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The Hayek hypothesis in experimental auctions: institutional effects and market power.

THE HAYEK HYPOTHESIS IN EXPERIMENTAL AUCTIONS: INSTITUTIONAL EFFECTS AND MARKET POWER

We report twelve market experiments utilizing a "seller market power" supply and demand structure where two of five sellers can unilaterally increase their profit by withholding supply. The data indicate that both the double auction and posted offer institutions result in traders extracting the bulk of the potential gains from exchange in the market; however, prices generally occur above the competitive equilibrium prediction. Market power in the form of strategic supply withholding does not appear to be responsible for the supra-competitive prices.

I. INTRODUCTION

One important result arising from experimental market research is that the information flows and contracting rules which define the institutional structure of a market can exert a pronounced influence on market performance. Such institutional features may be more important than some traditional structural characteristics in determining whether market outcomes will correspond to the predictions of the competitive model. In particular, a large and growing body of experimental data suggests that markets can generate efficient outcomes even when there are a relatively small number of buyers and sellers with incomplete information on the underlying structure of the market. Based on evidence from a wide variety of experimental double-auction markets, Vernon Smith [1982, 167] has expressed this more formally as the "Hayek Hypothesis":

Markets economize on information

in the sense that strict privacy

together with the public messages of

the market are sufficient to produce

efficient CE (competitive equilibrium)

outcomes.

In this statement, however, the notion of an "efficient CE outcome" could be interpreted as (1) a simple efficiency claim that all exchange surplus will be extracted, or (2) a price claim that all exchange surplus will be extracted via trades at the competitive equilibrium price.

A recent study by Holt, Langan and Villamil [1986] (hereafter "HLV") examines the validity of the Hayek Hypothesis using the double auction institution and a market structure designed to provide a rather difficult test for the competitive model. HLV's "market power" design provides a subset of sellers with an incentive to unilaterally generate a price increase via the strategic withholding of supply. The resulting price deviation from the competitive equilibrium is substantial but results in a relatively small loss of market efficiency. Thus, the "price interpretation" of the Hayek Hypothesis is violated in this design if holders of market power recognize their position and successfully affect prices to their advantage. The "efficiency interpretation," however, will still hold (approximately) even with the successful exercise of market power. In fact, the price interpretation of the Hayek Hypothesis tends to break down in HLV's markets, but the efficiency interpretation tends to hold. HLV report deviations from the competitive equilibrium price consistent with the exercise of market power in three of five seller market power experiments. They also conjecture that deviations from the competitive equilibrium may increase as participants become more experienced with the trading institution.

This paper reports the results of twelve experiments that build on HLV's research. Our experiments compare market performance in HLV's seller market power (SMP) design using both the double auction and posted offer trading institutions. Our purpose in conducting these experiments is twofold. First, we are interested in examining the effects of changes in trading institutions on deviations from the competitive equilibrium price in the SMP design. Second, to the extent that competitive equilibrium price deviations are observed, we are interested in assessing whether the exercise of market power in the form of strategic withholding is the source of these deviations.

All of our experiments are conducted on the University of Illinois PLATO computer network. The procedural details for both the PLATO double auction and the PLATO posted offer are well documented elsewhere and are not repeated here.(1) The asymmetry of actions available to buyers relative to sellers in the posted offer institution bears emphasis. Unlike the double auction, where sellers and buyers have symmetric price quoting and accepting capabilities, posted offer sellers control both offer prices and quantities, while posted offer buyers have only the option of purchasing or not purchasing. A priori, we expected this institutional asymmetry to foster the successful exercise of market power in the SMP design.

II. EXPERIMENTAL DESIGN

Figure 1 illustrates the induced supply and demand arrays for HLV's seller market power design. The figure also indicates the individual marginal value (marginal cost) assignments for each of the five sellers (buyers) in the market. Sellers (buyers) earn price minus marginal cost (marginal value minus price) for each unit traded, plus a $.05 commission intended to motivate the exchange of zero profit units. The competitive equilibrium trading volume is sixteen units per period, with total gains from exchange of $18.75 ($7.50 to sellers and $11.25 to buyers) plus $1.60 in commissions.

