Directory UMM :Data Elmu:jurnal:J-a:Journal of Economic Behavior And Organization:Vol41.Issue2.Feb2000:

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Vol. 41 (2000) 147–157

Quantity precommitment in an experimental

oligopoly market

Astri Muren

Department of Economics, Stockholm University, S-106 91 Stockholm, Sweden Received 14 February 1997; accepted 12 July 1999

Abstract

The paper describes an experiment designed to test if the equilibrium in a market characterized by capacity precommitment followed by price competition, as in the Kreps and Scheinkman model, conforms with the outcome predicted by that model, which is that capacities coincide with Cournot output levels. Sessions were run with capacity precommitment in inexperienced and experienced triopoly markets. The conclusion is that with inexperienced subjects capacity choices are more rivalistic than the model suggests, but in line with those of the Cournot experiments by Fouraker and Siegel. With experienced subjects capacities are quite close to the prediction of the Kreps and Scheinkman model. ©2000 Elsevier Science B.V. All rights reserved.

JEL classification: C92; D43; L13

Keywords: Capacity precommitment; Kreps–Scheinkman model; Oligopoly experiment

1. Introduction

The choice of a model to describe competition in oligopoly markets is an important issue in industrial economics and its applications. The two main candidates are the Bertrand and the Cournot models, which share the advantage of being analytically tractable. However, the two models give quite different equilibrium predictions, which implies that in many applications the choice of model will have a significant influence on the results.

In the Bertrand model firms set prices under the assumption that other firms keep their prices constant. When products are homogeneous, the equilibrium price will be equal to the marginal cost (of at least one of the firms). This means that in the Bertrand model the

q_{Communicated by Dr. R. Day}

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degree of competition increases from zero to its maximum level already when the number of firms increases from one to two.

In the Cournot model, where quantity of output is the strategic variable, the number of firms plays a role in that the equilibrium price goes down when additional firms enter, which seems intuitively reasonable. The problem lies in the theoretical motivation for the equilibrium — it would seem appropriate for any oligopoly model to let firms set prices rather than just output levels.

Kreps and Scheinkman (1983) formulated a two stage model where firms first choose production capacity and then, in stage two, set their prices. Under certain circumstances the equilibrium in this model will be identical to the Cournot equilibrium. Kreps and Scheinkman’s theoretical result integrates the Bertrand price setting model with the Cournot model of quantity competition, and provides a rationale for using the Cournot model to de-scribe an industry with steeply increasing marginal costs, i.e. where the capacity choice is a binding constraint for the firm, while the Bertrand model would be more suitable for an industry with a technology such that the marginal cost of production increases slowly with output.1 Testing the Kreps and Scheinkman model could provide useful information for policy makers on the appropriateness of the Cournot model.

One experimental test of the Kreps and Scheinkman hypothesis is provided by Mestelman and Welland (1988), who study the effects of advance production on the relative performance of posted offer and double auction markets. They find that advance production, which is essentially the same as capacity precommitment, leads to competitive outcomes under both trading institutions. However, as noted by Holt (Holt, 1995, p. 376), the design used by Mestelman and Welland does not distinguish well between competitive outcomes and Cournot outcomes (nor is that the purpose of their study).

The experiment described in this paper was designed to test whether the Kreps and Scheinkman results emerge in an experimental market organized according to the assump-tions of that model. To achieve this end we have followed the assumpassump-tions of the Kreps and Scheinkman model closely. In particular, we have used efficient rationing, which is a crucial assumption of the model, as demonstrated by Davison and Deneckere (1986) who show that under other rationing mechanisms, e.g. proportional rationing, the Kreps and Scheinkman result may not emerge.

Since the Kreps and Scheinkman model combines the two opposites of quantity-setting and price-setting, it is also interesting to compare the experimental performance of the model with those of the Cournot and Bertrand models. This is done using the Fouraker and Siegel (1963) results for the two market forms. After the presentation of Fouraker and Siegel’s results in Section 2, there follows a description of the experimental formulation and the set-up of the experimental sessions in Section 3. Section 4 derives equilibrium predictions. Section 5 analyzes the outcome of the experiment and Section 6 concludes.

