Two are few and four are many: number effects in experimental oligopolies

Journal of Economic Behavior & Organization
Vol. 53 (2004) 435–446
Two are few and four are many:
number effects in experimental oligopolies
Steffen Huck a, Hans-Theo Normann b, Jörg Oechssler c,?
a Department of Economics, University College London & ELSE, London, UK
b Department of Economics, Royal Holloway, London, UK
c Department of Economics, University of Bonn, Adenauerallee 24, 53113 Bonn, Germany
Received 12 July 2001; received in revised form 20 February 2002; accepted 30 October 2002
Abstract
In this paper we investigate how the competitiveness of Cournot markets varies with the number
of ?rms in an industry. We review previous Cournot experiments in the literature. Additionally, we
conduct a new series of experiments studying oligopolies with two, three, four, and ?ve ?rms in
a uni?ed frame. With two ?rms we ?nd some collusion. Three-?rm oligopolies tend to produce
outputs at the Nash level. Markets with four or ?ve ?rms are never collusive and typically settle at
or above the Cournot outcome. Some of those markets are actually quite competitive with outputs
close to the Walrasian outcome.
© 2003 Elsevier B.V. All rights reserved.
JEL classi?cation: L13; C92; C72
Keywords: Cournot oligopoly; Experiments; Collusion
1. Introduction
Since Fouraker and Siegel’s (1963) pioneering Cournot experiments, a considerable num-
ber of studies has deepened our understanding of the Cournot trading institution. For ex-
ample, various laboratory experiments investigated the impact of communication between
rivals, the provision of detailed information about ?rms’ actions and payoffs, and the role
of cost asymmetries—institutional details that might be of great importance for antitrust
policy issues. However, it seems surprising that up to now little is known about how the
number of ?rms affects competition. This paper tries to ?ll this gap.
? Corresponding author. Tel.: +49-228-73-9284; fax: +49-228-73-1785.
E-mail address: oechssler@uni-bonn.de (J. Oechssler).
0167-2681/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.jebo.2002.10.002

---

436
S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
We analyze how the number of ?rms affects the level of competition (relative to the
equilibrium prediction). For this purpose, we review the scattered evidence of previous
Cournot experiments as well as present new data. Furthermore, while most previous studies
used only an economic frame for the experiments, we introduce a control treatment with a
neutral frame.
In a classic paper, Selten (1973) argues that “four are few and six are many”, referring to
the number of ?rms that separates a small group of ?rms from a large one. This distinction
between small and large groups expresses the general belief (see, e.g., Chamberlin, 1933)
that cooperative behavior should be expected in small groups, whereas in large groups
non-cooperative (Nash equilibrium) behavior should prevail.1 While Selten’s prediction
depends on speci?c institutional assumptions regarding commitment possibilities in a quota
cartel, we want to test the general notion that a “large” group need not be very large indeed.
There are several papers pertaining to market structure and the competitiveness of out-
comes in posted-offer markets (see Holt, 1985, for a survey). In posted-offer experiments,
a key question is for how many ?rms the market price is above marginal costs. For ex-
ample, Issac and Reynolds (1989) analyze posted-offer markets with two and with four
?rms and conclude that four ?rms may be suf?cient for competitive performance. In the
Cournot model, the price–cost margin depends directly on the number of ?rms,2 a feature
that explains the dominance of the Cournot model in theoretical merger analysis. There-
fore, a systematic analysis of number effects in experimental Cournot oligopoly seems
promising.3
To this effect, we summarize the evidence of previous Cournot experiments in a meta-
analysis. A general problem with this approach is, however, that the existing experiments
differ with respect to numerous design features. Therefore, we supplement the meta-analysis
by a set of experiments that, for the ?rst time, compare experimental Cournot oligopolies in
a uni?ed frame for two, three, four, and ?ve ?rms. For both the meta-analysis and our own
data, we introduce a measure that relates actual total output to total output in equilibrium
and ?nd that it is increasing in the number of ?rms. More speci?cally, we conclude that
“many” may be even less than Selten suggested, namely about four ?rms.
As mentioned above, the number of ?rms is not the only factor affecting competition in
experimental markets. This implies that there exists no unique number of ?rms that deter-
mines a de?nite borderline between non-cooperative and collusive4 markets irrespective of
all institutional and structural details of the experimental markets. We will review this ex-
perimental research and summarize the impact other factors have on collusion in Section 2.
Section 3 presents the meta-analysis of the impact of the number of ?rms on competition.
Section 4 introduces our own experimental design and presents our data. In Section 5 we
present data from control treatments with a neutral frame. Section 5 concludes.
1 The notion that cooperation is harder to sustain as the number of ?rms grows larger is also supported by
repeated game arguments without, however, giving a speci?c critical number of ?rms.
2 In posted-offer markets, the market price may also directly depend on the number of competitiors if ?rms play
a mixed strategy equilibrium. However, the experimental evidence does not support the hypothesis that subjects
mix over prices (see Brown-Kruse et al., 1994).
3 A related study with differentiated Bertrand competition is by Dolbear et al. (1968), and one with homogenous
Bertrand competition is by Dufwenberg and Gneezy (2000).
4 We refer to all markets with prices above Nash prices as “collusive”.

