Intertemporal Collusion with Multiperiod Signaling∗
Artie Zillante
IFREE and George Mason University
September 15th , 2004
Abstract
Pre-announcement of product release dates may serve as a practice that facilitates
collusion by allowing firms to schedule their product releases so as not to coincide with
one another. An economic experiment is used to determine if subjects can collude
using these tools. This experiment differs from others in that a multiperiod signalling
mechanism is used as a proxy for costless product release announcements. The primary
finding is that while individual subjects show tendencies towards collusive behavior,
inexperienced groups are still unable to coordinate.
1
Introduction
It has been suggested that certain market practices could lead to collusive-like outcomes
without explicit communication on the part of participating firms. These suggestions date
back at least to the Ethyl case1 , when the Federal Trade Commission (FTC) attempted to
charge the four companies that produced lead-based anti-knock compounds with violating §5
of the Federal Trade Commission Act by engaging in “unfair methods of competition”. This
has become known as the “facilitating practices” doctrine. In the Ethyl case, charges were
based upon industry practices that had existed for three decades, including the use of Most
Favored Nation Clauses by firms and the provision of advance notice of price changes to the
press2 . The current study will focus on the announcement of future product release dates,
which is similar in spirit to announcing price changes. It is believed that the announcement
of future product release dates may lead to firms forming an alternating periods monopoly
(APM).
∗
I would like to thank seminar participants of Florida State University’s experimental economics seminar
and George Mason University’s ICES Lecture Series for helpful comments. Funding for the experiments
was provided by the John and Hallie Quinn Fellowship. As always, I claim responsibility for any remaining
errors.
1
See E.I. duPont de Nemours & Co. v. FTC, 729 F.2 128, 136-37 (2d Cir. 1984).
2
These practices are the explicit focus of the experiments in Grether and Plott [13].
1
The APM is a type of firm behavior whereby firms take turns receiving monopoly profits
by alternating the releases of their products over time3 . Thus, rival firms can avoid direct
competition within a market period by staking claims to release in specific market periods.
Using an algorithm developed in Herings and Peeters [14] to solve stochastic games numerically, Herings, Peeters, and Schinkel [15] shows that the alternating periods monopoly is a
symmetric stationary equilibrium for a duopoly market with identical firms. Furthermore,
in their example they show that regardless of which firm moves first both firms receive higher
profits from the APM than from Cournot competition as long as the discount rate is sufficiently high. Using a stochastic demand environment, Zillante [29] extends their results and
compares the APM to Cournot behavior as well as to another collusive strategy, one in which
each firm produces an equal share of the monopoly quantity each period (ESM). In both
cases conditions are derived under which it is more profitable for firms to use the APM. The
focus in the current study will be to use an economic experiment to determine if the APM
can arise endogenously when paired against the Cournot model, leaving the study of whether
or not the APM will arise when placed against ESM collusion for future investigation. A
non-stochastic version of the model is briefly discussed in section 3.
The decision to test the APM against Cournot behavior is made for a variety of reasons.
First, while a true test of whether individuals would settle on an APM equilibrium over an
ESM equilibrium would necessarily involve the trading of quantities of a good, a basic test
to see if the APM will be chosen over Cournot behavior can be formulated as a coordination
game. This formulation allows testing of the APM versus Cournot without having to
be concerned if a set of subjects will converge to the competitive, Cournot, or monopoly
output levels. As shown in Bru, Gomez, and Ordonez [2], subjects often “converge”4 to
various equilibria in market experiments with quantity as a choice variable. These equilibria
include the competitive outcome, the Cournot outcome, and the ESM outcome mentioned
above. In an attempt to reduce the observed set of equilibria, [2] investigate the effect that
the amount of observable history of actual actions in the experiment has on the equilibria
that arise. They find that the amount of observable history available does not reduce the
types of equilibria observed in these experimental markets. Second, a market experiment
would involve subjects learning about the supply and demand parameters in the experiment.
