214 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
scorer was awarded the role of producer.
5
Each subject was given a set of instructions and record sheets, a buyer demand schedule, and several offer forms. Copies of the instructions
for this experiment are available upon request. In this environment, the traders produced to order to avoid any problems associated with carrying inventories or exposing the traders
to risk. Each period, the producer was asked to set a price, which the traders were shown immediately. The traders were then invited to submit a contingent price to the buyers. The
buyers, who were programmed following the buyer demand schedule, ordered from the traders, given the set of offered prices. The buyers were ordered randomly each period and
programmed to approach the low-priced trader first, and in the case of a tie, to randomly choose a trader to deal with. The buyers were programmed this way in order to more
closely approximate reality. Because of the competitiveness of these downstream markets, ordering the buyers randomly never reduced the efficiency of the markets. The orders were
submitted to the traders, after which the traders made purchase requests from the producer. If the producer did not offer to supply enough units to satisfy the traders, the traders’
purchase requests were processed in a random order which the traders were informed of at the beginning of each period. In each experiment, one subject was paid a fixed payment
of 15 to run papers back and forth between the subjects and the experimenter to speed processing.
In the monopolymonopoly experiments, subjects were brought in one pair at a time and randomly assigned the roles of producer and trader. Since subjects were face to face
in the monopolycompetition experiments, these experiments were conducted face to face also. An asymmetry of information existed because the producer had enough information
to calculate the maximum profit that the trader could earn given each price the producer offered, but the trader had enough information to be able to compute only his own profit.
Each period, the producer was asked to post a price which was shown to the trader. The trader then offered a price to the buyers, and knowing the quantity demanded at that price,
made hisher purchasing decision.
4. Results
4.1. Comparison of monopolymonopoly and monopolycompetition outcomes The results from the monopolycompetition experiments are shown in Figs. 2 and 3, and
the results from the monopolymonopoly experiments are shown in Figs. 4–7. The com- petitive downstream price for the monopolycompetition experiments and the downstream
best response for the monopolymonopoly experiments are determined each period from the actual upstream price. Also shown on these graphs are the quantities sold and the market
efficiencies
6
each period. As a result of the automated buyers and the fact that the subjects
5
This practice has become common in experiments in which some portion of the subjects are given an economic advantage. Hoffman and Spitzer 1985 found that subjects were more likely to fully exploit their economic rights
when those rights were earned rather than assigned randomly.
6
Efficiencies are calculated in the usual way and do not include commissions.
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 215
216 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 217
218 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 219
220 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
Fig. 7. Monopolymonopoly results.
always supplied enough units to satisfy the buyers’ demand, these two measures report essentially the same information.
There are several issues to be considered when examining the data. First, do the subjects coordinate their actions in such a way as to achieve the predicted final price and quantity
outcomes in the market? Second, do the upstream and downstream subjects behave as the theory predicts? In other words, are final predicted outcomes achieved, and are they achieved
through both firms behaving as theory predicts or in some other way? Third, does the change in the downstream market structure affect the efficiency of the markets?
It seems fairly evident from a cursory examination of the monopolycompetition graphs that the theory predicts final prices fairly well. The downstream firms appear to behave
competitively as the theory predicts, and the upstream firm generally takes advantage of this. With the exception of MC104, the upstream monopolists lock onto the predicted price
of 405 pesos by the tenth period. By the eighth period, almost all of the downstream firms are charging a price of P
U
+ 100 or the downstream marginal cost. During the last eight
periods, occasional attempts by certain traders are made to raise price, but these traders
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 221
immediately find it unprofitable and return to the competitive price the next period. In the fourth monopolycompetition experiment, although the monopolist had some difficulty in
finding the profit-maximizing price, the downstream firms were behaving competitively. No price distortion is present in the downstream market.
In order to examine the questions addressed above more carefully, t-tests on mean prices across experiments were run. All tests are reported using a 5 significance level. In order
to determine if the markets behave as theory predicts, the null hypothesis, H : ¯
P
D
= 505,
is tested against the alternative hypothesis, H
a
: ¯ P
D
6= 505. Using standard t-tests
7
with 11 degrees of freedom, H
cannot be rejected in any of the final five periods.
