ability to withhold units to affect the price (i.e., market power).

In a posted offer market, for example, sellers set prices and buyers decide how many units to pur- chase. Holt (1989) notes that in such markets prices tend to approach the competitive equilibrium from above or fail to converge to it altogether. Davis and Holt (1994) show that posted offer prices tend to be higher—and efficiency lower—when supply is configured in such a way that one seller can profitably raise prices by withholding some of his output.

Markets with symmetrical message space and market power provide a weaker incentive to stra- tegically reduce, because the price effect of supply reduction may be offset by demand reduction, and vice versa. Yet even under these conditions traders may attempt to manipulate prices. Bronfman et al. (1996) conducted laboratory experiments on atatonnementauction, in which traders reported the quantity of units they were willing to buy and sell in response to provisional price announce- ments. They found that traders under-revealed supply and demand by about a third of their units.

McCabe, Rassenti, and Smith (1993) studied a uniform price double auction (UPDA) institution. In the UPDA, a provisional uniform price is iteratively reported in response to buy and sell orders from the traders, and all contracts trade at the uniform price when some market-closing criterion is met.

In at least 49% of their auctions one sixth or more of the profitable units were withheld. 2 But while the DA is generally more efficient than uniform price institutions, it has three unde- sirable features. First, the DA generates greater price volatility. A dramatic example is the 2010 “flash crash,” in which the Dow Jones Industrial Average fell by almost 1000 points only to recover a few minutes later. The event had spillover effects on futures markets as well, causing the E-mini S&P 500 prices to fall by over 5% (Easley, Lopez de Prado, and O Hara 2011). Price vola- tility may undercut the perceived fairness of the trading process, and may even drive risk averse traders from the market, reducing the available gains from trade (Pagano 1989). Moreover, Bud- ish, Cramton, and Shim (2013) have shown that stock market price volatility causes market corre- lations to break down at sufficiently small time intervals. This opens arbitrage opportunities for high frequency traders, who compete on response time rather than price. Budish, Cramton, and Shim (2013) argue that this creates an arms race for speed that is socially wasteful, widens the mar- ket spread and diminishes liquidity. To discourage this arms race they propose replacing the exist- ing DA market design with frequent two-sided call auctions. 1For a theoretical model showing that all uniform price multiple-unit auctions encourage demand reduction, see Ausu- bel and Cramton (2002). For evidence of demand reduction in laboratory experiments, see Alsemgeest, Noussair, and Olson (1998), Kagel and Levin (2001), and Porter and Vragov (2006). For evidence of demand reduction in multiple- unit field experiments, see List and Lucking-Reiley (2000) and Engelbrecht-Wiggans, List, and Reiley (2006).

2McCabe, Rassenti, and Smith (1993) do not report summary statistics of demand or supply reduction, but we were able to construct a lower bound of based on the reported of efficiencies in their Appendix B. Price Manipulation in Uniform Price Auctions761 Second, the discriminatory pricing structure of a DA also forces participants to reveal some information on their maximum willingness-to-pay (WTP) and willingness-to-accept (WTA). The buyer who pays the highest price in a DA has revealed information about himself that may be costly in later negotiations. Ditto the seller who accepted the lowest price. A uniform pricing rule, in contrast, eliminates intra-auction price volatility and minimizes the information on WTP and WTA that the winners must disclose.

Finally, DAs are not well suited to complex environments. For example, the FCC plans an incentiveauctionin2015totransferalargeportion of the radio frequency spectrum from broadcast television to mobile broadband. Television stations relinquishing their spectrum rights may do so in a number of different ways, including channel sharing with another station, moving from their cur- rent frequency to a VHF frequency, or going off the air altogether. Consequently, a broadcaster s chosen course of action will depend on the tradeoffs it poses and the prices offered for each. More- over, the geographic size of broadcast licenses may encompass multiple broadband licenses, so that single-unit transactions are not always possible. These features (among others) make the DA an inappropriate format for the incentive auction. Instead, the FCC plans to implement a design pro- posed by Milgrom et al. (2012) using sequential but interdependent auctions with price clocks. First, a set of descending price clock auctions (one for each method of relinquishing licenses) will deter- mine the supply of spectrum for a geographic region. Then, an ascending price auction will allocate the spectrum among buyers. In principle, these clocks can run simultaneously as we test here.

Given the interest in multiple-unit two-sided uniform price auctions—particularly auctions using a price clock—it is relevant to study these institutions in light of earlier work by McCabe, Rassenti, and Smith (1992)—hereafter MRS. They conducted experiments using clock auction formats, but none of their mechanisms used an ascending price as the sole method for price discov- ery. They did, however, test a descending price auction in which experienced traders obtained an average of 94% of the available surplus. It was dubbedDutch-English(DE) because the auction presented improving terms of trade (Dutch) to buyers and worsening terms of trade (English)to sellers as it progressed. The auction used a “price clock” which displayed an initial provisional price that was set high and then reduced by predetermined decrements. As the provisional price fell buyers could commit to buying additional units at or below the provisional price, while sellers could reduce the number of units they were willing to offer at or below the provisional price. The auction closed at the final price when the total commitments to buy equaled those to sell.

One of the striking features of the DE format is its performance in comparison to the two alternative two-sided uniform price institutions that MRS tested: theDouble English(EE) and Double Dutch(DD) auctions. These institutions used one price clock for buyers and a second for sellers. In the EE, the price on the buyers clock started low and ticked up at predetermined inter- vals. The price on the sellers clock started high and ticked down using the same intervals. At the ini- tial prices buyers and sellers indicated how many units they were willing to buy and sell at the prices on their respective clocks. Only one clock was active at a time. The price on the buyers clock increased until buyers had reduced their demand sufficiently to result in excess supply. At this point, the price on the sellers clock fell until sellers had reduced their commitments to sell sufficiently to result in excess demand. The auction concluded when both clocks displayed the same price.