---

S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
437
2. Factors facilitating collusion or competition
In this section, we discuss various factors that are known to affect competition and
collusion in experimental markets. With two exceptions, we restrict ourselves to evidence
from Cournot markets.
Folk theorem type results show that, strictly speaking, collusive behavior is only sus-
tainable when the Cournot stage game is repeated in?nitely (or inde?nitely) often and
the discount factor (the continuation probability) is suf?ciently high. Feinberg and Husted
(1993) tested this prediction by running Cournot sessions with high and low continuation
probabilities. Collusion was a subgame perfect Nash equilibrium only with the high proba-
bility, and the results show that a low probability, indeed, reduced the instances of successful
collusion.
In experimental praxis, an in?nite number of periods is not required to make cooperation
possible (often a few periods seem suf?cient). Thus, it makes sense to ask what other factors
facilitate collusion given an experiment of ?nite length. When subjects are randomly re-
matched with different subjects every period, obtaining tacit collusion through rewards and
punishments seems dif?cult. It is thus not surprising that (Holt, 1985) and Huck et al. (2001)
?nd that collusion occurs only when subjects are matched in ?xed groups for the entire exper-
iment. With random matching, there are few attempts to collude and virtually no successful
ones. As a result, with random matching the Cournot–Nash solution is a good prediction.
A second well-known factor facilitating collusion are pre-play communication and an-
nouncements. While this has not been investigated for Cournot markets, the effect is well
established for other experimental market institutions. For example, Davis and Holt (1990)
and Cason and Davis (1995) show that non-binding price announcements in posted-offer
triopolies lead to higher prices. In differentiated Bertrand oligopoly markets, Harstad et al.
(1998) found the same result. Even though these announcements are cheap talk, they render
markets signi?cantly more collusive.
In contrast to the pre-play announcements, the publication of actions and pro?ts after
each round makes markets more competitive. This effect was ?rst found by Fouraker and
Siegel who had two Cournot oligopoly treatments labelled as “complete” and “incomplete”
information. With “incomplete” information, only an aggregate measure of competition
was provided to subjects in each period (price and aggregate output). With “complete”
information, individual outputs and pro?ts were given. It turned out that this made markets
more competitive.
In Huck et al. (1999, 2000a) these results were con?rmed in various environments:
more information about competitors’ actions and pro?ts seems to increase competition.
Furthermore, in Huck et al. (1999) it is shown that more information about the market (in
the form of demand and cost functions, which might be provided in various forms) decreases
competition and reduces the variability of actions.
What is the impact of experience on market outcomes in experiments? While there is
no evidence on this reported for Cournot markets, Benson and Faminow (1988) show that,
in posted-price markets with differentiated products, experience plays a signi?cant role in
achieving equilibria predicted by tacit collusion. Even though the sessions with experi-
enced subjects were scheduled one month after the initial sessions, experience signi?cantly
increased prices.