8
In order to examine whether upstream firms behave as theory predicts, H
: ¯ P
U
= 405 was tested
against H
a
: ¯ P
U
6= 405. Standard t-tests with 3 degrees of freedom indicate that H
cannot be rejected in any of the last five periods. While these tests do not allow us to accept the null
hypothesis, they do provide some evidence that the firms are pricing near the theoretical predictions. Further, the mean of the downstream prices across experiments over the last
five periods is 505.67, with a standard deviation of 8.76, while the mean of the upstream prices across experiments over the last five periods is 405.50, with a standard deviation of
8.72. Both of these are very close to the predicted values. The vertical structure, as well as each of its component markets, behave in general as theory would predict. This final
outcome mirrors the outcome predicted for a vertically integrated firm.
Because these experiments tended to be fairly uninteresting for the subjects and behaved predictably, only four were run. Once price settled down to the competitive price in the
downstream market, the traders’ profits were, in effect, determined randomly by the buyer program. From discussions with the downstream subjects following the experiment, it was
clear that many of them felt they had little control over the outcome. Three firms provided enough competition in the downstream market to compel the firms to price a marginal cost.
Because the downstream firms found that they could do no better than act as price takers, the upstream firm had no incentive to place any restraints on them. Downstream competition
effectively controlled their actions. As in the Plott and Uhl middlemen experiments, the middlemen or traders in this case took no profit at the expense of the buyers or upstream
sellers. Spengler’s assertion that competition in the downstream produces the vertically integrated results and eliminates the incentive for vertical restraints because of the removal
of the vertical externality is supported.
In examining the monopolymonopoly experiments, one can see that there is much more variation in the data than there was in the monopolycompetition data. Subjects seemed to
be exploring the profit possibilities. It appeared to be especially difficult for the upstream firm to determine its best strategy as evidenced by the comments of many of the upstream
subjects who expressed concern that they could not figure out how the downstream firm was behaving and therefore had difficulty deciding which actions to take.
7
Of course t-statistics require the data to be normally distributed, but we have no way of verifying this. However, nonparametric tests, such as the sign test and the Mann-Whitney test, lead to identical conclusions. Therefore, we
will continue to report only the results from the t-tests.
8
It should be noted that because of the possible time dependence across periods, these t-tests may not be independent.
222 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
The conjecture that these experiments result in the Nash prediction consists of testing the two hypotheses H
: ¯ P
D
= 555 pesos and H
: ¯ P
U
= 410 pesos against H
a
: ¯ P
D
6= 555
and H
a
: ¯ P
U
6= 410, respectively. Using t-tests with 6 degrees of freedom, we cannot reject
the hypothesis that the true mean of the final price from the seven monopolymonopoly experiments is 555 pesos in each of the last five periods.
9
However, we can reject in period 14 that the true mean of the upstream prices is 410. The mean of the downstream prices
across experiments for the last five periods is 547.43, with a standard deviation of 33.44, while the mean of the upstream prices across experiments for the last five periods is 385.17,
with a standard deviation of 34.48. While these averages are not as close to their predicted values as was the case in the monopolycompetition experiments, as discussed before, there
is much more variation in the data. Overall we can conclude that there is evidence in these experiments favoring the Nash prediction. However, the rejection of the hypothesis that the
true mean of upstream prices is 410 in one of the last five periods may indicate that this is a case where the structure as a whole behaves as theory would predict, but may not be the
result of the individual firms behaving as predicted.
In all of the last five periods, we can reject H : ¯
P
D
= 505 pesos in favor of H
: ¯ P
D
505 to indicate that the monopolymonopoly structure tends to result in higher prices than the integrated outcome. This coincides with the results in Fouraker and Siegel, who found
support for the Bowley Nash rather than the Paretian integrated equilibrium in their bilateral bargaining experiments under incomplete information conditions. Subjects here
have more information than what was given the Fouraker and Siegel subjects, though it is presented in a different way. Rather than a table of profits, demand is given and subjects
can then either compute their own profits or explore the profit options using the market. The upstream firm has enough information to determine the downstream profits if heshe
wishes, but it requires some calculations.
An interesting issue to consider in these markets is whether the downstream firms are indeed creating a price distortion, the vertical externality. This can be tested by examining
whether the true mean of the actual downstream prices in each period is greater than the mean of what the competitive responses would have been to the upstream prices in each
of the last five periods. A t-test for a difference in means with 12 degrees of freedom was performed on H
: ¯ P
D
= ¯ P
DCR
against H
a
: ¯ P
D
¯ P
DCR
where ¯ P
DCR
is the mean of the competitive responses to the upstream prices in each of the experiments. The only period
in which we cannot reject the hypothesis that these two means are the same is in period thirteen. This supports the presence of a vertical externality in these markets.
