Collusion with Secret Price Cuts: An Experimental Investigation
Robert M. Feinberg
American University
Christopher M. Snyder
George Washington University
October 12, 2000
Abstract: Theoretical work by Stigler (1964), Green and Porter (1984), and Abreu, Pierce, and
Stachetti (1990) suggests that collusion may be difficult to sustain in a repeated game with secret
price cuts and demand uncertainty. Compared to equilibria in games of perfect information, triggerstrategy equilibria in this context result in lower payoffs because punishments occur along the
equilibrium path. We tested the theory in a series of economic experiments. (A novel aspect of our
design is that players could choose a third action, a punishment action, distinct from collusive and
deviating actions: the punishment action carried an extra cost for both the punishing and punished
players.) Consistent with the theory, treatments with imperfect information were less collusive than
treatments with perfect information. However, in the imperfect-information treatments, players
seemed to settle on the static Nash outcome rather than using trigger strategies. Players did resort to
punishments for undercutting in perfect-information treatments, and this sometimes led to successful
collusion afterward.
JEL Codes: C90, L13, C73, D81
Permanent address information for Feinberg: Department of Economics, American University, 4400 Massachusetts
Avenue N.W., Washington DC 20016, tel. (202) 885-3788, fax. (202) 885-3790, email feinber@american.edu. Current
address (while on leave for the 2000-2001 academic year): Program Director for Economics, National Science
Foundation, 4201 Wilson Boulevard, Room 995, Arlington, VA 22230, tel. (703) 292-7267, fax. (703) 292-9068, email
rfeinber@nsf.gov.
Permanent address information for Snyder: Department of Economics, George Washington University, 2201 G Street
N.W., Washington DC 20052, tel. (202) 994-6581, fax. (202) 994-6147, email cmsnyder@gwu.edu. Current address
(while on leave for the 2000-2001 academic year): Department of Economics, M.I.T., 50 Memorial Drive, Building E52391c, Cambridge, MA 02142, tel. (617) 253-5067, fax. (617) 253-1330, email cmsnyder@mit.edu.
We would like to thank Sabine Bendanoun, Yvon Pho, and Tad Reynolds for research assistance and Doug Davis, Tom
Husted, and Roger Sherman for helpful comments. Financial support was provided by a grant from the College of Arts
and Sciences at American University.
1
I. Introduction
Stigler (1964) discussed the inherent difficulty in sustaining collusion in a repeated game in which
the actions of a firm’s rivals (say price or quantity choice) are unobservable. If industry conditions
are perfectly known, it may be possible for a firm to infer rivals’ secret actions from its own sales or
profit. If industry conditions are uncertain, say demand is subject to unobservable negative shocks
periodically, then a firm may not be able to distinguish a rival’s undercutting from an negative
demand shock. In Green and Porter’s (1984) formal model involving repeated quantity competition,
it was shown that firms can sustain some collusion with trigger-price strategies: firms remain in a
collusive phase as long as price remains sufficiently high, entering a finitely-long punishment phase
(involving the static Cournot outcome) if market price falls below a threshold. Abreu, Pierce, and
Stachetti (1990) extended the analysis to consider optimal trigger strategies.
In this paper, we use experimental methods to shed light on the practical relevance of the
theory. Does the combination of secret price cuts together with demand uncertainty reduce players’
ability to collude? Is demand uncertainty alone enough to impair collusion? Do players use trigger
strategies? Of what form and under what circumstances? Though theory suggests trigger strategies
are the best way of sustaining collusion in the presence of imperfect information, there are practical
difficulties in implementing them. As Slade (1992) notes, “…it is important that players know in
advance what constitutes a punishment and understand when they are being punished. When players
cannot meet to discuss their strategies, complex rules, which are difficult to communicate, can be
counter-productive.”
Our paper is related to two strands of the empirical literature. One strand, including, for
2
example, Porter (1983, 1985), Slade (1987, 1992), and Ellison (1994), tests models of dynamic
competition using industry data. Ellison (1994) is closest in spirit to our work. He tests the Green
and Porter (1984) model by examining determinants of Markov transition probabilities between
collusive and competitive phases in the rail transportation industry, cartelized by the Joint Executive
Committee during the late 1800s. Consistent with the theory, he finds that unobservable demand
shocks significantly increase the probability of transitioning from collusive to competitive phases.