Seller 1's and Seller 2's unilateral market power in the SMP design is evident from careful examination of Figure 1. If either Seller 1 or Seller 2 withhold the sale of their two zero profit units, the market supply curve shifts back two units for all prices at and above the competitive equilibrium generating a $.25 increase in the effective competitive equilibrium price and a one unit reduction in volume. If the predicted $.25 price increase is realized, strategic withholding by Seller 1 or Seller 2 results in a $.65 increase in profit per period for the withholder. If Seller 1 and Seller 2 each withhold one unit, the benefit of withholding is $.95 to each.(2) Counter-speculation by buyers is not a profitable single-period strategy since this requires buyers to forego purchasing two units to counteract a $.25 per unit price increase effected by seller withholding. The maximum net benefit per period of counter-speculation under these conditions is -$.85.(3) Note, however, that counter-speculation by buyers as well as strategic supply withholding by Sellers 3, 4, and 5 may represent viable intertemporal strategies. As is discussed in more detail below, the market design and the institutional rules can interact to induce market power holders to undertake strategies other than simple supply withholding.

Table I lists information on the twelve markets presented below. Subjects were male and female undergraduate students at Indiana University. To examine HLV's conjecture that experienced subjects exercise market power more frequently than inexperienced subjects, half the experiments in each institutional cell used experienced subjects (designated by an "X" in the experiment name). Subjects were classified as experienced if they participated in a previous market using the same trading institution.

TABLE I

Experiment Classification Information
Experiment Simulated Experienced Exchange CE Final
 Name(*) Buyers? Subjects? Rate Price Period


POSTED OFFER MARKETS
 POS1 YES NO 1:1 2.60 10
 POS2 YES NO 1:1 6.10 10
 POXS1 YES YES 2:1 2.60 16
 POXS2 YES YES 2:1 6.85 25
 PO1 NO NO 2:1 6.10 20
 PO2 NO NO 2:1 4.60 20
 POX1 NO YES 2:1 6.10 20
 POX2 NO YES 2:1 7.25 25


DOUBLE AUCTION MARKETS
 DA1 NO NO 1:1 2.60 8
 DA2 NO NO 1:1 6.10 8
 DAX1 NO YES 2:1 7.70 11
 DAX2 NO YES 2:1 4.45 11


(*)The experiments are archived on the University of Illinois PLATO computer network under the following names. Posted offer experiments: POS1 = p166, POS2 = p176, POXS1 = iu03, POXS2 = iu26, PO1 = iu23, PO2 = iu24, POX1 = iu10, POX2 = iu25. Double auction experiments: DA1 = 3pd209, DA2 = 3pd210, DAX1 = 3pd255, DAX2 = 3pd256.

In four of the eight posted offer experiments buyer behavior was simulated by the computer (designated by a "S" in the experiment name). The buyer simulation algorithm generates full demand revealing buying decisions (buy if price [is less than or equal to] marginal value).(4) This explicitly controls for strategic demand withholding, giving sellers a "better shot" at successfully exercising market power. Posted offer markets using human buyers may generate lower prices if buyers engage in strategic withholding or if sellers expect buyers to withhold demand units if prices are too high.

In order to reduce subject payment expenses, subjects' "PLATO dollar" earnings were converted to U.S. dollars at 2 to 1 rate in eight of our twelve experiments. Subjects were informed of the exchange rate via a verbal announcement prior to the experiment. Even with this reduction in payments, subjects' total earnings in our posted offer markets were generally greater than in HLV's oral double auctions, as our markets had more than twice as many trading periods.

III. HYPOTHESES

Our analysis focuses on both the price and efficiency interpretations of the Hayek Hypothesis, stated below as propositions 1(a) and 1(b). PROPOSITION 1(a) (Hayek Hypothesis--Price Version): If a unique competitive equilibrium price exists, strict privacy together with the public messages of the market are sufficient to move a market to the competitive equilibrium price. PROPOSITION 1(b) (Hayek Hypothesis--Efficiency Version): Strict privacy together with the public messages of the market are sufficient to extract all gains from trade.

"Strict privacy" implies that information regarding individual marginal costs (values) is private to each seller (buyer). "Public messages of the market" are the price quotes and contracts allowed under the trading rules defining the institution of exchange. Public messages vary importantly across trading institutions. In double auction markets, a rich public information set is generated as both buyers and sellers enter and accept publicly displayed price quotes within trading periods. In posted offer markets, the single offer price posted by each seller each period constitutes the only public information. Such considerations, combined with early evidence from experimental posted offer markets, led Smith [1982,177] to posit that the Hayek Hypothesis generally performs better in double auction markets than in posted offer markets.