MRS s DD auction was precisely the reverse of the EE. The price on the buyers clock started high and ticked down over time, while the price on the sellers clock started low and ticked up. As the buyers price fell they increased their demand for units until there was excess demand. The sellers price would then rise until they had increased their commitments to sell enough units to result in excess supply. Like the EE, the auction concluded when both clocks displayed the same price. 762Winn, Parente, and Porter The distinguishing feature of the EE is that it provides worsening terms of trade to both sides of the auction. MRS s traders engaged in significant demand and supply reduction in an effort to stop their own price clock and extract price concessions from the other side of the market. In con- trast, the DD provides improving terms of trade to both sides of the auction. In response, traders did not withhold as much of their demand or supply. These differences in behavior resulted in more trades (and higher efficiency) in the DD than the EE. Across the last five auctions of their sessions, the average efficiency was less than 80% in the EE, but almost 100% in the DD.

We have already noted that the DE achieved 94% efficiency. This is remarkable, because the DE presents improving terms of trade only to buyers, yet it was almost as efficient as the DD, which presents improving terms to both sides. The high efficiency of the DE relative to the EE sug- gests that buyers are more responsive to the direction of the clock price than are sellers. If this is true, then anEnglish-Dutch(ED) auction would not perform as well as the DE. An ED auction would use an initially low provisional price that increases over time, and allow buyers and sellers to respond by decreasing demand and increasing supply respectively. However, MRS did not con- duct an ED auction, so we cannot know for certain if there is an asymmetry in the behavior of buyers and sellers. This omission is significant in light of the prevalence of ascending price auc- tions in both the laboratory and the field.

In this study, we report the results of a set of laboratory experiments that explicitly test the impact of clock direction on under-revelation among buyers and sellers. Our experiments were designed to answer the following three research questions:

Q1: Do worsening terms of trade encourage a greater increase in under-revelation among buyers than among sellers?

Q2: If buyers are more responsive than sellers to worsening terms of trade, does the clock direction affect an auction s efficiency?

Q3: If buyers are more responsive than sellers to worsening terms of trade, does the clock direction affect an auction s uniform price?

The results of our experiments indicate that we can answer the first two research questions in the affirmative. Buyers reduced demand more when they faced an ascending price, but sellers reduced supply by the same amount whether the price clock was ascending or descending. As a result the ascending clock led to more under-revelation, which in turn rendered it less efficient than the descending clock. For research questionQ3, we find the answer to be a qualified yes. On average, prices were lower in the ascending auction, but for the experiments we conducted by hand this can be explained by differences in the Nash Equilibrium price across clock directions. For the experiments, we conducted on computer terminals, however, the difference in prices was greater than the game theoretic prediction for most auctions. 2. Experimental Design Trading Environment As a testbed for comparing ascending and descending price clocks, we adopt MRS s schedule of induced costs and values. This is shown in Figure 1 along with the trader role associated with each step of the supply and demand curves. This environment is well suited to the study of supplyPrice Manipulation in Uniform Price Auctions763 and demand reduction for three reasons. First, the supply and demand curves are symmetrical about the competitive equilibrium. Consequently, the optimal strategies of buyers and sellers are symmetrical when facing improving or worsening terms of trade. For instance, trader B1 in an ascending clock auction faces precisely the same problem as trader S1 in a descending clock auc- tion. Second, the environment contains a mix of “large traders” and “small traders.” The former were those who could buy or sell 6 units in an auction, the latter could buy or sell 3 units. Large traders had an advantage in attempting to manipulate the price in that they could reduce demand or supply by a greater number of units. Finally, for a given price direction there is a family of Nash Equilibria that is consistent with the competitive equilibrium and there are no Nash Equilibria that are inconsistent with the competitive equilibrium. This provides a straightforward baseline against which to compare buyer and seller behavior.

For the following analysis, it is important to note that prices in our experiments were always multiples of 5 cents. LetMequal the price, in cents, consistent with the mid-point of the competi- tive equilibrium price tunnel. If the price is ascending, then the Nash Equilibrium price isM25 and no trader under-reveals supply or demand. To see that this is an equilibrium note that if all other traders truthfully reveal their costs and values, the marginal seller S4 can stop the price clock atM25 with his final unit to earn a profit of five on each of his 3 units. (This need not be done by the marginal seller, sellers S1, S2, or S3 could also stop the clock at that price if all other sellers revealed their costs truthfully.) In response to this any buyer could reduce their demand by 1 unit to force the clock to stop early atM210. But this reduction is not profitable for any buyer.

Table 1 displays the profit that each buyer would earn from buying all of his units at a price ofMorM25 or dropping 1 unit to achieve a price ofM210. (Buyer B5 is excluded from the table because he would earn zero profit at any of these prices.) Notice that all inframarginal buyers earn a greater profit by purchasing all of their units atM25 than by purchasing one fewer unit at M210. However, notice that if seller S4 attempted to stop the price atMthere are three buyers (B1, B3, and B4) who would be willing to reduce demand by 1 unit to stop it atM210. Moreover, as we show in the Appendix, there is no coalition of buyers who could profitably reduce demand to hold the price belowM210, nor is there a coalition of sellers who could profitably withhold supply to push the price aboveM25. Thus, all Nash Equilibria with an ascending clock are -60 -40 -200 20 40 60 0 6 12 18 24 Units Normaliz ed values (costs) B1 B3 S5 B2 B4 S1S3B5 S2S4 Figure 1.Experimental Environment with Values and Costs (in Cents) Normalized Such that the Midpoint of the Competitive Equilibrium Tunnel Is Zero.

764Winn, Parente, and Porter characterized by a price ofM25 and no strategic reduction. By symmetry, all Nash Equilibria with a descending clock are characterized by a price ofM15 and no strategic reduction.

However, the traders in our experiments knew only their own values or costs. Consequently, they could not calculate any Nash Equilibria ex ante and we have no reason to believe that they would refrain from attempting to influence the price through under-revelation.

Replicating MRS, we added (or subtracted) a random constant from the interval [$1.00, $4.90] to all values and costs each period to maintain uncertainty about the market clearing prices.