The other strand is the experimental literature on collusion in repeated duopoly markets.
Mason and Phillips (1999) study the use of trigger strategies in a perfect-information setting.
Consistent with our findings in our perfect-information benchmark, they find evidence supporting
players’ use of trigger strategies. Strategies with long periods of less intense punishments fit the data
better than short periods of intense punishments. Of course the main difference between our work
and theirs is our central focus on the imperfect-information setting.
Another related literature studies markets in which participants have incomplete information
about the structure of the game. For example, players may not know demand or cost or rival’s
actions spaces. The general finding in this literature (see, e.g., Dolbear et al. (1968) and Benson and
Feinberg (1988)) is that profits are lower in a repeated game with incomplete information compared
to the complete information analogue. Our present study differs from this literature in that we are
interested in a setting with complete information about the structure of the game but imperfect
information about demand shocks and rival’s actions.
There is a series of papers in the literature studying repeated duopoly markets under imperfect
information. Mason and Phillips (1997) and Cason and Mason (1999) focus on endogenous
information sharing, while the information structure in the market is exogenous in our setting. The
3
closest paper to ours is Holcomb and Nelson (1997). They study a duopoly market with shocks of a
different form: half the time, profits are determined by the quantities chosen by the player and his/her
rival; the other half, a randomly-drawn quantity is substituted for the rival’s choice. The shocks
occur randomly, and players are not informed ex post whether a shock occurred. The authors find
that output is higher on average in the imperfect-information treatment compared to the treatment
without shocks. This result may be due to imperfect information causing a breakdown in collusion,
as the authors contend; it may simply be because the joint-profit-maximizing outputs are in fact
higher in the treatment with imperfect information. In our experimental design, we include a
treatment that involves shocks but perfect information about a rival’s actions so that clearer
inferences can be made. Another difference is that our design is closer to the familiar Green and
Porter (1984) model. In spite of these differences in experimental design, our results are consistent
with Holcomb and Nelson’s (1997) findings, both supporting the conclusion that imperfect
information impairs collusion significantly.
II. Theory
In what follows we summarize Tirole’s (1988) discussion of the Green and Porter (1984) model. The
stage game of the infinitely-repeated game has two firms, i = 1,2, simultaneously choosing prices
pi∈[0, ∞). Firms produce a homogeneous product, splitting demand equally if they charge equal
prices, the low-price firm obtaining all the demand if they charge unequal prices. The firms have a
constant marginal and average cost of production c. Market demand is subject to fluctuations,
equaling D(p) with probability α and zero with probability 1- α. It will be convenient to define the
monopoly price pm ≡ argmaxp [(p-c)D(p)] and monopoly profit πm ≡ maxp [(p-c)D(p)].
4
II.A. Secret Price Cuts First consider the infinitely-repeated version of the above stage game in
which a firm does not observe its rival's past actions directly but can only draw inferences from the
level of its own realized demand. Suppose firms play the following trigger strategy: begin by
charging price p; if own demand is D(p)/2, continue charging p next period and repeat the process; if
own demand drops to zero, enter a price war phase, charging c for T periods before returning to p. In
equilibrium, no firm will undercut the collusive price p, yet there will still be price wars since firms'
demands will be driven to zero by the exogenous demand shock.
Let V+ be the present discounted value of the stream of equilibrium profits earned by a firm
starting in the non-price-war (collusive) phase and V- that earned starting in the first period of the
price-war phase. Assuming that firms have to set price before learning the state of demand, we have
(1)

π
V + = (1 − α ) + δV +  + αδV −
2

(2)
V − = δ TV +
where π ≡ (p-c)D(p).
The maximal collusive profit can be found by solving the constrained optimization problem
(3)
max π ,T
V+
subject to
(4)
V + ≥ (1 − α )(π + δV − ) + αδV −
where the right-hand side of (4) is an upper bound on the present discounted value of deviating from
collusion. By undercutting the collusive price p slightly, the deviator can obtain almost all of the
5
profits π, but this touches off a price war. Equations (1) and (2) can be solved simultaneously and
the results substituted into (3) and (4) to generate the equivalent expression of the problem:
(5)
max π ,T
(1 − α )π
2[1 − (1 − α )δ − αδ T −1 ]
subject to
(6)
2(1 − α )δ − 1 − (1 − 2α )δ T +1 ≥ 0.