Since learning the market is a time intensive process, the choice experiment allows for more
repetitions of the stage game by removing this learning process. Finally, a choice experiment
gives the APM its best chance at evolving as there is no other method of collusion that can
evolve. If the APM fails to evolve it is either because subjects understand how the APM
can increase payoffs but still choose not to use it because the costs of forming an APM are
too high or because they do not understand the dynamics that would lead to the APM.
In addition to providing an experimental test of the conditions necessary for the APM to
arise, this paper also extends the literature on how signaling devices may affect the possibility
of collusive (or cooperative) outcomes. Prior experiments show that face-to-face commu3
A parallel can also be drawn between the APM and the repeated auction literature. A bid rotation
scheme involves the formation of a cartel among bidders, with the high-valued (or a pre-determined) bidder
submitting a substantially lower bid than he would in the competitive case, and all other bidders submitting
even lower bids or not partaking in the auction.
4
Whether or not these markets have actually converged to a stable outcome (either theoretically or in the
experiment) is an open question. The fact is that there is no one state to which these markets converge.
2
nication generally leads to a larger degree of collusion, but that one-period ahead signaling
fails to lead to collusive outcomes. This may be due to the personal nature of the communication. However, Dickhaut et al. [7] provide evidence that face-to-face communication is
not necessary to sustain cooperation, as their subjects achieve a great deal of cooperation by
sending text messages and communicating interface-to-interface. This suggests that it is not
the personal relationship developed in the meeting that allows cooperation but some other
factor. It may be that free-form communication (either face-to-face or interface-to-interface)
allows the subjects to inform others of the dynamic aspects of the collusion problem, which
pre-period signaling is unable to accomplish unless subjects are able to recall the signals
used each period. The introduction of multi-period signaling in the current study will allow
subjects to communicate dynamic strategies during each period of play, which may foster
collusive outcomes.
Section 2 of the paper discusses prior results in coordination games and presents some
stylized facts. The section also includes evidence from market experiments that some groups
of subjects choose an APM or a slight variant when given the opportunity to collude. A
brief overview of the conditions derived in [29] that support the APM as an noncooperative
equilibrium strategy is provided in section 3. Section 4 discusses the experimental design
used. Section 5 presents the results of the experiments and section 6 concludes.
2
Prior Experimental Research
There is a vast literature on the effects of communication on coordination (or collusion) in
experimental economics. Papers are categorized into two groups. The first group focuses
on coordination experiments and is used to develop some stylized facts on what should be
expected with different design treatments. The second group consists of market experiments.
Although the market experiment approach is not used, these papers are discussed to provide
evidence that subjects do discover the APM in market experiments.
2.1
Coordination Experiments
One of the earliest uses of experiments involved the repeated Prisoner’s Dilemma. The
goal of the experiments was to determine if subjects could learn to cooperate even though
defection was the Nash equilibrium of the stage game. Since those early experiments the
literature on coordination and cooperation experiments has increased dramatically, as various extensions have been added to the Prisoner’s Dilemma game, as well as coordination
experiments with other popular games.
One set of papers, all featuring a similar experimental design, are based on the market
entry game of Selten and Guth [25]. The number of subjects is usually 20, and the games
are typically structured such that there is a pure strategy Nash equilibrium for some number
c < 20 subjects to enter the market each period, where c represents the market capacity. If
more than c subjects enters the market, then all subjects who enter receive a payoff less than
they would have if they remained out. The value of c is randomly drawn each period. In the
first paper, Sundali, Rapoport, and Seale [27], a treatment with no feedback and a treatment
with feedback were run. In the no feedback treatment they find that there is positive
3
correlation between c and the number of entrants, but no evidence of tacit coordination.