---

438
S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
Most Cournot experiments involve symmetric ?rms. Deviating from this, Mason et al.
(1991, 1992) ran sessions with asymmetric Cournot duopolies and found that outputs be-
come signi?cantly higher with asymmetric cost as compared to the symmetric control. It
appears that cost asymmetries not only reduce collusion in the sense that there are fewer
successful attempts to reduce outputs, but also that outputs are pushed even above the
static Nash equilibrium value. Rassenti et al. (2000) conducted ?ve-?rm oligopolies with
asymmetric cost and report failures of the Nash prediction at the ?rm level. Play was only
consistent with the Nash prediction at the industry level.
Finally, Mason et al. (1991) investigate whether or not gender affects choice behavior in
Cournot duopolies. They report that women initially tend to be more cooperative. But these
differences vanish later on during the game.
Summary 1. Factors reducing competition in laboratory markets are repeated interaction
(in particular in combination with high discount factors), pre-play communication, and
experience. Information about market parameters and cost symmetries reduce the variability
of outputs and are conducive to Nash equilibrium play. Information about rivals’ actions
and pro?ts increases competition.
3. A meta-analysis of n-?rm Cournot experiments
We now proceed to compare several Cournot experiments with respect to “number
effects”.5 To facilitate this comparison, we select treatments that share the following fea-
tures: (i) ?xed groups of ?rms interact repeatedly over several periods; (ii) the design does
not allow for communication; (iii) feedback after each round is such that subjects receive
only aggregate information about the behavior of other ?rms; (iv) there is complete infor-
mation about the own payoff function; (v) ?rms are symmetric; (vi) there is no discounting;
(vii) products are homogeneous;6 and (viii) framing of the experiments is economic rather
than neutral. In Table 1 we list all experiments with these properties.7 Note that most of
these properties are conducive to Cournot–Nash outcomes.8
Despite these similarities, the experiments in Table 1 differ with respect to several aspects.
With two exceptions, payoffs in the experiments were based on linear demand and cost
functions.9 The exceptions are Feinberg and Husted (1993) and Offerman et al. (2002).10
In most cases, information about the model was given indirectly by providing payoff tables.
Deviating from this, Binger et al. (1990) and Offerman et al. (2002) gave demand and
5 We are grateful to several colleagues for providing unpublished data.
6 For experiments with differentiated Cournot competition, see Davis and Wilson (2000) and Huck et al. (2000a).
7 We include the experiment of Rassenti et al. (2000) with asymmetric costs because there is only one other
experiment with ?ve ?rms.
8 Clearly, property (i) is not, but as there is no rematching in real industries it seems to be the more important
case.
9 In Mason et al. (1991) there is a ?xed cost. In Holt (1985), Bosch-Domenech and Vriend (2003) and Huck
et al. (1999), there are negative ?xed costs. In Binger et al. (1990), there is an intial capital endowment.
10 In Feinberg and Husted, the functional forms of the model are not given. Inspecting the payoff table, it appears
that they are not derived from linear demand and cost.