To the extent that deviations from the competitive price are observed, we are interested in assessing whether the exercise of market power via supply withholding is responsible for these deviations. In either institution, strategic withholding of at least two units by Seller 1 and / or Seller 2 generates a $.25 increase in the supply / demand intersection, and increases profits for both sellers. Our empirical analysis of strategic withholding behavior focuses on the validity of proposition 2. PROPOSITION 2 (Seller Market Power Through Strategic Withholding): Sellers recognize and successfully exercise their ability to unilaterally increase the market price through strategic supply withholding.

It is worth emphasizing that the absence of strategic withholding does not necessarily indicate the nonemployment of market power in a more general sense. As will be discussed in the next section, behavior other than supply withholding may generate prices above the competitive equilibrium prediction.

Note that there are both strong and weak versions of the above propositions. A strong version suggests that the prediction holds exactly, even at the outset of an experiment. A weak version suggests that the prediction is approximated after subjects experience successive replications of a market structure over the course of an experiment. Since such learning inevitably occurs, only the weak interpretation of these propositions can be seriously considered.

IV. EXPERIMENTAL RESULTS

Contract Prices: Proposition 1(a)

Figures 2, 3 and 4 display the time series of mean contract prices for the double auction experiments, posted offer experiments with computer-simulated buyers, and posted offer experiments with human buyers, respectively. The mean price series for markets using experienced subjects are indicated with a heavy solid line, and mean price series for markets using inexperienced subjects are indicated with a lighter dotted line. We evaluate the validity of proposition 1(a) by examining the contract price data in Figures 2, 3 and 4. If prices converge to the competitive equilibrium, support for proposition 1(a) is observed.

Examination of the four double auction experiments in Figure 2 reveals that our double auction markets generated price deviations of approximately the same magnitude as HLV. Price performance across our double auction experiments, however, was much more homogeneous. HLV's experiments converged to the competitive equilibrium about half the time. In each of our experiments, the final period mean price was somewhat above the competitive equilibrium. Moreover, the homogeneity of price performance in our experiments does not reenforce HLV's conjecture that subject experience increases the likelihood of supra-competitive prices.

The eight experiments illustrated in Figures 3 and 4 indicate that posted offer prices also tend to stabilize above the competitive price. In fact, mean prices in the posted offer experiments were often much higher than in the double auction experiments. In all four posted offer markets with simulated buyers and in two of the four posted offer markets with human buyers, the final period mean price was above the $.25 deviation predicted by strategic withholding. The posted offer data also suggest that, as in the double auction experiments, subject experience is not an important determinant of price performance in the SMP design.

Comparison of Figures 3 and 4 suggests that the use of human buyers may affect the size of deviations from the competitive price prediction. In each market with simulated buyers, prices exceeded the competitive prediction by at least $.20 after period 3. Posted offer markets using human buyers were much less homogeneous. Only one of these markets generated sustained price deviations from the competitive prediction (POX2). In the other three markets, mean prices were initially high but fell to a level near the competitive prediction; quite rapidly in PO2 and POX1 and more slowly in PO1. Experiment PO2 is striking in that prices clearly diverge from the competitive prediction beginning in period 13 to nearly a $.30 deviation in periods 18-20. Reports of similar instances of divergence from the competitive prediction are fairly rare in the experimental literature.(5)

POX1 is noteworthy because it is the only experiment where a buyer consistently withheld demand and brought prices down. Buyer 4 purchased no units in ten periods (periods 2, 3, 6, 7, 8, 9, 10, 12, 15, 16), purchased only one of three available units in another period (period 4), and purchased two of three available units in two other periods (periods 11 and 14). The reduction in effective demand increased excess supply at and above the competitive equilibrium price. This induced a sufficient increase in competition among sellers intent on trading marginal units (marginal cost = competitive equilibrium price) so as to generate competitive equilibrium price convergence.(6) The novelty of Buyer 4's behavior bears emphasis. Only one additional instance of less than full demand revelation was observed in the other three posted offer experiments using human buyers reported here.(7) Nevertheless, the increased incidence of convergence toward the competitive price prediction in posted offer markets with human buyers leads us to conjecture that our buyer simulation procedure may not always replicate the performance observed in markets with human buyers. Although the data are limited, they suggest that sellers may initially be less resistant to competitive pressures to reduce price in the presence of human buyers, even when the buyers fully reveal demand.