They find similar results for the treatment with feedback. The remaining papers extend the
treatments. Rapoport et al. [22] is primarily interested in testing hypotheses of loss aversion
by allowing for losses as well as gains if subjects remain out of the market. This addition of
losses does little to change the results from the initial paper. Erev and Rapoport [9] adds
information about other players’ payoffs. They find that this information increases entry
slightly, suggesting a relative or peer effect. Rapoport, Seale, and Winter [23] allows players
to enter one of two markets with potentially different capacities or to stay out of the market.
The most recent paper, also by Rapoport, Seale, and Winter [24], adds asymmetric payoffs
to the players, where one player gains a larger amount from entering than another player.
While these asymmetric payoffs should alleviate the coordination problem, it does so only
slightly. The main result gained from this framework is that subjects typically choose close
to the pure strategy single-period Nash equilibrium level of entry but no tacit coordination
seems to evolve.
Multiple experiments attempt to determine how an equilibrium is selected from a set of
equilibria. The results of these experiments show that subjects who participate in the APM
experiments may choose a strategy that has a lower expected payoff but also a lower variance.
Using a stag hunt game where subjects can choose high effort or low effort, Van Huyck,
Battalio, and Beil [28] find that as the number of subjects in a group decreases the payoff
dominant equilibrium (all choose high effort) becomes more likely to emerge. Also, when
there is no harm from choosing high effort it typically emerges in the experiment. However,
when choosing high effort is costly some groups converge towards the secure equilibrium,
which is for each subject to choose low effort. Cooper et al. [4] look for equilibrium
selection in coordination games. By varying the payoffs in off-equilibrium cells of the game
matrix they find that subjects do not always choose the Pareto dominant Nash equilibrium.
Perhaps the most closely related paper to the current study is [7]. A pair of subjects
play a Shapley game, which has no pure strategy Nash equilibrium to the stage game.
While there is a mixed strategy Nash equilibrium to the stage game, the payoffs to the
mixed strategy Nash equilibrium are much lower than those that can be obtained if the
subjects coordinate intertemporally. The authors’ primary treatment is whether or not they
allow interface-to-interface communication between each pair of subjects. In the treatments
with communication, each subject is essentially allowed into a chat room with the other
subject in his pair. Subjects are allowed to discuss any topics, including coordination
and punishment strategies. This interface-to-interface communication greatly increases the
amount of cooperation between subjects. While this is not an unexpected result, it is
important in two respects. First, unlike many of the market experiments discussed in the
following section, the only possible method of coordination is intertemporal. Second, it
is commonly believed that face-to-face communication is needed to establish intertemporal
cooperation schemes in non-market experiments5 . However, it may simply be that allowing
free-form communication of any type, either face-to-face or written, is all that is needed. The
key seems to be that if one person realizes that coordination must occur intertemporally and
can explicitly tell the other person, then coordination becomes more likely.
5
An earlier paper, Brown-Kruse, Cronshaw, and Schenk [1], also uses anonymous freeform communication
in spatial markets and obtains this result.
4
2.2
Market Experiments
Instances of individual behavior in market experiments that are consistent with the APM
can be seen in market experiments as early as Fouraker and Siegel [11]. In one of their
quantity experiments6 , number 10, group number 43 falls into a fairly stable pattern of one
subject producing 25 units and another subject producing 8 units. Although this is more
of a quasi-APM than a true APM, group 43 did almost as well in terms of profits as a
set of subjects (groups 40 and 41 of experiment 10) who were able to produce one-half the
monopoly quantity each period7 . Instances such as these are scattered throughout market
experiments, and can be seen in Davis and Holt [5] and Isaac, Ramey, and Williams [17].
In [5], a group of subjects discuss possible collusive strategies and settle on the APM even
when the payoff stream generated is suboptimal when compared to another collusive strategy
such as ESM8 . A posted-offer market experiment where subjects are allowed to verbally
communicate between rounds of the experiment is used in [17]. The market parameters are
such that there are four sellers in the conspiracy sessions and the monopoly quantity is three
units. One group’s collusive strategy involved rotating the seller who would not sell a unit
each period. Isaac and Smith [19] suggest that firms in their predatory pricing experiment
may follow an APM. However, the de facto equilibrium that emerges from their experiment
is the Stackelburg equilibrium and the necessary conditions derived in [29] are not met for
the large firm.