It is easy to see that the solution involves the highest value of π possible, namely π∗ = πm, and the
lowest value of T satisfying (6). Treating (6) as an equality and solving yields
(7)
T* =
ln(2(1 − α )δ − 1) − ln(1 − 2α )
−1
ln δ
ignoring the issue that T* must be an integer. (It is easy to take into account the integer problem--simply set T* equal to the least integer greater than or equal to the right-hand side of (7)---but we
ignore it here to simplify subsequent calculations.) Substituting these values of π∗ and T* into the
objective function (5) and simplifying, we obtain the following expression for the maximal collusive
firm profit in expected present value terms:
(8)
V+ =
(1 − 2α )π m
.
2(1 − δ )
II.B. Observable Price Cuts Compare the solution from the previous section to a model that is in
all ways identical except in one respect: a firm can observe its rival's past actions. This allows firms
to avoid costly price wars in equilibrium since firms distinguish between zero demand due to an
exogenous demand shock and zero demand due to rival undercutting. Price wars need only follow
6
undercutting, which can be prevented in equilibrium by the threat of grim-strategy punishments
(marginal cost pricing forever).
The fact that firms must choose prices before the state of demand is realized makes the
calculation of equilibrium nearly identical to the usual case of Bertrand competition without
fluctuating demand. As usual, the monopoly outcome (or any other collusive price) is sustainable for
δ ≥ 1/2; for lower values of δ, the unique equilibrium involves marginal cost pricing. If δ ≥ 1/2, each
firm can earn a present discounted stream of profits
(9)
(1 − α )π m
.
2(1 − δ )
II.C. Comparison
The two cases, secret vs. observable price cuts, lead to quite different
implications. With secret price cuts, price wars must occur in equilibrium, whereas they need not
with observable price cuts. The minimum discount factor necessary to sustain collusion with secret
price cuts, δ ≥ 1/[2(1-α)], is higher than with observable price cuts, δ ≥ 1/2. Comparing expressions
(8) and (9), it is evident that the present discounted value of the stream of maximally collusive
profits is lower with secret than with observable price cuts.
III. Experimental Approach
Our experimental approach involves a discrete version of the game from Section II. Two players in a
market simultaneously choose one of three prices: a “collusive” price C, an “undercutting” price U,
and a “punishment” price P. The resulting payoffs from this symmetric game are given in Table 1.
The novelty of our experimental design is that we are able to maintain a simple choice set, with a
7
small number of actions, and still retain the flavor of the continuous-price model from Section II.
Specifically, by adding a third action (P), undercutting and punishment can potentially be
distinguished, whereas they are convoluted in cruder, two-action setups (such as the prisoners’
dilemma). In the continuous-price model in Section II, too, undercutting is logically distinct from
punishment: the undercutting price is only slightly lower than the collusive price, whereas the
punishment price equals marginal cost.
On February 2, 2000 we conducted two experimental sessions (each lasting about one and a
half hours) with undergraduate participants from American University. Eight students participated in
each session. Students were randomly grouped into duopoly markets (they did not know the identity
of their rival) and given instructions for the initial treatment, which we will refer to as Treatment 1.
In Treatment 1, there were no demand shocks and rival choices were revealed after each period. The
participants were told that the game would be played for eight periods with certainty; thereafter a die
would be rolled to determine whether the game would continue for an additional period, with a 2/3
probability of continuing. The rolling of the die allowed the game to have an uncertain ending in
finite time, effectively simulating a supergame with discount factor δ = 2/3 in the treatment’s latter
stages. (See Feinberg and Husted (1993) for experiments on varying discount factors in a repeated
duopoly setting.) The same two participants played together for the duration of the treatment.
Following the end of Treatment 1 in both sessions, new instructions (for Treatment 2 in one
session and Treatment 3 in the other) were given out, market pairings were reassigned---still
unknown to participants---and the same stage game was played with certainty for 18 periods, with
continuation beyond that point with a 2/3 probability determined by throw of a die. Again, the
pairings were maintained for the duration of the treatment. Treatments 2 and 3 differed from
8
Treatment 1 in two ways. First, in Treatments 2 and 3, participants were only informed about their
own payoffs after each period but not about rival’s actions. Second, in Treatments 2 and 3, negative
demand shocks giving zero payoffs regardless of choices made were imposed in periods 10 and 16.