Spengler’s assertion is that the vertically integrated solution can be duplicated by in- troducing competition in the downstream market, and that both aggregate profit and con-
sumer surplus will increase because of this. Using a difference of means test, we can reject the hypothesis in each of the last five periods that aggregate profits in the two structures
are equal on average in favor of the hypothesis that aggregate profits are higher in the monopolycompetition markets than in the monopolymonopoly markets. The null hypoth-
esis that consumer surplus is, on average, equal across treatments, can also be rejected in all but one period of the final five periods, in favor of greater consumer surplus in the
monopolycompetition treatment. The fact that the null hypothesis could not be rejected in
9
Possible dependence of tests is recognized again.
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 223
period 13 is due in large part to experiment MM107, where the firms priced low enough to sell 30 units. Not surprisingly then, using the usual measure of consumer plus producer
surplus to measure the efficiency of the markets, in all but one of the last five periods, we can reject the hypothesis that the monopolymonopoly markets are on average as efficient as the
monopolycompetition markets in favor of the hypothesis that the monopolycompetition markets are more efficient. These results strongly support Spengler’s assertion that firms,
consumers, and society as a whole are better off with competition, and therefore, a vertically integrated monopolist rather than two successive monopolists.
In addition, we also find that average final prices are higher in the monopolymonopoly treatments than in the monopolycompetition treatments. H
: ¯ P
MM
= ¯ P
MC
could be rejected in favor of H
a
: ¯ P
MM
¯ P
MC
in each of the last five periods. The difference in quantities sold between treatments is fairly evident just from examining the data, but we can
reject the null hypothesis that the quantities exchanged are equal on average between the two treatments in favor of the alternative hypothesis that the average quantity exchanged in
the monopolycompetition experiments is greater than the average quantity exchanged in the monopolymonopoly experiments in each of the last five periods.
4.2. Examination of individual behavior and coordination To summarize the results discussed so far, there appears to be strong evidence supporting
the Spengler conclusion of a vertical externality when the downstream market is monopo- lized and the argument that the elimination of that externality increases welfare. There are
also several questions involving individual behavior and coordination in these experiments which deserve more detailed attention. For example, how close is the downstream firm to
its best response function, and does it get better at finding this best response over time? Does the downstream firm’s proximity to its best response function affect how close the
upstream firm is to the Nash prediction? How might the upstream firm predict the actions of the downstream firm in order to make its pricing decision? Some models are presented
below which are designed to provide some insight into the answers to these questions.
Once the upstream firm has set a price, the downstream firm has a unique best response. The downstream firm’s best response function is a linear function of the upstream price and
is specified as follows:
10
P
DBR
= 350 + 0.5P
U
In order to determine if downstream prices follow this best response path, a fixed effects model
11
was used to estimate P
Dit
= α
1
D
1it
+ · · · + α
7
D
7it
+ βP
Uit
+ ε
it
, where D
kit
equals 1 for experiment k and 0 otherwise. Results from this regression can be found in Table 2. The joint hypothesis that α
1
= α
2
=· · · = α
7
= 350 and β=0.5 is rejected
12
10
Because of the discreteness of the demand function, when the upstream price ends in a five, the actual best response is 2.5 pesos higher than this. The data was adjusted to reflect this.
11
A random effects model was rejected which is not surprising with only seven individuals.
12
A test for different slope coefficients across experiments in this model was rejected at the 5 significance level.