2. Fouraker and Siegel’s oligopoly markets

Experimental investigations of quantity competition markets are reviewed by Holt (Holt, 1995, pp. 403–404), who concludes that the outcomes of Cournot experiments with more

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than two sellers tend to be more competitive than is predicted by the Cournot model. The results reached by Fouraker and Siegel provide a standard of comparison for both the price setting and the quantity setting cases.

Fouraker and Siegel report results from two triopoly quantity competition experiments, which differ with respect to the amount of information provided to subjects. In the incom-plete information formulation, sellers know only their own profits for each quantity choice, as dependent on the combined quantities of the other two sellers. In the complete infor-mation formulation, sellers know also the effect of their and the sum of their competitors’ quantity choices on the combined profits of the other sellers. In our capacity precommit-ment experiprecommit-ment the information to sellers is cast in terms of costs and demand instead of profit tables, and sellers have identical costs, which means that they can infer the effects on other sellers’ profits. This suggests that of Fouraker and Siegel’s two Cournot triopoly ex-periments, the complete information formulation would provide our most relevant Cournot outcome comparison.

Fouraker and Siegel summarize the results of their quantity competition experiments in terms of the support for each of three types of equilibria: cooperative, Cournot and competitive/rivalistic (see Table 9.10, p. 150).2 Their definition of ‘support’ is that the outcome supported an equilibrium solution if it was closer to the corresponding numerical quantity prediction than to any other. There were 11 triopoly markets in their complete information experiment. The cooperative solution was supported by 0 markets, the Cournot solution was supported by 5 markets, and the competitive solution was supported by 6 markets. Thus, the competitive solution was (just) dominant over the Cournot solution.

In the Bertrand competition case in Fouraker and Siegel there are also two experimental formulations of triopoly markets, differing in informational structure. In both formulations the market outcome was strongly competitive, with the ruling price being equal to the Bertrand price in every market.3

3. Experimental formulation

The subjects were all recruited from the group of students of economics at the introductory level at Stockholm University. The experiments were conducted in two rounds, during April 1998 and during May 1999. A total of 30 students participated.

Each of the sessions had subjects divided into several markets. Subjects were informed about the number of firms in their market (three), but they were not told who else in the room was in the same market. Demand and cost information was common knowledge. The demand side was simulated in a demand curve, since it was not part of the purpose of the experiment to investigate buyer behavior. In all markets the market demand curve was

P (Q) =38−Q, whereP is market price andQis total market output, and the cost of installing a unit of capacity was 10.

2_{The results reported are from the 21st round of 22, where the fact that round 22 was the last one was not}

announced until the beginning of that period.

3_{Here, results reported are from round 14 which again was the last period before the end-of-game period was}

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The markets were all organized to simulate a Kreps and Scheinkman market in that sellers first chose capacities, next they were informed about the other sellers’ capacity choices and then they set their prices. After each period all prices were listed. If needed, the rationing mechanism was that the seller with the lowest price in each market was the first-priority seller, then the seller who set the second lowest price could sell and so on until all units demanded at the going price were sold.

In the first (1998) round a total of nine triopoly markets were run, six with subjects who did not have any experience of this kind of experiment and three with subjects who had already participated in one of the previous unexperienced sessions. In the second (1999) round a total of seven markets were run, four inexperienced and three experienced. All sessions had ten market periods. The time allowed between the respective inexperienced and experienced rounds was approximately two weeks.