Other market experiments testing for collusion include Isaac and Plott [16], Isaac and
Walker [20], and Cason and Davis [3]. In [16], a double oral auction mechanism is used.
In each session, either buyers or sellers are given the opportunity to verbally communicate
before each round. In most periods, the group that is allowed to communicate begins
by making collusive offers, but by the end of the period offers tend to move towards the
competitive level. It should be noted that both sides of the experiment used human subjects,
so there may have been some strategic demand withholding by the side of the market that
was not allowed to collude. The effects of verbal communication in both a single unit and
multi-unit first-price sealed-bid auction are tested in [20]. Subjects receive independently
drawn values each period, and are allowed to discuss anything other than the quantitative
value, side payments, or physical threats. While some groups began with a bid rotation
scheme similar to the APM, most groups switched to a scheme where they qualitatively
signalled their value. While both schemes were stable, the qualitative signaling scheme
allows subjects to extract a higher level of monopoly profits each period in a setting where
values are randomly drawn each period. Thus, the switch should not be seen as evidence
against the APM as it is constructed in section 3, as all firms receive the same payoff each
period. One of the treatments in [3] allows nonbinding pre-period price signaling in a multimarket experiment. Sellers in the experiment were able to participate in three markets, with
one of those three markets a low-cost market. Even with the additional of multiple markets,
most “collusive” regimes existed only because one or two sellers tolerated defections by the
6
The exact page number is 271.
The difference is partially due to the fact that group 43, by focusing on a rotation of 25 units and 8
units each period, produced slightly more than the monopoly level of 30 units.
8
The APM is suboptimal to ESM due to increasing marginal costs of production for the experimental
units.
7
5
third group member. The price signals sent did not lead to collusive schemes.
Kwasnica and Sherstyuk [21] find a result similar to the APM in their experimental study
of collusion in multiple unit auctions with complementarities. They find that experimental
subjects are able to collude using bid rotation in two-bidder two-object simultaneous ascending auctions with large complementarities. Bidders would take turns submitting the
minimum bid each round in order to avoid competing away the complementarity. The use
of an APM is similar to using bid rotation to capture complementarities, where the complementarity in the oligopoly can be defined as the amount each period by which one-firm
monopoly profits exceed the sum of monopoly profits when k firms agree to split the market.
Davis and Wilson [6] examine the effects of free-form communication and endogenous costs,
among other variables, in a procurement auction type setting. They find that bid rotation
schemes form in both the communication and non-communication endogenous cost settings,
but that the bids in the communication cost sessions are less correlated with seller costs.
As the experiments show, the APM should be a real concern of antitrust authorities.
Although few of these market experiments are explicitly designed to capture the APM, they
all show evidence that some subjects are considering it as a possible collusive mechanism.
3
Overview of APM Theory
Zillante [29] relies on folk theorem results to derive the conditions necessary for the APM to
exist as a noncooperative equilibrium. It is assumed that firms use a grim trigger strategy,
where all firms cooperate by maintaining an APM until a defection is observed. The initial
defection occurs when one firm produces in another firm’s market period, which is a perfectly
observable act. All firms then produce the Cournot quantity each time period after the initial
defection occurs.
Suppose an industry consists of k risk-neutral firms facing non-stochastic market demand
c
in each period9 . Let Πm
i,t be the monopoly profit to firm i at time t and let Πi,t be the
Cournot profit to firm i should all k firms produce at time t. Both the participation and
incentive compatibility constraints, equations (1) and (2) respectively, must be satisfied if
the firms are to choose the APM over Cournot behavior. Also, the incentive compatibility
constraint insures that firms will not attempt to deviate from the APM. The deviation profit
is denoted Πdi,t . Thus, the APM strategy, as developed here, is for firms to follow a set order
of releasing products coupled with the active firm producing its monopoly quantity, and, if
deviation occurs, all firms will produce the Cournot quantity every period for the remainder
of the game.