224 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
Table 2 Regression results
Variable Coefficient
Standard Error Regression results: P
dit
= α
1
D
1it
+ . . . +α
7
D
7it
+ βP
Uit
+ ε
it
D
1
264.567 35.236
D
2
283.200 34.840
D
3
257.762 35.293
D
4
272.798 34.868
D
5
278.369 32.043
D
6
264.934 35.633
D
7
243.465 34.868
P
U
0.707 0.087
N=105; R
2
= 0.4716; F[7,97]=12.37; SSE=73246.0: Durbin–Watson=1.57
Corrected for autocorrelation D
1
274.47 34.698
D
2
293.37 34.380
D
3
268.84 34.916
D
4
281.29 34.258
D
5
288.53 32.001
D
6
276.64 34.755
D
7
253.23 34.337
P
U
0.68 0.084
Rho 0.22
0.096 N=105; R
2
= 0.4684; F[8,96]=10.57; SSE=69885.6; Durbin–Watson=1.8540
Pooled data from first six experiments: Regression results: P
Dt
= α+βP
Ut
+ ε
t
Constant 316.65
37.050 P
U
0.59 0.094
Rho 0.27
0.102 N=90; R
2
= 0.3172; F[2,87]=20.21; SSE=68827.0: Durbin–Watson=1.830
at the 5 level, which on the surface seems to imply a rejection of the theory. There is some evidence of the presence of serial correlation in the data. However, correcting the data for
this still does not prevent H from being rejected. The results from the corrected regression
are also found in Table 2. Closer analysis indicates that rejection of H stems from MM107,
because when tests are conducted on only the first six experiments, we can no longer reject the hypothesis that the intercept is 350 and the slope is 0.5. When only the data from the first
six experiments are used, there is no evidence that individual-specific effects are present, so this test can be conducted on pooled data. Results from this regression can also be found
in Table 2. This indicates that the downstream firm in MM107 behaved in a significantly different manner than the other downstream monopolists. There does appear to be some
evidence that the downstream firms, at least in the first six experiments, are approximating their best response functions.
Another issue that is worth considering is the question of whether the downstream firms are getting better at playing their best strategies over time. This hypothesis was tested by
estimating the following equation |
P
Dit
− P
DBRit
| = α
1
D
1it
+ · · · + α
7
D
7it
+ β
1
D
51it
+ · · · + β
7
D
57it
+ ε
it
,
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 225
Table 3 Regression results: |P
Dit
− P
DBRit
|=α
1
D
1it
+· · · + α
7
D
7it
+ β
1
D
51it
+· · · + β
1
D
57it
+ ε
it
Variable Coefficient
Standard Error D
1
24.000 4.175
D
2
17.000 4.175
D
3
15.000 4.175
D
4
14.500 4.175
D
5
65.000 4.175
D
6
4.500 4.175
D
7
23.000 4.175
D
51
− 15.000
7.232 D
52
5.000 7.232
D
53
− 12.000
7.232 D
54
3.500 7.232
D
55
− 40.000
7.232 D
56
3.500 7.232
D
57
16.000 7.232
N=105; R
2
= 0.6389; F[13,91]=12.39; SSE=15865.0; Durbin–Watson=1.8061
where D
5kit
is a dummy variable that equals 1 if it is one of the last five periods is experiment k and 0 otherwise.
13
Results from this regression can be found in Table 3. The hypothesis that learning is occurring would indicate that the β’s would be negative. β
1
, β
3
, and β
5
were all significantly different from zero β
3
is only significant at the 10 level while the others are significant at the 5 level and negative, while β
2
, β
4
, and β
6
were positive and not significantly different from zero. β
7
was significantly different from 0 and positive, again providing indication that experiment MM107 behaved contrary to the other experiments.
It is clear from the graph of MM107 that the downstream price moves away from the best response in the last four periods in that experiment. β
6
was insignificant because the downstream firm in MM106 was very close to his best response all along and really had very
little learning to do. In summary then, we see some limited evidence, except for MM107, that learning may be occurring in this environment in the downstream market.
Does the upstream price get closer to the Nash prediction of 410 pesos when the down- stream firms get closer to their best response? In order to answer this question, the fixed
effects model below was estimated: |
P
Uit
− 410| = α
1
D
1it
+ · · · + α
7
D
7it
+ β |P
Dit−1
− P
DBRit−1
| + ε
it
. Coefficient estimates and standard errors from this regression can be found in Table 4.
Upstream prices getting closer to the Nash prediction as downstream firms get better at finding their best responses would imply a β0. The hypothesis that β=0 cannot be rejected
in this model.
14
This model provides no evidence that the closeness of downstream price to its best response is significant in determining how close the upstream price is to the Nash
prediction.
13
Pooling the data was inappropriate here because the presence of individual-specific effects could not be rejected.
14
Correcting for the presence of autocorrelation has no effect on this result.