In summary, we find that contract prices deviate from the competitive equilibrium price in the direction predicted by the successful exercise of market power by sellers in both our double auction and our posted offer experiments. Based on this evidence, we reject proposition 1(a) for markets using the SMP design.

Market Efficiency: Proposition 1(b)

Proposition 1(b) is evaluated by examining mean trading efficiency under each market institution. Support for proposition 1(b) is obtained if mean efficiency levels approach 100 percent, indicating that nearly all possible gains from trade were extracted.(8) Note that strategic withholding of two units is not necessarily inconsistent with proposition 1(b) in the SMP design. If Seller 1 and / or Seller 2 withhold two units, one zero surplus unit and one unit generating a surplus of $.75 will not trade. Thus, 96 percent of total efficiency ($18.00 of $18.75) may still be extracted.

Table II summarizes mean efficiency information for all periods common to experiments in each treatment cell.(9) Examining the first column of Table II, it is clear that our double auction experiments extract the bulk of possible gains from exchange from the outset. Mean double auction efficiency is 96 percent or above in all but the first period of the double auction experiments. This result parallels HLV's finding for double auction markets in the SMP design.

The efficiency data for the posted offer experiments, summarized in columns 2 and 3 of Table II, provide weaker support for proposition 1(b). Mean efficiency is below 90 percent in eight of the ten periods common to the simulated-buyer markets and in six of the first ten periods in the human-buyer markets. Nevertheless, the posted offer markets eventually tend to extract the bulk of available gains from exchange. Mean efficiency equals or exceeds the 96 percent efficiency level consistent with the exercise of market power in eight of the last fifteen periods using simulated buyers, and in ten of the last fifteen periods using simulated buyers.

TABLE II

Mean Market Efficiency
 Double Auction Posted Offer
Trading Simulated Real
Period Buyers Buyers
 1 91.87 79.27 74.40
 2 96.80 80.07 82.73
 3 100.00 80.87 80.87
 4 99.67 88.87 85.27
 5 96.00 84.87 91.00
 6 99.00 86.60 90.00
 7 100.00 87.60 93.00
 8 99.00 91.67 89.67
 9 96.00(a) 87.60 93.67
 10 99.30(a) 91.53 95.00
 11 98.60(a) 92.93(b) 98.00
 12 94.67(b) 91.67
 13 95.34(b) 97.00
 14 98.00(b) 99.00
 15 95.34(b) 96.00
 16 92.67(b) 94.00
 17 96.00(c) 97.67
 18 96.00(c) 97.67
 19 96.00(c) 97.67
 20 98.67(c) 96.67(c)
 21 89.33(c) 98.67(c)
 22 90.67(c) 90.67(c)
 23 96.00(c) 96.00(c)
 24 97.33(c) 89.33(c)
 25 96.00(c) 96.00(c)
 1-8 97.79 84.97 85.87


Overall

Average 97.84 91.44 92.46 (a)Based on two markets in this cell with more than eight periods. (b)Based on three markets in this cell with more than ten periods. (c) Results from a single market in this cell with more than twenty periods.

On the basis of this evidence, we do not reject proposition 1(b) in either the posted offer or in the double auction institution. Note, however, that the posted offer data support a rather weak version of proposition 1(b).

Strategic Withholding: Proposition 2

We evaluate proposition 2 by comparing the number of units traded by market power holders with the number of units available to them. Support for proposition 2 is generated by (1) Seller 1 and / or Seller 2 foregoing the trade of two units, and (2) no other apparent motivation for less than full supply revelation. Review of the limited instances of less than full supply revelation in posted offer markets do not suggest the exercise of market power. In the eight posted offer experiments, Seller 1 and Seller 2 offered less than nine of the ten units collectively available to them in only eight out of one hundred and forty-six periods. Five of these instances occurred in the first two trading periods of four different experiments, while the remaining three instances were isolated instances in three different experiments.

Similarly, little evidence of the exercise of market power through strategic withholding is evident in three of the four double auction markets (DA2, DAX1 and DA1). In these markets, Seller 1 and / or Seller 2 failed to fully reveal supply in only one period. Closer examination of end-period behavior in each of these three periods suggests that inefficient negotiations rather than strategic withholding explain the deviations. Two of these instances occurred in the first period of an experiment (DA2 and DAX1) and in each instance the seller with unsold units (Seller 1) ended the period with a standing offer at least $.10 below the price of the preceding contract. In the third instance (DA1, period 2), although Sellers 1 and 2 had three unsold units between them, prices were sufficiently erratic that sixteen units were still traded. Sellers 1 and 2 closed the period with standing offers at the competitive equilibrium and $.05 above the competitive equilibrium, respectively.