It should be noted that both constraints focus on the firm that is scheduled to release in
the k th spot in the rotation, as shown by the δ k−1 term in front of the LHS of each equation.
The intuition behind basing the condition on the firm in the last spot in the rotation is that
if firm i is willing to participate when placed in the last spot, it would certainly be willing
to participate if it was slotted earlier and received a slightly less discounted payoff stream.
δ
k−1
∞
∞ h
X
¡ k ¢t m i X
£ t c ¤
δ Πi,t ≥
δ Πi,t ∀i ∈ (1, 2, ..., k)
t=0
9
t=0
The primary results remain the same if iid random demand shocks occur each period.
6
(1)
δ
k−1
∞
∞ h
X
X
¡ k ¢t m i
£ t c ¤
d
δ Πi,t ≥ Πi,0 +
δ Πi,t ∀i ∈ (1, 2, ..., k)
t=0
(2)
t=1
Although equations (1) and (2) differ by the first term on the RHS, both yield the same
necessary condition in order for a discount rate to exist that will ensure the APM is an
equilibrium strategy. The exact form of the deviation payoff is unspecified but the proof of
existence of a discount rate to support the APM is unchanged and only the magnitude of
the discount rate necessary to support collusion changes. The proof is based on the results
of Fudenberg and Maskin [12], and is contained in [29]. Using the standard framework of
linear demand and constant marginal costs, the discount rate necessary to support the APM
over Cournot behavior in a 4-firm industry is 0.765.
In addition to the formal results, [29] also hypothesizes about factors that would increase
the likelihood of observing an APM in an actual industry. Although those factors are not
explicitly incorporated into the derivation of the conditions above, their inclusion in the
model would only serve to strengthen the possibility of an APM. One factor, an innovation
cost each time a firm enters the market, is included in some experimental treatments. This
innovation cost can be viewed as the cost needed to develop and market a new product.
One feature of the APM is that multiple equilibria exist. Although the conditions
are derived assuming a deterministic pattern in which one of k firms produces every kth
period, other non-sequential patterns are also consistent with the APM and tend to lower
the discount rate necessary for firms to benefit from using the APM. It is also the case that,
given 4 firms, the alternation may occur with 2 firms producing every other period, rather
than the firms alternating over 4 periods. While these quasi-APM schemes do not provide
as high a payoff as a true APM, the payoffs to following this scheme are better than those to
following Cournot behavior. Thus, the experimental results may not coincide perfectly with
the pattern assumed in the theory, but any deviations away from Cournot behavior may be
viewed as attempts to induce others into joining in an APM.
4
Experimental Design
The experiment is designed to test if the APM can arise without free-form communication
between subjects, while allowing for multiperiod signaling. The experiment is a simple
choice experiment where subjects choose whether to be “in” the market during a period or
“out” of the market.
There are two principal factors that are investigated, creating four possible treatment
cells. The first factor is the number of subjects in a group, with either 3 or 4 subjects in
each group. The second factor is the payoffs to the subjects. In the first treatment subjects
received Cournot payoffs from a 3-firm or 4-firm industry with linear demand, depending
on how many subjects were in the group. In the second treatment subjects received the
Cournot payoffs from a 3-firm or 4-firm industry, minus a cost of entry which can be viewed
as an innovation cost. The treatments are referred to as 4N, 3N, 4I, and 3I, where the
number stands for the number of subjects in a group while the letter N corresponds to the
treatment with no innovation costs and I corresponds to the treatment with innovation costs.
All sessions were conducted with at least 2 full groups of subjects. In addition, a group of
7
experienced subjects were brought back for one session. The session was run using the 3I
parameters, and is labelled as 3IEXP.