226 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
Table 4 Regression results: |P
Uit
− 410|=α
1
D
1it
+· · · + α
7
D
7it
+ β|P
Dit−1
− P
DBRit−1
|+ε
it
Variable Coefficient
Standard Error D
1
14.353 5.336
D
2
18.701 5.316
D
3
14.364 4.956
D
4
23.381 5.101
D
5
55.069 8.200
D
6
21.204 4.786
D
7
36.065 5.892
|P
Dt−1
− P
DBRt−1
| 0.175
0.122 N=98; R
2
= 0.4762; F[7,90]=11.69; SSE=28325.1; Durbin–Watson=1.3200
The downstream firm has a clear best response in these markets. The upstream firm, however, must predict what the downstream firm’s response will be in order to choose
a ‘best response’. Three models of this predictive process are hypothesized. A myopic prediction occurs when the upstream firm assumes that the downstream firm will post the
same price this period as it did last period. The best response to this prediction is for the upstream firm to post
P
Ut
= α + βP
Ft−1
where α = −100
and β = 1
a A constant markup prediction occurs when the upstream firm predicts that the down-
stream firm will mark the price up this period by the same amount as it did the last period. The best response to this prediction is to post
P
Ut
= α + βP
Dt−1
− P
Ut−1
where α = 455
and β = −0.5.
b An OLS prediction assumes the upstream firm observes the downstream firm’s pricing
responses and estimates a linear function relating that price to the upstream price heshe posted. This estimate is updated after each period. This prediction involves the upstream
firm running the regression P
Dt
= γ +δP
Ut
+ ε
t
each period with all the observations available up to that point in time. Once he has made an estimate of a and b, his best response is to
charge P
Ut
= α + β
1 δ
− η
γ δ
where α = 155, β = 302.5,
and η = −0.5. c
Two separate fixed effects models were run to estimate models a and b.
15
Results from both models can be found in Tables 5 and 6. In both cases, the hypotheses that
the coefficients are equal to their theoretical values are rejected. In addition, the R
2
’s for both models are very low. These are joint tests of the prediction model and whether the
upstream firms respond optimally to their predictions. If the upstream firms are making
15
This method was not applied to model c because model c would require estimating γ and δ in stage 1 and using these estimates as regressors in stage 2. The resulting generated regressors problem would invalidate
standard inference procedures.
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 227
Table 5 Regression results: P
Uit
= α
1
D
1it
+· · · + α
7
D
7it
+ βP
Dit−1
+ ε
it
Variable Coefficient
Standard Error D
1
309.885 50.334
D
2
303.267 51.643
D
3
312.021 49.537
D
4
309.332 50.845
D
5
273.800 48.739
D
6
320.144 50.590
D
7
309.767 48.197
P
Dt−1
0.159 0.091
N=98; R
2
= 0.2142; F[7,90]=3.50; SSE=87342.5; Durbin–Watson=1.9028
either myopic or constant markup predictions of downstream behavior, there is no evi- dence that they are using the best responses to these predictions to make their pricing
decisions. In order to discover if there is any evidence that the upstream firm is using an OLS-type
prediction to choose his price, a test of the equality of means between the actual up- stream prices and the best response prices given OLS predictions was conducted. We
cannot reject the hypothesis that the true means of the two populations are equal in any of the last eight periods, suggesting some evidence that the upstream firms are pricing
on average as if they are making optimal responses to an OLS prediction of downstream behavior.
An alternative way to test these prediction models is to examine which method provides the best forecasts of upstream behavior. Using the last 8 periods of each experiment and
examining mean squared errors, we find that c has the lowest MSE in all experiments but MM103, where b does better. This is to be expected because the OLS prediction
uses two parameters to estimate while the other two prediction methods use only one. Since we can never know what method, if any, upstream firms use to predict downstream
behavior, the best that can be done is to find a method which is consistent with the data. a and b do not seem to be consistent with the data, while there is some evidence that c
is.
Table 6 Regression results: P
Uit
= α
1
D
1it
+· · · + α
7
D
7it
+ βP
Dit−1
− P
Uit−1
+ε
it
Variable Coefficient
Standard Error D
1
389.795 18.748
D
2
384.250 20.868
D
3
390.137 17.958
D
4
389.235 20.058
D
5
349.622 21.684
D
6
400.377 18.639
D
7
386.442 16.618
P
Dt−1
− P
Ut−1
0.044 0.113
N=98; R
2
= 0.1886; F[7,90]=2.99; SSE=89014.8; Durbin–Watson=1.7887
228 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
5. Conclusion