Participants were instructed at the outset that there would be such shocks roughly 10 to 15 percent of
the time but not which periods they would occur. In Treatment 2, participants were told immediately
after periods 10 and 16 that a negative shock occurred (referred to as “revealed” demand shocks).
Given that participants were informed of their own profits and whether or not a negative demand
shock occurred, in principle each had enough information to deduce whether or not its rival had
deviated from the collusive outcome. In Treatment 3, participants were never informed about the
occurrence of the shock (referred to as “secret” demand shocks). Hence, it was impossible for them
to distinguish undercutting by a rival from an adverse demand shock since both would give the
player zero profit. Of course if a player were to repeatedly earn zero profit after choosing C, it might
begin to believe that it was increasingly unlikely to be due to random demand shocks, but rather due
to undercutting.
Table 2 summarizes the essential characteristics of the various treatments. Treatment 1,
involving full information and no demand shocks, was meant to initiate participants in the structure
and logic of the basic game. The formal test of the theory comes from a comparison of Treatments 2
and 3. In moving from Treatment 2 to 3, the amount of information players have about demand, and
by inference the information they have about their rival’s past actions, is reduced.
The stage game forming the basis of all of our treatments, given in Table 1, has two Nash
equilibria (U,U) and (P,P), though (P,P) is in weakly dominated strategies. One can use arguments
paralleling those in Section II to determine the conditions under which trigger strategies can sustain
9
collusion (both participants playing C each period) in a repeated game. As in Section II, let
α ∈ [0,1) be the probability of the negative demand shock and δ∈ [0,1) be the discount factor.
First consider the case of revealed demand shocks. (Note that by setting α = 0 we can also
nest the case of no demand shocks.) If players use trigger strategies involving reversion to the (U,U)
outcome for T periods, it can be shown that collusion is sustainable for large enough T if and only if
α < 2/3 and δ > 1/(3-3α). It can be checked that these conditions are easily satisfied by the
parameters in our experimental setup since we have δ ≥ 2/3 and either α = 0 (in the absence of
demand shocks) or α ≤ 0.15 (in the presence of demand shocks). For our parameters, it can be
shown that only one period of reversion (T = 1, in essence a “tit for tat” strategy) is required to
sustain collusion, though obviously a grim strategy (involving the threat of reversion until the end of
the game) would also be successful in sustaining collusion. If players use trigger strategies involving
reversion to the (P,P) outcome for T periods, collusion is sustainable under weaker conditions than
with (U,U) reversion, conditions that continue to be satisfied with our parameters, again, even for
only one period of reversion.
Next, consider the case of secret demand shocks. Here, we resorted to numerical methods,
performing a grid search over T to find the first value that makes the collusive profit greater than the
deviating profit. It turns out that only one period of reversion is required to sustain collusion with
trigger strategies, whether the trigger strategies employ (U,U) or (P,P) reversion.
Although in principle collusion can be more difficult to sustain with secret price cuts and
secret demand shocks, the parameters in our experimental setup are such that collusion on (C,C) can
be sustained whether or not there are demand shocks, and whether or not the demand shocks are
secret. Our results will allow us to determine whether the theory captures all relevant considerations,
10
so that collusion is equally easy in all treatments, or whether reducing the amount of information
about rival’s actions and increasing the uncertainty has strategic implications beyond the theory.
IV. Results and Interpretation
The results are presented in Tables 3 through 6. Combining the results for Treatment 1 (the
benchmark treatment with full information about rival’s past actions and no demand shocks) from
both sessions (Tables 3 and 5), an argument can be made that there was some convergence to the
collusive outcome in about half of the markets. As another measure of the degree of collusion in the
treatment, C was played by all participants 62 percent of the time (68 percent in the first session
reported in Table 2 and 52 percent in the second session reported in Table 4).
In Treatment 2 (the treatment with revealed demand shocks), the results for which are
reported in Table 4, there was little decline in the ability to collude. There is a fair degree of
convergence to the collusive outcome in three of the four markets. C was played 68 percent of the
time, the exact fraction these same players played in Treatment 1. Thus we conclude that merely
adding the demand shock, but still allowing players to infer rival’s past actions by informing them of
the demand shock after it occurred, did not reduce players’ ability to collude.