Figure 2 shows the midpoint of the competitive equilibrium (CE) price tunnel in each period, which ranged from $2.50 to $6.00. In addition, we rotated buyers and sellers along their respective demand and supply curves. Across 15 iterations (or periods) in each session, a trader participated at each of the five respective buyer or seller roles three times.

Institutions Our design (displayed in Table 2) consisted of two treatment variables. The first was whether the price ascended (ED) over the course of the auction or descended (DE). The ED treatment pre- sented buyers with worsening terms of trade and sellers with improving terms of trade, while the DE treatment reversed these terms for both sides of the market. We can address research question Table 1.Profit for Each Buyer If He (i) Buys All of His Units at a Price ofM, (ii) Buys All of His Units at a Price ofM– 5, or (iii) Drops 1 Unit of Demand to Achieve a Price of M210 Buy all units at priceMBuy all units at priceM25Drop 1 unit to achieve price M210 RoleUnits BoughtProfit per UnitTotal ProfitUnits BoughtProfit per UnitTotal ProfitUnits BoughtProfit per UnitTotal Profit B1 6 40 240 6 45 270 5 50 250 B2 3 30 90 3 35 105 2 40 80 B3 6 20 120 6 25 150 5 30 150 B4 3 10 30 3 15 45 2 20 40 Buyer B5 earns no profit at any of these prices and is, therefore, excluded from the analysis. 200 300 400 500 600 700 0481216 Pe r io dCompetitive Equilibrium Price Figure 2.Midpoint Competitive Equilibrium (CE) Prices for Periods 1–15. Price Manipulation in Uniform Price Auctions765 Q1by comparing under-revelation across price clock treatments to determine whether the terms of trade affected buyer behavior more than seller behavior. By comparing efficiency and average prices across these treatments, we can also answer research questionsQ2andQ3.Notice,however, that the Nash Equilibrium prices are different for the ED and DE treatments (M25andM15, respectively), so that forQ3, we are interested in whether the clock direction results in price differ- ences that are greater than the game theoretic prediction.

The second treatment variable was whether the auction format was (i) hand-run (Hand), (ii) facilitated by a human auctioneer, or (iii) computerized (Comp) and facilitated by a price clock.

MRS ran their auctions by hand, and our hand-run treatment was an attempt to find an asymme- try between buyers and sellers using their protocols. We then conducted the computerized experi- ments as a robustness check. 3The interaction of our two treatment variables gives us four treatments: ED_Hand, DE_Hand, ED_Comp, and DE_Comp. We describe the pricing institu- tions first.

Characteristic of clock auctions, the prices were announced and traders adjusted quantities in response. In the ED sessions, the starting price was set to zero in each period and increased in response to excess demand. By default, at the starting price buyers automatically demanded all of the units on their demand schedules, totaling 24 units, while sellers supplied 0 units. Thus, the ini- tial excess demand was always 24.

As the price ascended, buyers could reduce their demand in single unit decrements and sellers could increase their supply in single unit increments, although they were allowed to make multiple reductions/additions at the same price. In either case, excess demand fell by 1 unit each time a trader initiated an alteration. Initially the price rose by 10-cent increments; when excess demand fell to 10 units or less the price increment was reduced to 5 cents. When the excess demand con- verged to zero the auction was closed. All of the units that were still demanded by buyers were sat- isfied by the units that had been supplied by sellers and all transactions occurred at the final, market-clearing price.

In the sessions with a DE pricing rule, both sides of the market were presented with a single descending price. We consistently started the price at $7.00, above all traders values and costs. At the starting price buyers were (by default) unwilling to purchase any units and sellers offered every unit on their supply schedules, creating an excess supply of 24 units. In response to decreasing price announcements, sellers could reduce supply and buyers could increase demand, both of which reduced the excess supply by single-unit decrements. The price continued to fall by 10-cent decre- ments with excess supply greater than 10 and by 5-cent decrements thereafter until a price was Table 2.Treatment Design TreatmentAuction formatClock direction SessionsParticipants per sessionTotal participantsAuctions PER sessionTotal auctions ED_Hand Hand-run Ascending 3 10 30 15 45 DE_Hand Hand-run Descending 3 10 30 15 45 ED_Comp Electronic Ascending 4 10 40 15 60 DE_Comp Electronic Descending 4 10 40 15 60 Total: 14 140 210 3The hand-run experiments were conducted at an East Coast university, while the computerized experiments were con- ducted at a university on the West Coast. Consequently, the computerized sessions simultaneously test for robustness to the auction implementation and the subject pool.

766Winn, Parente, and Porter reached at which quantity supplied equaled quantity demanded. All transactions occurred simul- taneously at this price.

Now, we turn to the auction format. In the hand-run experiments, a human auctioneer coor- dinated the auctions. The auctioneer called out prices verbally and traders indicated a desire to alter their quantities supplied or demanded by raising an ID card. To recognize an alteration, the auctioneer called out the trader s ID number (in first-come, first-served order), then announced the new excess supply or demand, and finally repeated the price to allow for additional alterations by the same trader or others at that price. When no more traders raised their ID cards, the auction- eer announced a higher price, using the price increments or decrements described above.

In the computerized experiments, the role of the auctioneer was supplied by an interactive software interface. An automated price clock on their screens showed traders the current price.

The price clock incremented or decremented the price every 2 seconds so long as there was excess demand or supply. A button on traders screens allowed them to alter the number of units supplied or demanded. Each click of the button altered a trader s supply or demand by 1 unit. Each time the button was clicked, the price clock paused on its current price for an additional second. This allowed traders to alter the number of units supplied or demanded by multiple units at the same price.

The exact excess demand or supply was prominently displayed on the screen with a colored background. At the start of each period the background was green, indicating that excess demand or supply was greater than 10 units and the price would adjust in 10-cent increments or decre- ments. When the displayed excess demand or supply fell to 10 units the background color changed to yellow, indicating that the price would adjust in 5-cent increments or decrements. When supply equaled demand the background color changed to red to indicate that the auction had concluded.