The remaining market, DAX2, may represent an instance of strategic withholding. Sellers 1 and 2 sold less than nine units in six of eleven periods (periods 1, 6, 8, 9, 10, and 11) and end-period behavior in four of these six periods is not inconsistent with strategic withholding. Neither seller had an offer standing at the end of period 6, 8, 9, or 11, suggesting that they were intentionally withholding units.(10) In the two remaining periods (1 and 10), Seller 1 or 2 ended the period with a standing offer near or below the price of preceding contracts and close to the competitive equilibrium price.(11)

If DAX2 is in fact an instance of strategic withholding, Sellers 1 and 2 were remarkably unsuccessful at raising mean prices. Comparing the mean price series in DAX2 to other double auctions (Figure 2) reveals that prices in DAX2 were as close to the competitive equilibrium as any of the other experiments in the treatment cell. Moreover, the mean price path substantially overstates the price-increasing effects of strategic withholding in DAX2. At the conclusion of DAX2, Buyer 2 mentioned that he had bought at unusually high prices in periods 7, 9, and 10 just to see if he could have any effect on the market.

HLV observed somewhat higher levels of withholding in their five double auction experiments conducted using the SMP design. In a total of forty periods (five eight-period experiments) Seller 1 and / or Seller 2 sold a total of eight or fewer units in eleven periods. Detailed analysis of end-period behavior is not possible from HLV's data. Some casual observations, however, may be made. First, nearly half of the total instances of potential withholding (five of eleven periods) occurred in one experiment (IIe). In IIe, Seller 1 withheld in each period. (Seller 2 sold only four of five possible units in period 1, however, Seller 1 sold only three of five units in that period). These data suggest that Seller 1 recognized his capacity to affect the market. Prices were about $.30 above the competitive equilibrium in the last several periods of this experiment. The remaining six instances of less than full revelation are spread evenly over three experiments (IIa, IIc and IId). These markets look much more like our data. In each case, incomplete revelation occurred early in the experiment and prices either converged to the competitive prediction (in two instances) or rose $.15 to $.20 above it.

In summary, Sellers 1 and 2 rarely exercised market power by engaging in strategic withholding in either the double auction or posted offer markets. Pooling the possible instances of strategic withholding from HLV's and our double auction experiments, we find evidence of persistent withholding (more than two periods) in two of nine experiments. In one of those two experiments, strategic withholding was clearly unsuccessful in raising prices. Thus, the proposition that strategic withholding is the primary explanation of contract prices occurring above the competitive price in the SMP design must be rejected.

At this juncture, it is important to note that strategic supply withholding is not the only way for sellers to exercise market power. For example, a particularly savvy double auction seller with market power may negotiate the first four trades at supra-competitive prices and the last trade at the competitive price.(12) In posted offer markets, sellers may effectively exercise market power by simply offering all units at a supra-competitive price and selling until quantity demanded at that price is exhausted. In fact, market power of this type may have been exercised in PO2. Figure 4 shows that prices fell to near the competitive prediction in period 12 of PO2. In period 13, however, Seller 2 raised his price to $.39 above the competitive prediction and sold three of four units offered. In period 14, Seller 2 remained a solitary price leader, posting a price $.29 above the competitive prediction, and sold all five units offered. Upon seeing the elevated offer price repeated, two other sellers followed Seller 2 in period 15. Eventually the remaining two sellers joined in the price increases, and mean prices rose to nearly $.30 above the competitive prediction by the end of the experiment. In general, a strategy of exercising market power by offering high prices may be very difficult to distinguish from the "normal" price dynamic in many posted offer markets, particularly when prices start and remain above the competitive level (as in POS1, POS2, POXS1, POXS2 and POX2).(13)

V. SUMMARY OF EXPERIMENTAL RESULTS

Although prices consistently deviate from the competitive prediction, our double auction and posted offer markets eventually extract the bulk of the gains from exchange. Thus, strict privacy and the public messages of the market appear sufficient to support an efficiency but not a price interpretation of the Hayek Hypothesis using the SMP design. These results parallel HLV's findings in double auction markets.