Sessions were conducted with pen and paper. Subjects calculated their own earnings after each market period using pocket calculators. As stated in the instructions, subjects were paid the accumulated earnings in all odd or even periods, where odd or even was determined by throwing dice at the end of the experiment. A participation payment of SEK 100 was added (150 for the 1998 experienced markets). For recruitment reasons losses were not subtracted. All information was given at the beginning of the experiment. Sessions lasted between 1 and 3/2 h including the reading of instructions (the experienced sessions were quicker).4

4. Equilibrium predictions

The predictions of the Kreps and Scheinkman model is that, under appropriate circum-stances, the market outcome will be as in the Cournot model. With constant marginal costs and linear demand, equilibrium market output is:

Qc= n

n+1Q

∗

wherenis the number of sellers andQ∗_{is the perfectly competitive market equilibrium}

output level.

In the capacity-constrained price game of the experiment sellers make their strategic de-cisions in two stages; first they determine their maximum capacity and then their price (both variables in whole units). Each unit of capacity costs SEK 10. Up to the number of units of capacity installed, the marginal cost of production is zero. In each market period, the firm can sell up to the number of units for which it has capacity installed. If sales have to be rationed, the assumed rationing mechanism is efficient rationing. We will consider the exis-tence of pure-strategy equilibria in the price-setting stage and determine their characteristics where they exist.

When setting its price, each seller knows its own capacity and the combined capacity of the other sellers, together with the demand curve and the number of sellers in the market. There are two basic types of strategies available to a firm: to attempt to undercut other sellers

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or to expect the other sellers to undercut. The latter strategy implies setting a price at least as high as all other sellers, the former setting a lower price than at least some other seller.

Consider the high-price strategy first. With efficient rationing, the lower priced firms will sell to consumers with high willingness to pay for the good. The high-price firm,i, will face a residual demand curve of the formP (Q)=38−Q−i−qi, whereQ−iis the combined capacity of the two other sellers andqiis firmi’s sales. The high-price firm will set its price to maximize revenue, i.e. atpi =(38−Q−i)/2 if its capacity is large enough for this. If not, that is ifqiis smaller than(38−Q−i)/2, the firm will set its price to clear the market. If a firm’s capacity is well above the revenue-maximizing sales level for the high-price strategy, a low-price strategy might yield higher profits. Not all firms can successfully apply low-price strategies since they would then have no other firm to undercut, so under-cutting would involve mixed strategies. For a detailed determination of equilibria including mixed-strategy equilibria we refer to Kreps and Scheinkman (1983). We will here limit our-selves to describing the pure strategy equilibrium, i.e. with all firms applying the high-price strategy.

Consider situations where all firms are capacity constrained in the price-setting stage in the sense defined above, i.e.qi ≤ [38−(q1+q2+q3−qi)]/2 for all firmsi. All firms will then set the market-clearing price, and since all firms sell to capacity there will be no incentive to undercut by lowering the price. To get a sense of the values ofq1, q2andq3that we are considering, note that e.g. values at or belowq1=10, q2=q3=9 are consistent with a high-price strategy on the part of all firms.

Under the condition that all firms are capacity-constrained in the price-setting stage, we now know that firms will set the market clearing price. The capacity-setting stage is then identical to the Cournot quantity-setting game and the prediction for that stage is that firms’ capacity choices will be equal to the Cournot equilibrium quantities. In this experiment the Cournot market output with three sellers is equal to 21 units and the Cournot equilibrium prediction is thus that each seller would produce 7 units. Replacing the Cournot output volumes with capacities, the prediction is that sellers will install 7 units of capacity each, and sell these at price SEK 17, which is also the market clearing price.

5. Experimental outcome

5.1. Capacities

The data on market capacities for the inexperienced markets are shown in Table 1.5 In the inexperienced sessions most of the markets produce aggregate capacities above the Kreps and Scheinkman prediction of 21 units. In some of the inexperienced markets there is a difference between decisions taken at the beginning of a session — in the first four periods — and decisions in the latter part of the session, in that market capacities are closer to the prediction in the later periods. This difference appears in the A1, A2, B2, C2, A3 and C3-markets and is reflected in lower mean and median market capacities from period five onwards.

