150 A. Muren J. of Economic Behavior Org. 41 2000 147–157
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 32 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: Q
c
= n
n + 1
Q
∗
where n is the number of sellers and Q
∗
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
4
English translations of the instructions are available from the author.
A. Muren J. of Economic Behavior Org. 41 2000 147–157 151
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 form P Q = 38 − Q
− i
− q
i
, where Q
− i
is the combined capacity of the two other sellers and q
i
is firm i’s sales. The high-price firm will set its price to maximize revenue, i.e. at p
i
= 38 − Q
− i
2 if its capacity is large enough for this. If not, that is if q
i
is 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. q
i
≤ [38 − q
1
+ q
2
+ q
3
− q
i
]2 for all firms i. 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 of q
1
, q
2
and q
3
that we are considering, note that e.g. values at or below q
1
= 10, q
2
= q
3
= 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