Posted offer and double auction markets do not perform identically in this design, however. Competitive price deviations in posted offer markets are often much larger than those observed in double auctions, and high efficiency is attained more slowly.(14) The posted offer data also suggest that the use of demand-revealing computer-simulated buyers may generate qualitatively different results than similar posted offer markets using human buyers, even if the human buyers fully reveal demand. Posted offer sellers appear initially to employ more tentative pricing strategies when facing human buyers than when facing simulated buyers. This conjecture bears further analysis.

Finally, although all observed deviations from the competitive price were in the direction predicted by the exercise of market power, we are unable to determine how frequently the recognition and successful exercise of market power explains these deviations. The data suggest that strategic withholding by Sellers 1 and 2 does not explain the observed price deviations. Supply withholding, however, is not the only way to exercise market power. Particularly in posted offer markets, strategic behavior may be very difficult to distinguish from a "normal" price dynamic using the SMP design. It is clear that contract prices can occur substantially above the competitive price without Sellers 1 or 2 ever recognizing their market power. [Figures 1 to 4 Omitted]

(1)Exchange under posted offer rules is a two-stage procedure. In each period, sellers privately enter an offer price and quantity while buyers are in a waiting loop. After all sellers have entered their decisions, buyers (in a random sequence) are given the opportunity to make purchases. Trading periods end when all buyers finish purchasing. Sellers incur production costs only for units actually sold. There is no penalty for offering units to the market which are not sold. See Ketcham, Smith, Williams [1984] for a detailed discussion of the PLATO posted offer institution.

Under double auction rules both buyers and sellers continuously enter price quotes (bids to buy and offers to sell). Contracts occur when a price quote is accepted by someone on the opposite side of the market. In HLV's oral double auctions only price quotes which reduce the bid-ask spread were admissible (Holt et al. [1986, 110, n. 5]). Our markets use this same bid-ask spread reduction rule in combination with a limit order file; bids to buy below the highest (standing) bid and offers to sell above the lowest (standing) offer are queued in the limit order file rather than being rejected. After a contract, the highest queued bid and lowest queued offer are automatically entered as the new bid-ask spread. Subjects are continuously informed of their position in the limit order file and can withdraw a price quote from the limit order file at any time. Trading periods end after a prespecified number of seconds (300 in these experiments) or via a unanimous vote. See Smith and Williams [1983] for more discussion of this "rank queue" variant of the PLATO double auction. (2)In the case where a single seller forgoes the sale of two units, the withholding seller realizes $.25 increases on each of the three units sold after withholding ($.75), less $.05 commissions on the two zero surplus units withheld ($.10), for the net increase of $.65. The nonwithholding seller with market power receives an additional $.25 per unit on each of five units, for a total return increase of $1.25 per period. In the case where Seller 1 and Seller 2 each withhold one unit, they each receive $.25 increases on each of four units sold ($1.00), and forego only a $.05 commission on one zero profit unit. (3)Withholding two units costs any buyer $1.10. A buyer must forego $.50 in profit on each of two units ($1.00) plus $.10 in commissions. Successful counter-speculation drives the price down on the remaining unit by $.25, generating a net return of -$.85. (4)Sellers knew they were facing computer-simulated buyers, but were not explicitly told the nature of the buyer simulation algorithm. See Isaac and Smith [1985], Coursey et al. [1984], or Davis and Williams [1986] for other studies that utilize simulated buyers in PLATO posted offer markets. (5)Cason and Williams [1990] report a posted offer market with simulated buyers that diverges from the competitive price using a supply and demand structure (the "swastika design") with zero producer surplus. Also, some of the posted offer markets reported by Benson and Faminow [1988] and Alger [1987] diverged from the competitive price after initial convergence. As noted by an anonymous referee, it remains an open question as to the number of trading periods required for these markets to reach a behavioral equilibrium. (6)Buyer 4's strategy was costly. He earned $17.25 (in PLATO dollars), roughly half as much as the other buyers in POX2. Buyer 4's strategy, however, was not "irrational." His average profit per period was $.86. While this figure is somewhat lower than the $1.15 per period earned on average by buyers in the other posted offer experiments, Buyer 4's marginal contribution to earnings in periods sixteen to twenty averaged $2.49 per period. At that rate, his average earnings per period would have exceeded average earnings for buyers in the other posted offer experiments if the experiment had lasted only three more periods. (7)In period 3 of experiment PO1 a buyer chose not to trade two profitable units. It is also relevant to note that in four posted offer buyer market power experiments focusing on the ability of posted offer buyers to recognize unilateral gains from demand withholding, Davis and Williams [1990] report no strategic withholding. (8)We use the standard efficiency index: E = 100 (actual gains from trade) / (maximum potential gains from trade), exclusive of commissions. (9)Efficiency does not vary importantly with experience in either institution. Thus, efficiency data in Table II is pooled across experience levels in both posted offer and double auction markets. (10)We can not rule out the possibility that technical problems contributed to the apparent withholding behavior in DAX2. Noise on the communications link between the PLATO computer in Illinois and the lab in Indiana temporarily disrupted contract negotiations during a portion of periods 8 and 9. (11)Seller 1 ended period 1 with two unsold units and a standing offer at the competitive equilibrium price, which was the price for the five preceding contracts. Seller 2 ended period 10 with two unsold units and a standing offer $.22 less than the preceding contract. The last period 10 contract was, however, aberrantly high, and Seller 2's closing price was still $.07 above the competitive equilibrium. (12)Simple supply withholding is never optimal in the double auction in a static single period sense. If a seller holds back offers to force prices up early in a trading period, it is optimal to make any profitable sales in the last seconds of the period. Seller withholding in the double auction must be motivated by the fear that a low-price sale at the end of one period may reduce prices in the next. (13)In fact, the competitive price has little drawing power in the SMP design, as every seller can unilaterally increase minimum profits over those realized at the competitive prediction by raising prices $.24. Although movement away from a $.24 deviation reduces minimum profit per period for all sellers, this is not a Nash equilibrium since any seller can increase profits by slightly undercutting all other sellers and thereby trade their last unit. A fuller discussion of this issue is available in a longer unpublished version of this paper. (14)The prices observed in posted offer markets using the seller market power environment are somewhat different than reported in previous research. Using "normal" supply and demand configurations, posted offer markets do tend to converge to the competitive prediction, but it typically requires more trading periods than in comparable double auctions. For example, Davis and Williams [1986] report that five of six posted offer markets were within $.05 of the competitive prediction after seven periods. In contrast, each of the eight posted offer markets reported here generated prices more than $.20 above the competitive price after seven periods, and these deviations persisted in six of eight instances.