---

S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
439
Table 1
Previous Cournot experiments
Study
n
Treatment
Periodsa
¯Q
QN
r
Binger et al. (1990)
2
2 w/o comm.
4–43
40.61
40
1.02
Bosch-Domenech and Vriend
2
Easy
1–23
37
40
0.93
(2003)
Holt (1985)
2
First market
1–13
16.05
16
1.00
Holt (1985)
2
Second market
1–9
15.92
16
1.00
Feinberg and Husted (1993)
2
No discounting
5–11
30.89
34
0.91
Mason et al. (1991)
2
All subjects
25
21.56
32
0.67
Mason et al. (1992)
2
LL/HH
1–35
57.6/50.4
64/56
0.90
Mason and Phillips (1997)
2
LL/HH
1–35
54.02/47.23
64/56
0.84
Huck et al. (2001)
2
Fixed matching
1–10
7.64
8
0.95
Fouraker and Siegel (1963)
2
Incompl. info.
21
41.8
40
1.05
Offermann et al. (1997)
3
Q
1–100
233.52
243
0.96
Bosch-Domenech and Vriend
3
Easy
1–23
69.6
66
1.05
(2003)
Fouraker and Siegel (1963)
3
Incompl. info.
21
48.1
45
1.07
Davis et al. (1999)
3
UC and AC
1–45
12.33
12
1.03
Beil (1988)
4
NM
1–20
35.47
36
0.99
Huck et al. (2002)
4
A
20–40
83.98
79.2
1.06
Huck et al. (1999)
4
Best
20–40
82.56
79.2
1.04
Rassenti et al. (2000)
5
75-no-showb
50–75
454.6
425
1.07
Binger et al. (1990)
5
5 w/o comm.
4–43
51.53
50
1.03
a Periods used to compute the averages.
b Asymmetric costs.
cost schedules to the subjects, and Huck et al. (1999, 2000a, 2002) provided a “pro?t
calculator”.11
The size of the strategy space ranges from 2 (Feinberg and Husted) to 85 (Offerman et al.)
output levels. In Huck et al. (1999, 2000a, 2002) a continuous action space is approximated
by allowing for two decimal points when entering quantities between 0 and 100. The number
of repetitions is between 9 (Holt, 1985) and 100 (Offerman et al.). There are three types
of rules for the termination of the experiment. Offerman et al. (2002), Bosch-Domenech
and Vriend (2003), Huck et al. (1999, 2000a, 2001, 2002) have a publicly known ?nite
number of periods. In Fouraker and Siegel (1963), Beil (1988), Mason et al. (1991, 1992),
Binger et al. (1990), Mason and Phillips (1997), Davis et al. (1999) and Rassenti et al.
(2000) the number of periods was not given to subjects in advance. A random end with a
publicly known termination rule and with an observable randomization device was used in
Holt (1985) and Feinberg and Husted (1993).12
We compare the results of all those studies with respect to the ratio of average total
quantity in the market to the total quantity predicted by the Cournot–Nash equilibrium,
r := ¯Q/QN. Since in many cases complete data was not available, we had to refer to the
published averages to compute r, which implies that different periods of the game had to be
11 For a description, see Section 4.
12 Concerning the pros and cons of these termination rules, see Holt (1985) and Selten et al. (1997).

---

440
S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
used (see the column “periods” in Table 1).13 We are interested in how r varies with respect
to the number of ?rms in a market. A clear trend emerges: r is increasing with the number
of ?rms. While the average ratio for duopolies is 0.927, it becomes 1.027 for three ?rms,
1.029 for four ?rms and 1.050 for ?ve ?rms. Pearson’s correlation coef?cient between r
and n, the number of ?rms, is 0.51 and is signi?cant at the 5 percent level.
Summary 2. Previous studies indicate that collusion sometimes occurs in duopolies and
is very rare in markets with more than two ?rms. On average, total outputs in markets
with more than two ?rms slightly exceed the Cournot prediction. There is a weak trend
suggesting that this effect may become stronger as the number of ?rms increases.
4. Cournot oligopolies in a uni?ed frame
In this section we introduce a new experiment that allows testing for number effects
in oligopoly in a uni?ed economic frame. In Section 5 we describe treatments with a
neutral frame. In a series of computerized14 experiments, we studied linear symmetric
n-?rm Cournot oligopoly markets. We decided to design the experiment such that it is
best compatible with the studies reviewed in Section 3 by satisfying properties (i)–
(viii).
Common to all markets were the following demand and cost functions. The demand side
of the market was modeled with the computer buying all supplied units according to the
inverse demand function
p = max{100 ? Q, 0}
with Q =
n
i= q
1
i denoting total quantity. The cost function for each seller was simply
C(qi) = qi,
that is, constant marginal cost was equal to one.
It is straightforward to derive the Nash equilibrium for this market. The individual equi-
librium output is
qNi = 99
n + 1
and the equilibrium pro?t is ?N
i = (qN
i )2. Total equilibrium outputs QN = 99n/(n + 1)
are shown in Table 2. Alternative benchmark outcomes are the symmetric collusive output,
which is qCi = 99/(2n) for an individual ?rm and QC = 49.5 in total, and the competitive
(or rivalistic) outcome where price equals marginal cost at qRi = 99/n and QR = 99,
respectively.
Subjects could choose quantities from a ?nite grid between 0 and 100 with 0.01 as
the smallest step. The number of periods was 25 in all markets, and this was commonly
known.
13 However, in most experiments where complete data is available, no clear time trend emerges.
14 We use the software toolbox “Z-Tree”, developed by Fischbacher (1999).