Procedures We randomly recruited subjects from a pool of undergraduate students who had agreed to receive invitations to economic experiments on campus. 4Before each session, we took the subjects through a hypothetical example of how the auction would proceed. 5They were allowed to ask questions throughout the instructions, after which they participated in a practice round to become familiar with the trading rules. In the hand-run treatments, the same auctioneer announced prices and managed traders in all sessions and periods to maintain uniformity across pricing rules within the hand-run treatment cells.

In addition to a $7 participation bonus, traders in the hand-run sessions earned $20.00 on average. In the computerized sessions, the average trader earned $19.96 in addition to the partici- pation bonus. Including time for instructions, the hand-run sessions typically lasted 45–60 min, while the computerized sessions lasted 25–35 min.

Hundred and forty students participated as traders, with 10 traders in each experimental ses- sion. We conducted three sessions of the ED_Hand and DE_Hand treatments, yielding 90 auc- tions for analysis. In addition, we conducted four sessions of the ED_Comp and DE_Comp treatments, giving us 120 auctions. 4This method of recruitment was used at both universities.5The instructions and example we used are available in Appendices B, C, and D in a preliminary version of this article.

It may be found at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2560064. Price Manipulation in Uniform Price Auctions767 3. Results Summary statistics are provided in Table 3 by treatment of the prevalence of under- revelation, efficiency and price deviation from the midpoint of the CE price tunnel, and trader earnings as a percentage of the Nash Equilibrium baseline. There was considerable evolution in trader behavior over time, so for each category we provide the average in the first five and final five auctions. Under-Revelation We measure under-revelation as the percentage of units not demanded (or supplied) at mar- ket clearing prices below value (or above cost). This measure is consistent for buyers or sellers irre- spective of clock direction. Specifically, the under-revelation by traderiin periodt,d it,canbe expressed asd it¼Q it2q it ðÞ=Q it,whereQ itis the total number of units on the demand (supply) schedule of traderivalued more (costing less) than the market clearing price in periodtandq itis the number of trades transacted by traderiin periodt.

Under-revelation was widespread although it was not an individually profitable strategy and became less common with experience (see Figures 3, 4). Across all of our experiments, there were 1680 instances in which traders who were not extramarginal could under-reveal to manipulate the uniform price. They did so in 919 cases, a frequency of 54.7%. For each case of under-revelation, we calculated the trader s profit and compared it to the profit he would have earned if he had acted as a price taker at the Nash Equilibrium price. An overwhelming majority of the under-revelation was unprofitable, with earnings lower than the price-taking baseline in 820 cases (89.2%). The profitability of under-revelation did not vary systematically by role or treatment cell.

Figure 3a, b display the average delta among buyers in the hand-run and computerized ses- sions respectively. The buyers show a distinct sensitivity to clock direction. In the hand-run treat- ments, demand reduction was higher, on average, with an ED rule than a DE rule in 13 of 15 periods. In the computerized treatments, average demand reduction was higher with an ED clock in 14 periods, although it did show convergence in periods 12 through 15. This was primarily due to an increase in demand reduction under the DE clock in those periods.

Sellers reduced supply at very similar rates under both an ascending and descending clock (see Figure 3c, d). In the hand-run experiments, average supply reduction was substantially higher under a DE price rule for the first two periods, but appears to have converged by period three or Table 3.Descriptive Statistics of Experimental Results for the First Five and Last Five in Auctions Each Treatment Under-revelation as a % of traders endowments EfficiencyPrice deviation from CE midpointBuyer Profits relative to Nash equilibriumSeller profits relative to Nash equilibrium TreatmentAuctions 1–5Auctions 11–15Auctions 1–5Auctions 11–15Auctions 1–5Auctions 11–15Auctions 1–5Auctions 11–15Auctions 1–5Auctions 11–15 ED_Hand 23.6% 1.8% 72.3% 80.5%27.726.0 74.0% 77.3% 69.7% 85.4% DE_Hand 32.2% 11.9% 65.7% 89.4% 1.021.3 82.6% 116.1% 54.2% 71.1% ED_Comp 42.6% 24.5% 50.9% 73.8%218.822.2 80.7% 65.7% 7.4% 85.6% DE_Comp 30.3% 24.9% 62.9% 76.4% 12.8 4.0 42.1% 84.7% 77.1% 70.6% 768Winn, Parente, and Porter four. In the computerized experiments, average supply reduction was indistinguishable throughout the sessions.

To formally test for the influence of the clock direction, we use the following random-effects regression model:

y it¼a1b 1ED1b 2ftðÞ1l i1e it (1) In Regression 1,y itis the dependent variable of interest in periodtof sessioni 6andEDis a dummy variable indicating whether an ED clock was used. The termftðÞis a regression-specific time trend variable taking on one of three functional forms. For data sets in which they itasymp- totically converge to a value from above or below, we specifyftðÞ¼1=tandftðÞ¼logt ðÞrespec- tively. For data sets in which they itshow a linear relationship witht, we specify thatftðÞ¼t.The l iare random effects assumed to be Nð0;r 2Þand we correct the error term for an AR(1) process.

We organize our findings around our dependent variables measuring under-revelation, efficiency, and deviations in price from the competitive equilibrium. For each of these variables we fit the regression model to the data from the hand-run and computerized experiments separately.

Table 4 displays the estimates from separately fitting under-revelation among buyers and sell- ers to Regression model 1. The estimates for the hand-run data indicate that demand reduction under the ED and DE rules diverged over time, whereas supply reduction converged rather quickly under these pricing rules. The hand-run buyer regression estimates that buyers under-revealed an additional 16.1% in ED_Hand relative to DE_Hand (p50.027). This corresponds roughly to large buyers reducing demand by one additional unit, or small buyers reducing 0.5 additional units on average. This is moderated in the early periods by the estimated time trend for the Figure 3.Average Under-Revelation by Trader Type and Treatment.