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Alger, Dan. "Laboratory Tests of Equilibrium Predictions with Disequilibrium Data." Review of

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Experimental Duopoly Markets." Journal of Economic Behavior and Organization, 9(4), 1988,

345-65. Cason, Timothy N. and Arlington W. Williams. "Competitive Equilibrium Convergence in a Posted-Offer

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1990, 331-52. Coursey, Donald R., R. Mark Isaac, Margaret Luke, and Vernon L. Smith. "Market Contestability in the

Presence of Sunk (Entry) Costs." Rand Journal of Economics, Spring 1984, 69-84. Davis, Douglas D. and Arlington W. Williams. "The Effects of Rent Asymmetries in Posted Offer

Markets." Journal of Economic Behavior and Organization, 7(3), 1986, 303-16. ______. "Market Power and the Institutional Asymmetry of the Posted Offer Trading Institution."

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Markets." Economic Inquiry, January 1986, 107-23. Isaac, R. Mark and Vernon L. Smith. "In Search of Predatory Pricing." Journal of Political Economy,

April 1985, 320-45. Ketcham, Jon, Vernon L. Smith, and Arlington W. Williams. "A Comparison of Posted-Offer and

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Hypothesis'." Economic Inquiry, April 1982, 165-79. Smith, Vernon L. and Arlington W. Williams. "The Effects of Rent Asymmetries in Experimental Auction

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DOUGLAS D. DAVIS and ARLINGTON W. WILLIAMS, Assistant Professor, Virginia Commonwealth University and Professor, Indiana University, respectively. Financial support from the National Science Foundation via grant SES 8319688 is gratefully acknowledged. We wish to thank Charles Holt and Anne Villamil for extensive comments on an earlier version of this paper. All errors remain our own.

The data generated by this research is permanently archived on the University of Illinois PLATO computer system. Contact the authors for information on accessing the data archive via microcomputer dialup.
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Date:Apr 1, 1991
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