---

S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
441
Table 2
Average total quantities
Number of ?rms
QN
¯Q
¯
1–25
r1–25
Q17–25
r17–25
2
66.00
59.36 (3.76)
0.89
60.44 (7.05)
0.91
3
74.25
73.47 (6.85)
0.99
72.59 (4.53)
0.98
4
79.20
77.26 (7.75)
0.98
80.67 (4.85)
1.02
5
82.50
86.21 (7.11)
1.05
88.43 (8.80)
1.07
Standard deviations of ¯
Q across groups in parenthesis.
Subjects had information about demand and cost conditions to calculate best replies to
the quantities of the other ?rms. This information was provided verbally and in the form of a
“pro?t calculator”. When fed with data regarding the other ?rms (total quantities of the other
?rms), the calculator allowed subjects to try out the consequences of own actions. After
each period, subjects were informed about their own quantity and pro?t and the aggregate
quantity their competitors produced.15
For each number of ?rms, we conducted six markets. The six duopolies were run in one
session. For the three and four-?rm markets, we had two sessions, and for the ?ve-?rm
oligopolies, there were three sessions.16 Subjects were randomly allocated to computer
terminals in the lab such that they could not infer with whom they would interact. The 84
subjects for this experiment were recruited via telephone and email at Humboldt University,
Berlin. No subject participated in more than one session nor had any subject previous
experience with market experiments.
Subjects were paid according to their total pro?t in the ?ctitious currency ECU earned in
the 25 periods. We varied the exchange rates into DM such that, depending on the number
of ?rms, subjects would have made identical earnings at Nash equilibrium play. For all
subjects there was an initial capital of 500 ECU. The average payoff was about DM 22
(Euro 11). Sessions lasted about 45–60 min including instruction time.
Instructions (see Appendix A) were written on paper and distributed in the beginning of
each session. After the instructions were read, we explained the different windows of the
computer screen. When subjects were familiar with both the rules and the handling of the
computer program, we started the ?rst round.
Table 2 and Fig. 1 compare total quantities as implied by the Nash equilibrium prediction.
We report total quantities in the experiment, averaged over all rounds and the ?nal eight
rounds, respectively.17 In all cases average total quantity increases with the number of
?rms. The differences are all signi?cant at the 1 percent level according to a MWU test for
rounds 17–25. For rounds 1–25, the differences between three and two ?rms are positive
15 Note that a pro?t calculator essentially gives the same information as the pro?t tables normally used in Cournot
experiments. With a pro?t table, the necessarily rather coarse discrete action space often leads to multiple Nash
equilibria (Holt, 1985). With a pro?t calculator, a continuous action space can be approximated such that additional
Nash equilibria are arbitrarily close to the prediction.
16 Some of these sessions served as control treatments in an experiment on mergers in Huck et al. (2000b).
17 There is no signi?cant time trend in the data after the ?rst three or four rounds. In a regressions of total
quantities on time the trend variable is not signi?cant for rounds 5–25 in any treatment (markets with three and
?ve ?rms show no time trend even when the ?rst four rounds are included).