(a) Buyers in the Hand-Run Experiments (b) Buyers in the Computerized Experiments (c) Sellers in the Hand-Run Experiments (d) Sellers in the Computerized Experiments 6In the case of under-revelationiindexes the subject rather than the session. Price Manipulation in Uniform Price Auctions769 ED_Hand treatment. Notice that the coefficient of ED * 1/tis20.339 (p50.002). Fort 2, this overwhelms the estimated coefficient of ED. Astincreases, however, the marginal effect of the time trend diminishes, so that by period 3 buyers under-reveal more under an ascending clock than a descending clock.

For sellers in the hand-run experiments, the model finds no significant main effect of the pric- ing rule. However, the coefficients for 1/tand ED * 1/tare 0.554 (p<0.001) and20.487 (p<0.001) respectively. Thus, supply reduction was higher under the DE rule in early periods, but converged as the sessions progressed. We conducted period-wise Wald tests to determine how many periods supply reduction was statistically significantly higher in DE_Hand than in ED_Hand. The tests revealed statistically significant differences in only the first four periods (p<0.05).

The regression estimates using data from the computerized experiments also show that buyers responded asymmetrically to the clock direction (although this faded over time) while sell- ers did not. In the buyer regression, the estimated coefficient of ED is 0.311 (p<0.001), equivalent to nearly two (one) additional unit(s) reduced by large (small) buyers under an ED clock. The esti- mated time trend for the ED sessions is negative and significant (p50.027), however, and indi- cates that demand reduction fell by 1.7 percentage points each period. Period-wise Wald tests indicate that the difference in under-revelation was statistically significant for the first eleven Figure 4.Evolution of Average Efficiency by Treatment.

(a) Hand-Run Sessions (b) Computerized Sessions 770Winn, Parente, and Porter periods (p<0.05) and insignificant thereafter (p>0.1). In the seller regression the estimates for ED and ED *tare both small and statistically insignificant. We may, therefore, conclude that sell- ers in the computerized session were unresponsive to the direction of the clock.

Our results indicate that we may answer research questionQ1in the affirmative: worsening terms of trade encouraged a greater increase in under-revelation among buyers than among sellers.

To our knowledge, these are the first experiments to show a link between clock direction and under-revelation, and an explanation for these results is not readily available in the extant auction literature. The tendency of buyers in multiunit English auctions to reduce demand has been known for quite some time. Alsemgeest, Nousair, and Olson (1998), Kagel and Levin (2001), and Porter and Vragov (2006) all found that English auctions for multiple units encouraged under-revelation and generated lower revenue relative to uniform price sealed bid auctions. Kagel and Levin (2001) showed (and Porter and Vragov 2006 speculate) that this was due to the fact that bidders in the English auctions had information about one another s withdrawals, which facilitated collusion.

However, this does not explain our findings because traders in our experiments received informa- tion on changes in excess supply or demand in both the ED and DE treatments, yet it was primar- ily the buyers whose under-revelation changed.

The experimental investigation with results most similar to our own was performed by Brown, Plott, and Sullivan (2008). They conducted laboratory auctions in which eight buyers bid for eight items in simultaneous auctions. Valuations were assigned so that each buyer had the highest value for one item, the second highest value for another item, and so on. This pro- vided an opportunity for collusive under-revelation, in which each buyer bid only on his own most highly valued item, winning it at the lowest possible price. In one treatment they sold the items with simultaneous open outcry English auctions (i.e., prices ascended but were not con- trolled by a price clock). In a second they used simultaneous Dutch clock auctions. Brown, Plott, and Sullivan (2008) report that buyers practiced the collusive strategy in the English auctions, but bid competitively in the Dutch auctions. However, they show that collusion was Table 4.Estimates from Regression Models of Under-Revelation Hand-run Computerized Regressor Buyers Sellers Buyers Sellers a0.072 0.087* 0.229** 0.430** (0.052) (0.036) (0.063) (0.053) ED 0.161* 0.036 0.311** 0.006 (0.073) (0.051) (0.084) (0.081) t——20.00220.012* (0.006) (0.005) ED* t — —20.017*20.008 (0.008) (0.008) 1/t 0.516** 0.554** — — (0.078) (0.080) ED* 1/t20.339**20.487** — — (0.108) (0.115) Observations 356 325 450 445 R 2 0.109 0.186 0.110 0.056 Waldv 2 51.19 52.51 23.22 18.07 *Significant at 5% level.

**Significant at 1% level. Price Manipulation in Uniform Price Auctions771 a Nash Equilibrium in the English auctions, butnot the Dutch auctions, due to the inability to punish defection in the latter. In our experiments, the Nash Equilibria were symmetrical across price institutions.

Finally, McCabe, Rassenti, and Smith (1990) conducted one-sided multiple-unit English and Dutch auctions. They found that prices were slightly lower than the theoretical prediction in the English auctions and higher than the theoretical prediction in the Dutch. However, although their auctions allocated multiple units, each bidder could win only 1 unit. Thus, under-revelation was not an equilibrium strategy in their experiments. The high prices in their Dutch auctions may, therefore, be due to risk averse bidders. The low prices in their English auctions may have been caused by bidders with relatively low values dropping out of the auction early.

Our own experiments were designed to determine the existence of an asymmetry between buyers and sellers, rather than to uncover the source of the asymmetry. However, we offer one hypothesis that we consider plausible, if speculative. Notice that under-revealing more in the face of worsening terms of trade is consistent with loss aversion (Kahneman and Tversky 1979; Tversky and Kahneman 1991). It is well-known that agents are often more eager to avoid losses than they are to avoid gains. In the ED treatments the buyers saw their potential profits falling over the course of the auction, whereas in the DE treatments they saw their potential profits increasing. Loss aversion may have motivated them to under-reveal more to stop the ED clock than to prolong the progress of the DE clock. If this was the case, then the fact that the sellers responded substantially less to the clock direction suggests that they had little or no loss aversion. That is, an agent s degree of loss aversion may be susceptible to framing effects, such as whether they are a buyer or seller. We believe this explanation should be the subject of future experimental inquiry.