In Treatment 3 (the treatment with secret demand shocks), the results for which are reported
in Table 5, there was a sharp decline in the ability to collude. There appears to have been
convergence to (U,U) in all four markets. C was played only 21 percent of the time, a 31 percent
reduction from Treatment 1 for these same players. Thus we conclude that secret price cuts
combined with secret demand shocks substantially reduces players’ ability to collude, perhaps even
beyond what theory would predict.
11
A comparison of payoffs reinforces this conclusion. In the second session, moving from
Treatment 1 to Treatment 3, caused average per-period, per-player payoffs to decline from 39.5 cents
to 25.8 cents, a decline of a third. In the first session, moving from Treatment 1 to Treatment 2
caused virtually no change in per-period, per-player payoffs (the decline was from 54.5 cents to 54.4
cents to be exact). Though the participants in the second session appear to be less cooperative on
average than those in the first session, considering the within-session variation purges any
participant-specific effects.
An interesting issue regards the use of the punishment action P and the response it engenders
in rivals. We find that players sometimes do resort to the punishment action, if only sparingly (30
times out of a possible 472 choices, i.e., six percent of the time). Most of the time P was chosen by a
firm that had chosen C and had been undercut by a rival in the period prior to triggering the
punishment (23 out of 30, i.e., 77 percent of the time). This suggests students understood the use of
the punishment strategy, consistent with theory. Typically, players reverted to P for only one period
and then returned to C, though there was one case where a player carried out the punishment P for
two periods and one case for three periods. From another perspective, undercutting a rival who
chose C led to an equal chance of the rival’s remaining with C (22 out of 62 cases, or 35 percent of
the time), punishing with U (19 out of 62 cases, or 31 percent of the time), or punishing with P (21
out of 62 cases, or 34 percent of the time). When P is chosen by a player to punish a rival who has
chosen U while the player had chosen C, the rival responds by changing his/her action to C 47
percent of the time. The aggregate statistic masks differences across treatments: in Treatments 1 and
2, the rival responded with a change to C 67 percent of the time while punishment never led a rival to
change from U to C in Treatment 3. Thus, trigger strategies involving the punishment P were
12
effective in restoring some collusion in Treatments 1 and 2, but not in the treatments with fully secret
price cuts (Treatment 3).
On the effects of the demand shocks, the observed shocks in Treatment 2 caused only one out
of 16 actions (six percent) to change. This is consistent with the theory: observable exogenous
shocks should not lead to a breakdown in collusion. The shocks in Treatment 3 also did not lead to a
breakdown in collusion but perhaps for a different reason: there was so little collusion to begin with
in periods preceding the shock that there was little possibility of further breakdown. In Treatment 3,
C had been chosen prior to the shock in only two of the 16 cases.
V. Conclusion
Our experiments showed that demand uncertainty alone had little effect on players’ ability to collude.
Just as they were in the treatment with no demand shocks, trigger strategies were used in the
treatment with revealed demand shocks, often having the effect of making the rival play more
collusively afterward.
The combination of secret demand shocks with secret price cuts was essential to impair
collusion. Theory suggests this should be the case: demand uncertainty is only important if it masks
rival’s secret deviations. What was surprising from our experiments was the extent to which the
combination of secret demand shocks and secret price cuts impaired players’ ability to collude. In
theory, given the parameters of our experimental setup, collusion should be sustainable with trigger
strategies requiring only one period of punishment. Our experimental results suggest that the
combination of secret demand shocks and imperfect information about rival pricing may prevent
players from sustaining collusion at all.
13
Appendix
Instructions for Treatment 1: Thank you for participating in this decision-making experiment.
You will make choices that, together with the choices of another person, will determine the
compensation you will receive; these funds have been provided by a research grant from the College
of Arts and Sciences at American University. It is very important that each of you make your
decisions alone and that you do not communicate with one another.
Before you is a profit table (see Table 1). The choices across the top (“Collusive price”,
“Undercutting price”, “Punishment price”) represent decisions of another firm in a duopoly (twofirm) market; another person in this room (who will not be identified to you) is making decisions for
this other firm. The similar choices down the left side represent your own decisions. A given choice
of the other firm identifies a column in the table and your choice identifies a row. The cell where the
column and the row intersect reveals the profit you will receive for the specific combination of
choices.