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Table 1

Aggregate market capacities in inexperienced rounds. The predicted market capacity is 21 units. (Markets A1 to C2 are from 1998 and markets A3 to D3 from 1999)

Period: 1 2 3 4 5 6 7 8 9 10

A1-market 23 28 29 43 24 26 28 25 26 26

B1-market 22 43 48 29 45 66 55 40 36 58

C1-market 38 27 37 33 25 55 49 25 26 30

A2-market 34 50 40 26 27 26 27 25 19 21

B2-market 39 35 32 34 17 17 18 18 19 19

C2-market 40 28 30 50 22 20 23 24 25 30

A3-market 23 30 42 33 36 20 24 45 22 26

B3-market 39 60 59 58 51 41 45 27 29 49

C3-market 37 45 50 49 32 26 26 37 18 18

D3-market 48 74 75 84 65 47 43 27 21 31

Mean 34.3 42.0 44.2 43.9 34.4 34.4 33.8 29.3 24.1 30.8

Median 37.5 39 41 38.5 29.5 26 27.5 26 23.5 28

Table 2

Aggregate market capacities in experienced rounds (A8 to C8 from 1998 and A9 to C9 from 1999)

Period: 1 2 3 4 5 6 7 8 9 10

A8-market 30 29 37 21 21 27 21 22 32 22

B8-market 16 21 20 23 25 25 29 20 22 27

C8-market 26 30 17 23 21 23 28 23 21 23

A9-market 23 26 25 26 27 27 29 31 34 32

B9-market 20 24 24 22 22 22 22 22 22 37

C9-market 19 18 19 21 20 20 21 19 20 19

Mean 22.3 24.7 23.7 22.7 22.7 24 25 22.8 25.2 26.7

Median 21.5 22.5 22 22.5 21.5 24 25 22 22 25

The median capacities for the inexperienced treatment are above the Kreps and Scheinkman prediction of 21 market units and 7 individual units, particularly in the first four periods. In fact, several markets have capacity levels well above the competitive equilibrium level of 28 units, which would be the Bertrand competition outcome. Table 2 shows market capacities for the experienced markets. The markets with experienced subjects are closer to the Kreps and Scheinkman prediction from the beginning and throughout.

To compare the outcome of our capacity precommitment experiment with Fouraker and Siegel’s results we computed the support for the same three equilibrium solutions in our data for both the inexperienced and the experienced sessions.6 These are displayed in Table 3.

For the inexperienced sessions these values have the same tendency as Fouraker and Siegel’s results in that there are more rivalistic markets than Cournot/Kreps and Scheinkman together with cooperative. For the experienced sessions the tendency is reversed and there

6_{The monopoly equilibrium market capacity is 14 units and the competitive equilibrium capacity is 28 units.}

Market capacities in the interval [0,17] were counted as cooperative, capacities in the interval [18,24] as Cournot and capacities≥25 as rivalistic.

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Table 3

Number of market outcomes supporting each of three equilibrium solutions

Period: 4 5 6 7 8 9 10 Fouraker and Siegel (period 21)

Inexperienced

Cooperative 0 1 1 0 0 0 0 0

Cournot/K-S 0 2 2 3 2 5 3 5

Competitive 10 7 7 7 8 5 7 6

Experienced

Cooperative 0 0 0 0 0 0 0

Cournot/K-S 5 4 3 3 5 4 3

Competitive 1 2 3 3 1 2 3

are now more Cournot/Kreps and Scheinkman outcomes than competitive ones (there are no cooperative outcomes in periods 4–10). This indicates that experience makes a difference. Table 3 does not take information about numerical capacity values within each of the three ranges into account but looking at means and medians there is a considerable difference between inexperienced and experienced markets. A period by period comparison shows that the market capacities are significantly greater in the inexperienced markets for periods 1, 2, 3 and 4.7 For the last six periods means and medians are still greater in the inexperienced markets. In the experienced treatment 7 out of 10 means (and 8 out of 10 medians) are within the Cournot/Kreps and Scheinkman range.