Efficiency Research questionQ2asks whether the clock direction affects an auction s efficiency. We have noted the close link between strategic reduction under-revelation and efficiency. As a result of this link, we would expect the clock direction to influence the observed efficiencies as well. If buyers reduce demand more under an ED clock but sellers are unresponsive to the clock direction then we would expect more under-revelation in the ED treatments relative to the DE treatments, and, therefore, lower efficiency. Moreover, since demand reduction diverged in the hand-run experiments and converged in the computerized experiments, we would expect similar patterns of divergence and convergence in the efficiency data, although the durations may be different. This is because the relationship between under-revelation and efficiency is a noisy one. Demand reduction among buyers with higher values will impact efficiency more substantially than reduction among those with lower values.

Figure 4 displays average efficiencies by period. In the hand-run experiments average effi- ciency shows a quick convergence after the first two periods, in which it was actually higher under the ED clock. This convergence ended in period nine, where there is a visible separation in which the DE_Hand dominates the ED_Hand. In the computerized experiments efficiency appears to be higher under a DE clock for the first six periods and virtually identical thereafter.

Our regression models support these findings (see Table 5). The model for the hand-run data estimates that efficiency was 45.5% in the first period of DE_Hand (p<0.001), while it was 18.1% points higher in the same period of ED_Hand (p50.008). However, the estimated coefficient for 772Winn, Parente, and Porter ED * log(t) is negative and significant (p50.001), indicating that efficiency grew faster under a DE clock. The model estimates that by the 10 thperiod of DE_Hand efficiency had increased by 42.7% points (p<0.001) to 87.7%. In the same period of ED_Hand it had increased by only 16.9% points to 80.5%. Using period-wise Wald tests, we find that efficiency was significantly higher (p<0.05) in DE_Hand for the last seven periods.

In the computerized sessions, our model estimates that efficiency was initially 15.1% points lower in ED_Comp than in DE_Comp (p50.017), but this difference disappeared over time. The estimated coefficient for ED *tis positive and significant (p50.027), and indicates that efficiency grew 1.1% points faster per period with an ED clock. Period-wise Wald tests find that efficiency was significantly higher in DE_Hand (p<0.05) for the first five periods and marginally signifi- cantly higher in period six (p50.069).

Finally, it is worth noting that the computerized auctions were noticeably less efficient than the hand-run ones, even though they started at a higher average level of efficiency. In the final five periods of the hand-run sessions, the average efficiencies were 80.5% for the ED clock and 89.4% for the DE. In the computerized sessions, these averages were 73.8% for ED and 76.4% for DE.

Using the average efficiency per session as our unit of observation we conducted three Mann– Whitney tests, one for each clock direction and a third pooling all observations. The first two tests indicate that efficiency is significantly higher in the hand-run experiments at the 5% level regard- less of the clock direction (p50.034 in both cases). The pooled test finds efficiency to be higher in the hand-run experiments at the 1% significance level (p50.003).

The hand-run and computerized experiments were conducted at separate locations, so it is possible that the differences in efficiency reflect differences across subject pools. It may also be that the hand-run format was more conducive to learning, so that traders in that format discarded fewer high value and low cost units. Yet another possibility is that the difference is inherent in the details of the formats themselves.

Under both auction formats a majority of traders activity tended to happen in the last few seconds of the auction. It was not uncommon, for instance, for excess supply or demand to fall from 10 or more units to 0 units in the final tick of the clock. In the hand-run Table 5.Estimates from Regression Models of Efficiency Regressor Hand-run Computerized a0.455** 0.588** (0.056) (0.045) ED 0.181**20.151* (0.069) (0.064) t — 0.014** (0.003) ED* t — 0.011* (0.005) Log(t) 0.427** — (0.056) ED* Log(t)20.258** — (0.079) Observations 90 120 R 2 0.531 0.333 Waldv 2 68.57 67.61 *Significant at 5% level.

**Significant at 1% level. Price Manipulation in Uniform Price Auctions773 experiments, traders were allowed to alter their trading commitments multiple times at the same price, but this required raising their ID cards multiple times. The auctioneer attempted to recognize IDs in first come, first served order, and in many cases multiple ID cards were raised at roughly the same time at the final price. Consequently, the auctioneer prioritized alterations at the final price by cycling through traders. In the computerized experiments, trad- ers did not have to wait to be recognized and alterations were prioritized by which traders clicked their buttons the fastest. Under this prioritization scheme, one buyer (seller) could reduce all of his units at a given price before any sellers had managed to supply (demand) them. One consequence of this could be that alterations were more evenly spread out between buyers and sellers in the hand-run experiments. A second consequence could be that, in the race to reduce units at the end of an auction, traders in the electronic experiments clicked the buttons on their screens more times than they intended. In either case the result would be lower levels of reduction in the hand-run experiments.

We tested whether reduction was lower in the hand-run experiments by conducting a Mann– Whitney test with average under-revelation by session as the unit of observation. Overall, partici- pants under-revealed by 20.5% in the hand-run sessions and 31% in the computerized sessions.

The two samples are significantly different at the 5% level (p50.014). To test whether the elec- tronic interface encouraged accidental reductions, we measured the frequency with which traders reduced all of their units. (We excluded auctions in which the trader was extra marginal and reduc- tion of all units was the Nash Equilibrium strategy.) Reducing all units strongly suggests an error on the trader s part because it guarantees that his earnings for the auction will be zero. The average trader reduced all of his units in 6% of auctions in the hand-run experiments and 10% of units in the electronic auctions. A Mann-Whitney test confirms that the distributions are statistically dif- ferent across auction formats (p50.043).