To make sure you understand the procedure, suppose both you and the other person choose
“Collusive price” (C); in this case you will each receive 75 cents in this period. If you choose
“Undercutting price” (U) while the other chooses “Collusive price”, you will earn one dollar in this
period (while the other person will receive nothing). However, as is likely to be the case in the next
period if you do this, if the other person also chooses “Undercutting price” you will each receive just
25 cents. There is also the possibility of choosing what is called a “Punishment price” (P): in this
case the other person will always receive nothing regardless of his or her choice; however you will
also receive nothing in this period. Choosing a “Punishment price” may remind the other person,
though, of the benefits of staying with a collusive price.
You will also find a decision sheet in front of you. Initially you will record your choice of
“Collusive price”, “Undercutting price”, or “Punishment price” (C, U, or P, respectively) on the first
line (“period 1") under the column headed “your decision”. We will then collect your sheet, record
the other firm’s choice (under the column headed “other’s decision”), determine your profit for that
period, and then return the decision sheet to you. You will then make a choice for the next period.
Starting after the 8th period, we will roll a standard die after each period, and if a “one” or a “six”
shows up we will terminate this experiment, and will then give you different instructions.
Instructions for Treatment 2: Now you will be making the same choices as before; however the
person making decisions for the other firm will be different from in the previous experiment. The
profit table is the same. However, you will no longer receive information on what price decisions
the other person is making. In addition, we have randomly pre-selected some periods in which your
profit will be zero regardless of what decisions you and the other firm make; we will tell you after
these periods occur (they will occur roughly 10 percent of the time).
You will find a new decision sheet in front of you. Again, initially you will record your
choice of “Collusive price”, “Undercutting price”, or “Punishment price” (C, U, or P) on the first line
(“period 1”) under the column headed “your decision”. We will then collect your sheet and record
your profit for that period. Your profit will be based on both your and the other firm’s choice but
you will not be informed of what price the other firm has chosen (remember that in the zero-profit
periods referred to above, profits will be zero regardless of what choices are made). We will return
the decision sheet to you, and you will then make a choice for the next period. Starting after the 18th
14
period, we will roll a standard die after each period, and if a “one” or a “six” shows up we will
terminate this part of the experiment.
Instructions for Treatment 3: Now you will be making the same choices as before; however the
person making decisions for the other firm will be different from in the previous experiment. The
profit table is the same. However, you will no longer receive information on what price decisions
the other person is making. In addition, we have randomly pre-selected some periods in which your
profit will be zero regardless of what decisions you and the other firm make (you will not be told
either before or after which periods these are); these will occur roughly 10 percent of the time.
You will find a new decision sheet in front of you. Again, initially you will record your
choice of “Collusive price”, “Undercutting price”, or “Punishment price” (C, U, or P) on the first line
(“period 1”) under the column headed “your decision”. We will then collect your sheet and record
your profit for that period. Your profit will be based on both your and the other firm’s choice--remembering also there will be the occasional pre-selected periods with zero profits---but you will
not be informed of what price the other firm has chosen. We will return the decision sheet to you,
and you will then make a choice for the next period. Starting after the 18th period, we will roll a
standard die after each period, and if a “one” or a “six” shows up we will terminate this part of the
experiment.
15
References
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with Imperfect Monitoring,” Econometrica 58: 1041-1064.
Benson, B.L., and R. M. Feinberg. (1988) “An Experimental Investigation of Equilibria Impacts of
Information,” Southern Economic Journal 54: 546-561.
Cason, T. N. and C. F. Mason. (1999) “Information Sharing and Tacit Collusion in Laboratory
Duopoly Markets,” Economic Inquiry 37: 258-281.
Dolbear, F. T., L. B. Lave, G. Bowman, A. Lieberman, E. Prescott, F. Rueter, and R. Sherman.
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of Economics 25: 37-57.
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Collusive Behavior in Duopoly Markets,” Journal of Industrial Economics 41: 153-160.
Green, E. J. and R. H. Porter. (1984) “Noncooperative Collusion Under Imperfect Price
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16
Supergame Strategies,” Review of Economic Studies 59: 257-276.
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17
Table 1: Profit Table (in Cents)
Other's choices
Collusive
price (C )
Your
choices
Undercutting Punishment
price (U )
price (P )
Collusive
price (C )
75
0
0
Undercutting
price (U )
100
25
0
Punishment
price (P )
0
0
0
Table 2: Summary of Treatments
Informed of rival's past action?