---

442
S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
100
90
80
70
60
Mean1-25
50
Mean17-25
40
Nash
30
average quantity
20
10
0
5
4
3
2
Number of firms
Fig. 1. Predictions and average quantities in rounds 1–25 and 17–25.
Table 3
Classi?cation of sessions
n
Nash
Session
1
2
3
4
5
6
2
66.00
53.80 (C)
57.36 (C)
58.44 (N)
60.40 (N)
61.28 (N)
64.86 (N)
3
74.25
63.24 (N)
69.84 (N)
72.48 (N)
74.64 (N)
77.04 (N)
83.56 (N)
4
79.20
72.12 (N)
73.00 (N)
74.24 (N)
75.36 (N)
76.00 (N)
92.82 (R)
5
82.50
76.80 (N)
80.04 (N)
83.52 (N)
89.00 (N)
93.36 (R)
93.96 (R)
Classi?cations: (C)ollusive, (N)ash, (R)ivalistic.
and signi?cant at the 1 percent level and between ?ve and four ?rms at the 5 percent level.
The difference between four and three ?rms is positive but not signi?cant.18
The ratio of actual to predicted total quantities, r, is also increasing with the number of
?rms. Most differences are not signi?cant when n is increased by 1. However, the crucial
difference in r between two and four ?rms (to which our title alludes) is signi?cant at
a 2 percent level of signi?cance for r17–25 and at a 5 percent level for r1–25 (one-sided
MWU tests). Furthermore, Pearson’s correlation coef?cient between r1–25 and n is 0.53
(signi?cant at 1 percent level). Between r17–25 and n it is 0.61 (also signi?cant at 1 percent
level).
Next we classify each individual session according to the degree of competitiveness.
Our measure for this is aggregate output, and we apply Fouraker and Siegel’s classi?cation
scheme by checking which of the three predictions: (C)ollusive, (N)ash, or (R)ivalistic,
the aggregate output is closest to and classify the outcomes accordingly.19 In Table 3, we
rank the six sessions according to their aggregate output. With ?ve ?rms, two sessions
qualify as rivalistic and three as Nash. Also with four ?rms, we ?nd that all sessions qualify
18 This seems to be caused by some very high quantities in rounds 15 and 16 (which appear to be punishment
actions) of the three-?rms treatment.
19 The three predictions refer to QC, QN and QR as derived above.

---

S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
443
either as Nash or as rivalistic. With two ?rms, two out of six sessions are Collusive and the
remaining are classi?ed as Nash.20 Thus, there is clear evidence that there is a qualitative
difference between two and four or more ?rms. Only with three ?rms, all sessions classify as
Nash.
Summary 3. In our experiments with a uni?ed economic frame, we ?nd that collusion
sometimes occurs with two ?rms. For three-?rm oligopolies Nash equilibrium seems to be
a good predictor. Markets with four or more ?rms are never collusive and typically settle
around the Cournot outcome while some of them are very competitive with outputs close to
the Walrasian outcome. Overall, the ratio of actual and predicted total output is signi?cantly
increasing with the number of ?rms.
5. A neutral frame
Most Cournot experiments so far were conducted with an economic frame; that is, labels
such as “?rms”, “market”, and “price” were used in the instructions. In our view this is
sensible since the purpose of the experiments is not to test some abstract game theoretic
concept but rather a speci?c economic institution. Nevertheless, in terms of experimental
methodology it may be interesting to know whether an economic and a neutral frame
produces different results. For example, the ultimatum game is equivalent to a posted-offer
market with a single seller and a single buyer. In the ?rst case, labelling is neutral; in the
second, it is economic. For the posted-offer institution, Hoffman et al. (1994) and Franciosi
et al. (1995) have compared economic versus neutral labelling. For the Cournot market
institution, this has so far not been done. Thus, in this section we provide additional data
from Cournot experiments with a neutral frame with two and ?ve participants.
The functional forms, and therefore the predictions of these sessions, are completely
identical to those above. In the instructions and on the computer screens, we did not use any
economic labelling. Rather than “?rms” we spoke of “participants”, and instead of “output”,
subjects had to choose a “number”. The relation between aggregate output and price was
described as follows. “The chosen numbers determine what you earn in each round. More
speci?cally, we will multiply the number you have chosen (X) with some other number (Y ),
and this product (X × Y ) will determine your earnings. The following important rule holds.
The larger the sum of all ?ve numbers chosen, the smaller the second number Y . Moreover,
Y will be ?1 from a certain sum upwards and you will make a loss if Y is below 0”.
For both of these neutral treatments we had six groups of subjects, so another 42 sub-
jects participated here. The sessions were conducted at Royal Holloway, London. Average
payments were 11.55 pounds, including a show-up fee of 5 pounds.
In games with ?ve participants, average outputs are 84.86 (4.14) for periods 1–25, and
81.32 (3.48) for periods 17–25.21 These values are smaller than those with economic
frame but not signi?cantly different from them according to MWU tests at all conventional
20 For n = 2, the mean of the second and the third session are almost equidistant from Nash and collusion. Given
some variability within a session, both classi?cations seem plausible. Also, for n = 5, session 4 could plausibly
be classi?ed as rivalistic.
21 Standard deviation across groups in parenthesis.