A final piece of evidence that the auction format influenced efficiency through under- revelation is the variance of traders reduction across rounds. For each participant, we measured the variance in the percent of units he reduced across all auctions in which he was not an extra marginal trader. In the electronic experiments, where the number of units reduced was dependent on whether one was among the first to start reducing, the average variance was 9 percentage points. In the hand-run experiments, where the auctioneer cycled through traders who tried to reduce simultaneously, the average variance was 6 percentage points. The distributions are statisti- cally different according to a Mann–Whitney test (p<0.001).

These results strongly suggest that efficiency was degraded by chaotic trader behavior in the last few seconds of an auction, and that a human auctioneer kept the chaos in check to some extent. In many applications in the field a human auctioneer would be impractical, yet it may still be possible to enhance a uniform-price auction s efficiency through simple rules that promote a more orderly processing of traders decisions. For example, rather than processing each decision sequentially, the auction software may process them in batches, with all orders submitted at the same price increment processed simultaneously. Under such a simultaneous processing rule, the software could cycle through each trader in much the same way as our human auctioneer did, executing one order from a given trader at a time until all orders were processed or there was no excess supply or demand. Alternatively, the software could explicitly favor higher trade volume by first executing all orders in the batch that increase the traders commitments, and then executing the orders that reduce them if there was still excess supply or demand. This processing rule may be appropriate as a counterbalance to traders tendency to under-reveal. 774Winn, Parente, and Porter Price Finally, we turn to whether the clock direction affects an auction s uniform price (research questionQ3). Because the Nash Equilibrium prices are slightly higher for the DE (M15) than the ED (M25), we are particularly interested in whether under-revelation generates a larger dif- ference in prices than the game theoretic prediction. Figure 5 displays the average deviation from the midpoint of the CE tunnel by period. In both auction formats, the clock direction influenced prices, although they were rarely exactly equal to the Nash Equilibrium in any treatment. In the ED sessions the final price was equal toM25 in 24.4% of the hand-run auctions and 20% of the computerized auctions. With a DE clock the final price equaledM15 in 20% of the hand-run auctions and 18.3% of the computerized auctions.

However, prices in the majority of auctions were within the CE price tunnel. In 55% of the computerized auctions (66 of 120) the final price was within 10 cents of the CE midpoint. The pri- ces were even more consistent with the CE in the hand-run experiments: 86.7% of the hand-run auctions (78 of 90) generated CE prices. In the computerized experiments, the two clock directions resulted in prices that were extremely disparate in the early periods but converged over the dura- tion of the sessions. In the hand-run experiments, the price differences were generally consistent with the Nash Equilibrium. Figure 5.Deviation from the Competitive Equilibrium Price by Treatment.

(a) Hand-Run Sessions (b) Computerized Sessions Price Manipulation in Uniform Price Auctions775 We use the deviation from the CE mid-point as a dependent variable in Regression model 1 for both auction formats (see Table 6). 7If prices did not systematically deviate from the Nash Equilibrium predictions then we would expect the estimated constant to be 5 and the sum of the constant and estimated coefficient of ED to equal25. For the hand-run experiments, the esti- mated constant term is 2.34, and this is not significantly different from 5 (Wald Test,p50.376).

The estimated coefficient of ED is28.27 (p50.052), and its sum with the estimated constant is 25.93. A Wald test cannot reject the null hypothesis that this sum is equal to25(p50.757). Thus, we can conclude that prices in the hand-run experiments were consistent with the Nash Equilib- rium on average. This was persistent across the duration of the experiments, as the time trend vari- ables are not significant in the hand-run model.

The model estimates using data from the electronic experiments confirm that in those ses- sions the clock direction s influence was profound in the initial auctions but waned over time. The estimated constant term indicates that prices in the DE_Comp were almost 19 cents above the CE midpoint in the first auction (p50.002). Prices for the same auction were more than 36 cents below the midpoint in the ED_Comp, as the coefficient for ED is255.30 (p<0.001). However, the time trend coefficients show strong convergence over time. Log(t) is negative and marginally significant (p50.062), while ED * Log(t) is positive and highly significant (p<0.001). Because the time trend variables are designated in logs of base 10, the most straightforward interpretation of their coefficients is the change in prices as of the tenth auction. Using this interpretation, prices in the DE_Comp had fallen by more than 12 cents and prices in the ED_Comp had risen by almost 45 cents. Using period-wise Wald tests, we find that prices in the DE_Comp were signifi- cantly greater than 5 in the first 4 auctions (p<0.043) and not significantly different than 5 there- after (p 0.092). A similar analysis indicates that prices in the ED_Comp were statistically Table 6.Estimates from Regression Models of Deviation from the Competitive Equilibrium Price Regressor Hand-run Computerized a2.34 18.72** (3.00) (5.90) ED28.27*255.30** (4.25) (8.36) t20.19 — (0.30) ED* t 0.11 — (0.42) Log(t) —212.61* (6.75) ED* Log(t) — 44.95** (9.66) Observations 90 118 R 2 0.162 0.381 Waldv 2 8.41 60.09 *Significant at 10% level.

**Significant at 1% level.

7Recall from Figure 1 that the price tunnel spans 20 cents, so taken from the midpoint of the tunnel a price in the inter- val [10, 10] is consistent with the competitive equilibrium.

776Winn, Parente, and Porter significantly less than25 in the first 12 auctions (p 0.025) and were consistent with the Nash Equilibrium in only the final 3 auctions (p 0.075).

4. Concluding Remarks MRS s early work in multiunit clock auctions suggested that buyers (but not sellers) under- reveal more when they face worsening terms of trade than when they face improving terms of trade. We explicitly test for this asymmetry in both a hand-run and computerized environment.

Our experiments reveal that the asymmetry is real, although its pattern is not consistent. In our hand-run auctions buyer and seller behavior diverges over time, so that it takes a few periods for the asymmetry to emerge. In our computerized auctions the asymmetry is apparent (and large) from the very first auction, but diminishes with experience.