To summarize the evidence on capacity levels we conclude that in the inexperienced sessions capacity levels are higher than predicted by the Kreps and Scheinkman model and in line with the results reached in Cournot triopolies by Fouraker and Siegel. With experience, within the experiment and more noticeably between experiments, capacity choices approach the Kreps and Scheinkman prediction quite well.

5.2. Prices

So far we have compared the capacity precommitment experiment with its theoretical prediction and with a Cournot experiment, which means that we have concentrated on the quantity/capacity dimension. To check if the capacity precommitment model yields the Kreps and Scheinkman outcome we also need to see to what extent the installed capacity is sold. This is interesting also because the efficient rationing mechanism that was used is complicated to understand.

In Section 4 we determined conditions under which firms will set the market-clearing price in the price-setting stage. This will be the case if capacities are not too high, specifically ifqi ≤[38−(q1+q2+q3−qi)]/2 for all firmsi. To test whether the Kreps and Scheinkman price-setting prediction is confirmed by the experimental data or not, we inquire if it is the case that sellers set the market-clearing price when the capacity constraints given above are satisfied.

Table 4 shows, for the inexperienced treatment, on the one hand the markets and periods where the capacity constraint is satisfied and those where it is not, marked with a C or a –,

7_{A Kolmogorov–Smirnov two-sample, one-tailed test rejects the null hypothesis that the two samples are from}

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Table 4

Capacity constraints and market clearing in inexperienced treatment

Period: 1 2 3 4 5 6 7 8 9 10

A1 C/– –/– –/– –/– C/– C/P C/– C/P C/P C/P

B1 C/– –/– –/– –/– –/– –/– –/– –/– –/– –/–

C1 –/– C/– –/– –/– C/– –/– –/– C/P C/P –/P

A2 –/– –/– –/– C/– C/– C/P C/– C/P C/P C/P

B2 –/– –/– –/– –/– C/P C/P C/P C/P C/P C/P

C2 –/– –/– –/– –/– C/P C/P C/P C/P C/P –/–

A3 C/– –/– –/– –/– –/– C/– C/– –/– C/– C/–

B3 –/– –/– –/– –/– –/– –/– –/– –/– –/– –/–

C3 –/– –/– –/– –/– –/– C/– C/– –/– C/P C/P

D3 –/– –/– –/– –/– –/– –/– –/– –/– C/– –/–

Table 5

Capacity constraints and market clearing in experienced treatment

Period: 1 2 3 4 5 6 7 8 9 10

A8 –/– –/– –/– C/– C/– –/– C/– C/– –/– C/P

B8 C/P C/P C/– C/P –/– C/P –/– C/P C/P –/–

C8 –/P –/– C/P C/P C/P C/P –/– C/– C/P C/P

A9 C/– C/– C/– C/– C/– C/– –/– –/– –/– –/–

B9 C/– C/– C/– C/– C/– C/– C/P C/P C/P –/–

C9 C/– C/P C/– C/– C/P C/P C/– C/P C/P C/P

and on the other hand whether all units were sold or not for the same markets, marked with a P or a –, respectively. Table 5 shows the same information for the experienced markets.

The tables suggest several conclusions about pricing behaviour. In the first place, although markets clear when the capacity constraint is satisfied in quite a few of the markets, they do not always. Looking at each market individually, we note that after a market has cleared once, it continues to do so in subsequent periods. One possible explanation for this could be that the efficient rationing mechanism was difficult for the subjects to understand and that they learned something about how to price when their market cleared.