---

444
S. Huck et al. / J. of Economic Behavior & Org. 53 (2004) 435–446
signi?cance levels. In games with two participants, average outputs are 64.85 (4.18) for
periods 1–25 and 65.86 (0.75) for periods 17–25, very close to the Nash output. These
averages are signi?cantly larger than those with an economic frame (at 5 percent level,
two-sided MWU test). It appears that the neutral frame leads to outcomes closer to the Nash
prediction than experiments with economic frame. In particular, collusive behavior may not
even be feasible with two ?rms.
The latter result seems to be in contrast to those of Hoffman et al. (1994) and Franciosi et al.
(1995) where neutral framing induced more cooperative outcomes. A possible explanation
might be that frames interact with the objective structure of a game. With a neutral frame in
the ultimatum game, it might appear obvious to participants that fairness is the main issue
of the experiment. By contrast, with the economic frame in posted-offer markets, this may
be less obvious. Hence, the economic frame yields outcomes closer to the game theoretic
prediction. In Cournot experiments, a neutral frame might let the game appear to subjects
as a non-trivial computational problem. The economic frame, however, might immediately
induce the idea of collusion. The general conclusion from this is that framing effects are
certainly important, but by no means do neutral frames always imply more cooperative
outcomes.22
Summary 4. The data from our experiments with neutral frame suggest that collusion
may be dif?cult to achieve even in markets with only two participants. In general, average
quantities are closer to the Cournot prediction than with an economic frame.
6. Conclusion
Number effects seem to play an important role in Cournot oligopolies. The review of
the existing literature on Cournot experiments and our own new experiments suggest that
while ?rms in duopolies sometimes manage to collude, this seems to be dif?cult to achieve
in markets with more ?rms. In fact, total average output often exceeds the Nash prediction
in those markets. Furthermore, the data suggest that these deviations are increasing in the
number of ?rms. Both effects may be of relevance when evaluating the potential effects of
proposed mergers.
Acknowledgements
We are indebted to Wieland Müller and Dirk Engelmann for help in conducting the ex-
periments, and to Claudia Keser for suggesting the title of the paper. Doug Davis and the
Co-Editor David Grether made very useful comments. We are also grateful for ?nancial
support by the Deutsche Forschungsgemeinschaft, grant OE-198/1/1. The ?rst author ac-
knowledges ?nancial support from the Economic and Social Research Council (UK) via
ELSE.
22 But neither does an economic frame exclude signi?cant fairness considerations. For example, Huck et al.
(2001) ?nd a substantial amount of inequality aversion in a Stackelberg duopoly with an economic frame.

---

Document Outline

• Two are few and four are many: number effects in experimental oligopolies
  • Introduction
  • Factors facilitating collusion or competition
  • A meta-analysis of n-firm Cournot experiments
  • Cournot oligopolies in a unified frame
  • A neutral frame
  • Conclusion
  • Acknowledgements
  • Translation of the instructions23
  • References

---