As a result of the observed behavioral asymmetry, prices and efficiency are generally higher when the auction uses a descending price rule. For two-sided call auctions this implies that the DE institution is preferable from a social perspective, although it will likely be more popular among sellers than buyers. An interesting question for future research is whether buyers response to the direction of the price clock carries over to one-sided auctions as well as two-sided auctions. If so, then sellers in multiunit auctions in the field may be able to enhance their revenues and improve social welfare simply by implementing a descending price rule.

In addition to the asymmetry in buyer behavior, our experiments indicate that the rules by which traders orders are processed can have a substantial impact on allocative efficiency. Gains from trade were 6.7 to 13 percentage points higher with a human auctioneer than with a compu- terized auction format. This seems to be due to the fact that the computerized format enabled a more chaotic entry of orders near the close of the auction, which promoted trader error and increased the amount of under-revelation. This shortcoming in the computerized auctions might be overcome by executing the traders orders in batches and giving priority to orders that will cre- ate trades. This type of processing rule may be especially appropriate in a field application such as the FCC s incentive auctions, where one of the primary aims is to maximize the amount of spec- trum released by the incumbent license holders. Appendix: Under Revelation and Trader Profits In section 1, we showed that in the case of an ascending price auction no buyer can profitably reduce demand to push the price fromM25toM210. In this Appendix, we demonstrate that no coalition of buyers could profit- ably reduce demand to reduce the price even further. We also show that no coalition of sellers could profitably reduce supply to increase the price. Since the supply and demand curves are symmetrical, our proof for the buyers (sellers) in the ED auctions holds for the sellers (buyers) in the DE auctions.

Given the supply curve, there are three prices less thanM210 that buyers could achieve through coordinated demand reduction. Reducing demand by 9 units would achieve a price ofM220, reducing demand by 15 units would achieve a price ofM230 and reducing demand by 18 units would achieve a price ofM240. In Table A1, we show the maximum number of units by which each buyer could reduce his demand and increase his profit for each of these prices. Notice that the buyers could not profitably reduce demand by enough units to achieve the lowest pri- ces ofM230 orM240. Buyers would be willing to reduce demand by a total of only 11 and 13 units to achieve these prices, while reductions of 15 and 18 units would be necessary to achieve them.

To achieve a price ofM220 the buyers could profitably reduce demand by 9 units, which is exactly the num- ber needed for that price. However, the sellers could easily reduce supply to make this demand reduction unprofitable.

They would need to reduce supply by only 1 unit to push the price back up toM210. Seller S3 s induced cost per Price Manipulation in Uniform Price Auctions777 Table A1.The Maximum Number of Units by Which Each Buyer Would Be Willing to Reduce Demand to Achieve a Price Lower ThanM25 Price M25M220M230M240 Buyer Units Bought Profit Units Bought Profit Units Bought Profit Units Bought Profit B1 6 270 5 300 4 280 4 320 B2 3 105 3 105 2 120 2 140 B3 6 150 4 160 4 200 3 180 B4 3 45 2 60 2 80 1 50 B5 0 0 1 10 1 20 1 30 Total Reduction 9 11 13 Reduction Needed 9 15 18 Reported profits (in cents) are the profits a buyer would receive if a lower price were achieved given the num- ber of units by which he reduced demand. Table A2.The Maximum Number of Units Each Seller Would Be Willing to Withhold to Achieve a Price Greater ThanM25 Price M25M110M120M130M140 Seller Units Sold Profit Units Sold Profit Units Sold Profit Units Sold Profit Units Sold Profit S1 6 210 5 250 4 240 4 280 3 240 S2 3 75 2 80 2 100 2 120 2 140 S3 6 90 4 120 3 120 2 100 2 120 S4 3 15 1 20 1 30 1 40 1 50 S5 0 0 0 0 1 10 1 20 1 30 Supply Reduction 6 13 14 15 Reduction Needed 3 9 15 18 Reported profits (in cents) are the profits a seller would receive if a higher price were achieved given the num- ber of units by which he reduced supply. Table A3.The Maximum Number of Units by Which Each Buyer Would be Willing to Reduce Demand to Achieve a Price ofM210 Rather ThanM110 Price M110M210 Buyer Units bought Profit Units bought Profit B1 6 180 4 300 B2 3 60 2 105 B3 6 60 3 160 B4 3 0 1 60 B5 0 0 0 10 Total reduction 8 Reduction needed 7 Reported profits (in cents) are the profits a buyer would receive if a lower price were achieved given the num- ber of units by which he reduced demand. 778Winn, Parente, and Porter unit isM220. Thus, he would be willing to reduce supply by 1 unit to achieve a price ofM210 and earn a positive profit. Consequently, there is no coalition of buyers that could profitably reduce demand to increase their profits.

Regarding the sellers, we have shown in section that the buyers would be willing to reduce demand to prevent a price equal toM. We now consider whether the sellers could profitably reduce supply to achieve a higher price. In Table A2, we show the maximum number of units each seller would be willing to withhold to achieve a price of M110,M120,M130, orM140. Notice that, similar to the buyers, there is no coalition of sellers who could profitably increase the price toM130 orM140. Those prices require supply reductions of 15 and 18 units, while sellers would only be willing to withhold 14 and 15 units to achieve them. The sellers would be willing to withhold a total of 13 units for a price ofM120, while only 9 units would need to be withheld. However, buyer B3 values 6 units at exactlyM120, and could, therefore, profitably withhold five of them to lower the price.

The final possibility is that the sellers withhold supply to push the price to the top of the equilibrium price tun- nel,M110. Sellers S1 through S4 could profitably withhold a total of 6 units to achieve this price, while only 3 units of reduction would be necessary. However, the buyers could then increase their profits by withholding a total of 7 units of demand to push the price back toM– 10. In Table A3, we show that buyers B1 through B4 would all be willing to withhold at least 1 unit of demand to prevent a price ofM110, and the total number of units by which demand could be profitably reduced is eight. Consequently, there is no coalition of sellers that could profitably reduce supply to achieve a price higher thanM25. Any coalition that tried to do so could be thwarted by a coalition of buyers who could profitably reduce demand to hold the price down.

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