In general it is interesting to notice that in the experienced markets capacities came close to the Kreps and Scheinkman prediction in spite of the fact that sellers did not seem to be entirely certain about the way the rationing mechanism worked. This suggests that the model’s predictions may be robust for slight divergences from efficient rationing, which strengthens the case for the Kreps and Scheinkman somewhat, particularly since efficient rationing is an extreme form which seems unlikely to appear with any frequency in real markets (see Davidson and Deneckere for a discussion of rationing mechanisms).8

8_{Davidson and Deneckere, who show that although the Kreps and Scheinkman result does not emerge under}

proportional rationing when the cost of capacity is small, note that when capacity costs increase, equilibrium capacities under proportional rationing approach Kreps and Scheinkman/Cournot values.

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Table 6

Frequency of losses in the inexperienced treatment

Mean # losses per seller # sellers receiving SEK 0

A1-market 4/30 1

B1-market 21/30 3

C1-market 12/30 3

A2-market 6/30 1

B2-market 5/30 1

C2-market 6/30 1

A3-market 14/30 1

B3-market 19/30 3

C3-market 12/30 2

D3-market 18/30 3

Table 7

Frequency of losses in the experienced treatment

Mean # losses per seller # sellers receiving SEK 0

A8-market 6/30 0

B8-market 1/30 0

C8-market 2/30 0

A9-market 8/30 1

B9-market 5/30 0

C9-market 1/30 0

5.3. Incentives

The average incentive payments made to subjects after sessions were SEK 39 for the inexperienced treatment and SEK 136 for the experienced treatment.9 In several of the sessions of the inexperienced treatment and on occasion in the experienced treatment, subjects made losses due to not being able to sell all their installed capacity in one or more periods. Since losses were not subtracted from the participation payment but only from earnings in the subsequent periods, large losses may reduce incentives to act as a profit-maximizer. To investigate whether this appears to have happened we computed the frequency of losses over all periods in each session and noted the number of sellers in each market who received less than zero in accumulated earnings. This information is displayed in Tables 6 and 7.

Clearly the frequency of losses is considerably lower in the experienced treatment and it seems reasonable to conclude that the fact that losses were not subtracted was not im-portant for experienced markets. In the inexperienced markets we note that the frequency of losses is lower in the A1, A2, B2, C2 and A3 markets, which are among the mar-kets where capacities seem to approach the prediction after period 4. Certainly the lower capacities associated with this contribute to lower losses, but it might also be the case

9_{An allowance for income tax dues (30 percent tax rate) was added to each subject’s payment and paid directly}

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that the preserved incentives resulting from lower losses have contributed to the fact that capacities approach the prediction. Looking at pricing behaviour in the inexperienced mar-kets (Table 4) we see that it is only in three out of the 10 marmar-kets that neither capac-ities nor prices eventually approach Kreps and Scheinkman results, which suggests that incentives to act as profit-maximizing sellers have been preserved for a majority of the subjects.

6. Conclusions

The purpose of the experiment was to test whether the Kreps and Scheinkman model of capacity precommitment and price competition predicts the equilibrium outcome in a laboratory market organized according to the assumptions of that model. The Kreps and Scheinkman equilibrium capacity choices coincide with those of the Cournot model but have the added advantage of allowing firms to set their own prices, so the model could be seen as an attempt to strengthen the case for the Cournot model in markets where firms are limited by previous decisions on capacities. Since the Cournot model is used frequently in practical applications e.g. in the anti-trust area, confirming or rejecting the Kreps and Scheinkman model would be of practical value.

The experimental formulation created capacity precommitment with subsequent price competition in markets with three sellers. In each market period the subjects acting as sellers first decided their maximum production capacity, then received information about the capacity choices of their competitors and finally decided on their price. The rationing mechanism used was efficient rationing.

Sessions were conducted at Stockholm University with introductory level Economics students as subjects. In some of these, the subjects had previous experience with this ex-perimental market. The outcome of the experiment was that in the inexperienced markets capacity choices are more rivalistic than the Kreps and Scheinkman model predicts. The discrepancy between the experimental outcome and the predicted outcome is reduced when subjects gain experience. This is true to some extent for experience within a session, after about four market periods, and more so for experience ‘between sessions’ i.e. by taking part in the same experimental market a couple of weeks later.