Demand
Shocks
No
Yes
No

Treatment 1
Yes,
revealed
Treatment 2

Yes, not
revealed
Treatment 3

Table 3: Results for First Session, Treatment 1
Period
Market Player
1
2
3
4
5
6
7
8
9
10
11
A
1.1
1.5
U
C
C
U
P
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
B
1.2
1.6
U
C
U
U
U
U
P
U
U
U
C
P
C
C
U
C
U
P
C
U
C
C
C
1.3
1.7
C
C
U
U
C
C
C
C
C
C
C
C
U
C
U
P
C
C
C
C
U
C
D
1.4
1.8
C
C
U
C
C
C
U
C
U
C
U
P
C
C
C
C
C
C
C
C
C
C
Notes: Treatment 1 involves full information about a rival's past actions and no demand
shocks. C stands for "Collusive price", U for "Undercutting price", and P for "Punishment
price". Game lasted until period 8 with certainty; die roll resulted in three additional periods,
9 through 11. In the naming convention for the players, the number before the decimal
represents the session and the number after the decimal represents the particular player. The
players here are the same as in Table 4 but are playing with different rivals.
Table 4: Results for First Session, Treatment 2
Period
Market Player
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
A
1.1
1.8
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
B
1.2
1.5
C
U
U
U
U
C
P
C
C
U
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
1.3
1.6
C
U
C
C
U
C
U
U
U
C
U
P
U
C
U
U
U
U
U
U
U
U
U
P
U
C
U
C
U
U
U
U
U
U
U
U
U
U
U
U
U
U
D
1.4
1.7
U
U
U
C
C
P
C
U
P
U
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
U
U
U
U
C
U
C
U
U
Notes: Treatment 2 involves demand shocks about which players are informed after they occur and no information about rival's past actions (but a rival's
actions can be inferred given information about demand shocks) . Demand shocks occurred in shaded periods (10 and 16). C stands for "Collusive price",
U for "Undercutting price", and P for "Punishment price". Game lasted until period 18 with certainty; die roll resulted in three additional periods, 19
through 21. In the naming convention for the players, the number before the decimal represents the session and the number after the decimal represents the
particular player. The players here are the same as in Table 3 but are playing with different rivals.
Table 5: Results for Second Session, Treatment 1
Period
Market Player
1
2
3
4
5
6
7
8
A
2.1
2.5
C
U
C
C
C
U
U
U
C
U
C
C
C
U
P
C
B
2.2
2.6
C
C
C
U
P
C
C
U
P
C
P
U
P
C
U
C
C
2.3
2.7
U
C
U
P
U
C
C
P
C
C
C
C
C
C
U
C
D
2.4
2.8
U
C
U
C
U
C
U
C
U
C
U
P
U
C
U
P
Notes: Treatment 1 involves full information about a rival's past actions
and no demand shocks. C stands for "Collusive price", U for
"Undercutting price", and P for "Punishment price". Game lasted until
period 8 with certainty; die roll resulted in game ending immediately
thereafter. In the naming convention for the players, the number before
the decimal represents the session and the number after the decimal
represents the particular player. The players here are the same as in
Table 6 but are playing with different rivals.
Table 6: Results for Second Session, Treatment 3
Period
Market Player
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
A
2.1
2.8
C
C
C
U
C
U
C
U
C
C
C
U
C
U
U
U
U
U
U
U
U
C
C
U
U
U
C
U
P
U
P
U
U
U
P
U
U
U
B
2.2
2.5
C
U
C
U
U
U
C
U
U
U
U
U
U
U
P
C
C
U
P
C
U
U
U
U
U
U
U
C
C
U
U
C
U
U
U
U
U
U
C
2.3
2.6
U
C
U
C
U
U
U
C
U
C
U
U
U
U
U
U
P
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
U
D
2.4
2.7
U
C
U
C
U
P
U
C
U
P
U
C
U
P
U
C
U
U
U
U
U
C
U
U
U
P
U
C
U
U
U
U
U
C
U
U
U
U
Notes: Treatment 3 involves secret, random demand shocks and no information about rival's past actions. Demand shocks occurred in shaded
periods (10 and 16). C stands for "Collusive price", U for "Undercutting price", and P for "Punishment price". Game lasted until period 18 with
certainty; die roll resulted in one additional period, 19. In the naming convention for the players, the number before the decimal represents the
session and the number after the decimal represents the particular player. The players here are the same as in Table 5 but are playing with
different rivals.