The capacity precommitment and price competition model also yields predictions about prices given capacities, but the support for price predictions in the experimental data was weaker than the support for capacity predictions.

Acknowledgements

I thank Peter Bohm and Hans Lind for constructive comments on the formulation of the experiment, and Helena Eklund, Johan Lindén, Lena Lundin, Helen Nilsson and Joakim Sonnegård for competent assistance in conducting the experiment. An anonymous referee made very helpful suggestions. Financial support from the Swedish Competition Authority and from the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.

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References

Davidson, C., Deneckere, R., 1986. Long-run competition in capacity, short-run competition in price, and the Cournot model. Rand Journal of Economics 17, 404–415.

Fouraker, L.E., Siegel, S., 1963. Bargaining Behavior, McGraw-Hill, New York.

Holt, C.A., 1995. Industrial organization: a survey of laboratory research. In: Kagel, J., Roth, A. (Eds.), Handbook of Experimental Economics, Princeton University Press, Princeton, pp. 349–443.

Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell Journal of Economics 14, 326–337.

Mestelman, S., Welland, D., 1988. Advance production in experimental markets. Review of Economic Studies 55, 641–654.

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Table 1

Aggregate market capacities in inexperienced rounds. The predicted market capacity is 21 units. (Markets A1 to C2 are from 1998 and markets A3 to D3 from 1999)

Period: 1 2 3 4 5 6 7 8 9 10

A1-market 23 28 29 43 24 26 28 25 26 26

B1-market 22 43 48 29 45 66 55 40 36 58

C1-market 38 27 37 33 25 55 49 25 26 30

A2-market 34 50 40 26 27 26 27 25 19 21

B2-market 39 35 32 34 17 17 18 18 19 19

C2-market 40 28 30 50 22 20 23 24 25 30

A3-market 23 30 42 33 36 20 24 45 22 26

B3-market 39 60 59 58 51 41 45 27 29 49

C3-market 37 45 50 49 32 26 26 37 18 18

D3-market 48 74 75 84 65 47 43 27 21 31

Mean 34.3 42.0 44.2 43.9 34.4 34.4 33.8 29.3 24.1 30.8

Median 37.5 39 41 38.5 29.5 26 27.5 26 23.5 28

Table 2

Aggregate market capacities in experienced rounds (A8 to C8 from 1998 and A9 to C9 from 1999)

Period: 1 2 3 4 5 6 7 8 9 10

A8-market 30 29 37 21 21 27 21 22 32 22

B8-market 16 21 20 23 25 25 29 20 22 27

C8-market 26 30 17 23 21 23 28 23 21 23

A9-market 23 26 25 26 27 27 29 31 34 32

B9-market 20 24 24 22 22 22 22 22 22 37

C9-market 19 18 19 21 20 20 21 19 20 19

Mean 22.3 24.7 23.7 22.7 22.7 24 25 22.8 25.2 26.7

Median 21.5 22.5 22 22.5 21.5 24 25 22 22 25

6_{The monopoly equilibrium market capacity is 14 units and the competitive equilibrium capacity is 28 units.} Market capacities in the interval [0,17] were counted as cooperative, capacities in the interval [18,24] as Cournot and capacities≥25 as rivalistic.

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Table 3

Number of market outcomes supporting each of three equilibrium solutions

Period: 4 5 6 7 8 9 10 Fouraker and Siegel (period 21)

Inexperienced

Cooperative 0 1 1 0 0 0 0 0

Cournot/K-S 0 2 2 3 2 5 3 5

Competitive 10 7 7 7 8 5 7 6

Experienced

Cooperative 0 0 0 0 0 0 0

Cournot/K-S 5 4 3 3 5 4 3

Competitive 1 2 3 3 1 2 3

5.2. Prices

price-setting prediction is confirmed by the experimental data or not, we inquire if it is the case that sellers set the market-clearing price when the capacity constraints given above are satisfied.

Table 4 shows, for the inexperienced treatment, on the one hand the markets and periods where the capacity constraint is satisfied and those where it is not, marked with a C or a –,

7_{A Kolmogorov–Smirnov two-sample, one-tailed test rejects the null hypothesis that the two samples are from} the same distribution at the 0.05 significance level for periods 1–4.

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Table 4

Capacity constraints and market clearing in inexperienced treatment

Period: 1 2 3 4 5 6 7 8 9 10

A1 C/– –/– –/– –/– C/– C/P C/– C/P C/P C/P

B1 C/– –/– –/– –/– –/– –/– –/– –/– –/– –/–

C1 –/– C/– –/– –/– C/– –/– –/– C/P C/P –/P

A2 –/– –/– –/– C/– C/– C/P C/– C/P C/P C/P

B2 –/– –/– –/– –/– C/P C/P C/P C/P C/P C/P

C2 –/– –/– –/– –/– C/P C/P C/P C/P C/P –/–

A3 C/– –/– –/– –/– –/– C/– C/– –/– C/– C/–

B3 –/– –/– –/– –/– –/– –/– –/– –/– –/– –/–

C3 –/– –/– –/– –/– –/– C/– C/– –/– C/P C/P

D3 –/– –/– –/– –/– –/– –/– –/– –/– C/– –/–

Table 5

Capacity constraints and market clearing in experienced treatment

Period: 1 2 3 4 5 6 7 8 9 10

A8 –/– –/– –/– C/– C/– –/– C/– C/– –/– C/P

B8 C/P C/P C/– C/P –/– C/P –/– C/P C/P –/–

C8 –/P –/– C/P C/P C/P C/P –/– C/– C/P C/P

A9 C/– C/– C/– C/– C/– C/– –/– –/– –/– –/–

B9 C/– C/– C/– C/– C/– C/– C/P C/P C/P –/–

C9 C/– C/P C/– C/– C/P C/P C/– C/P C/P C/P

and on the other hand whether all units were sold or not for the same markets, marked with a P or a –, respectively. Table 5 shows the same information for the experienced markets.

8_{Davidson and Deneckere, who show that although the Kreps and Scheinkman result does not emerge under} proportional rationing when the cost of capacity is small, note that when capacity costs increase, equilibrium capacities under proportional rationing approach Kreps and Scheinkman/Cournot values.

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Table 6

Frequency of losses in the inexperienced treatment

Mean # losses per seller # sellers receiving SEK 0

A1-market 4/30 1

B1-market 21/30 3

C1-market 12/30 3

A2-market 6/30 1

B2-market 5/30 1

C2-market 6/30 1

A3-market 14/30 1

B3-market 19/30 3

C3-market 12/30 2

D3-market 18/30 3

Table 7

Frequency of losses in the experienced treatment

Mean # losses per seller # sellers receiving SEK 0

A8-market 6/30 0

B8-market 1/30 0

C8-market 2/30 0

A9-market 8/30 1

B9-market 5/30 0

C9-market 1/30 0

5.3. Incentives

9_{An allowance for income tax dues (30 percent tax rate) was added to each subject’s payment and paid directly} to the Tax Authority, so that payment to subjects was net of taxes.

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6. Conclusions

Acknowledgements

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References

Davidson, C., Deneckere, R., 1986. Long-run competition in capacity, short-run competition in price, and the Cournot model. Rand Journal of Economics 17, 404–415.

Fouraker, L.E., Siegel, S., 1963. Bargaining Behavior, McGraw-Hill, New York.

Holt, C.A., 1995. Industrial organization: a survey of laboratory research. In: Kagel, J., Roth, A. (Eds.), Handbook of Experimental Economics, Princeton University Press, Princeton, pp. 349–443.

Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell Journal of Economics 14, 326–337.

Mestelman, S., Welland, D., 1988. Advance production in experimental markets. Review of Economic Studies 55, 641–654.

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Quantity precommitment in an experimental

oligopoly market

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