The payoffs are determined as follows. If a subject chose NOT to enter the market in
a particular period then that subject received 100 Experimental Currency Units (ECUs)
regardless of the decisions of the other subjects10 . The payoffs to those subjects who
entered the market were derived from the k-firm linear demand Cournot profit function
for k ∈ (1, 2, 3, 4). Letting P (Q) = a − bQ be the inverse demand function and each
firm’s constant marginal cost be c, the k-firm linear demand Cournot profit function is:
2
(a−c)2
. Since the term (a−c)
is independent of k, it is set equal 14, 400. In the 4N and
b
(k+1)2 b
3N treatments this yields a payoff of 3600 ECUs if only one subject enters, 1600 ECUs each
if two subjects enter, 900 ECUs each if three subjects enter, and 576 ECUs each if four
subjects enter. For the 4I session, each subject in a 4-subject group received the Cournot
payoff corresponding to the total number of subjects who entered minus an innovation cost
of 450 ECUs for entering11 . In the 3I session, a 3-subject group received the Cournot
payoff minus an innovation cost of 700 ECUs for entering. Subjects in the innovation costs
treatments are not given a two-part profit function comprised of the Cournot profit and the
innovation cost; instead, they are simply shown the profit net of the innovation cost. The
different innovation costs depending on the group size are used to drive the payoff when all
k firms entered towards the 100 ECUs a subject received when remaining out of the market
without changing the dominant strategy Nash equilibrium of the stage game. The hope is
that a payoff near the one subjects receive when staying out of the market will spur more
attempts at achieving the APM. The exchange rate was 5000 ECUs for $1 for the 4N and
3N treatments and 4000 ECUs for $1 for the 3I and 4I treatments.
The experiment was designed using the Z-Tree software12 . There were a total of four
sessions run using inexperienced subjects, one for each treatment. Between 6 and 12 subjects
participated in each of those four sessions and each inexperienced session was comprised of at
least two groups of subjects. Subjects were seated at a computer terminal and were randomly
and anonymously placed into groups of 3 or 4 depending on the treatment. Subjects knew
the total number of members in their group and were told that while the other members of
their group would remain anonymous, the group members would remain the same throughout
the duration of the experiment. They were also told that the experiment would last at least
80 periods, and that after 80 periods there was an 85% continuation probability after each
period. This randomly determined endpoint provides the stimulus to ensure that subjects
do not view the game as one with a fixed endpoint.
Subjects went through three screens in the experiment: the message-sending screen,
choice screen, and payoff display screen, which appeared after all subjects had made their
decisions for a period and showed each subject his earnings for the period as well as his
total earnings13 . The message-sending screen allowed subjects to send non-binding binary
10
The choice of 100 ECUs instead of 0 ECUs reflects a general opportunity cost for participating in the
experiment.
11
Subjects do not incur an innovation cost if they choose to remain out in a period, thus the innovation
cost is not a fixed cost.
12
The software package is described in Fischbacher [10].
13
The actual instructions for one version of the experiment are included in Appendix A.
8
messages (1 for “IN” and 0 for “OUT”14 ) to their group members for each of the next 10
periods. To send messages subjects had to toggle between the IN and OUT buttons, and
when their messages were set for the 10 periods they simply had to hit the submit button
to submit all the messages at once. To aid the subjects, a box appeared that showed the
signal they sent for a specific period when they sent their last set of messages. The last
piece of information that the subjects receive on this screen is the history of actual decisions
made by each group member in the previous rounds. The history screen is provided based
on the results of Duffy and Feltovich [8]. They investigate whether actions or words more
effectively enable coordination, and find that the result depends on the type of game. They
find that observation and communication increases the frequency of cooperation, and in
Prisoner’s Dilemma games actions speak louder than words. Also, the APM is based upon
the knowledge that one firm can observe when the other has produced and that this memory
is infinite, providing another reason for the inclusion of the history screen.
The choice screen is the screen where subjects make their decision whether to be IN
or OUT. Subjects make this decision by pressing the button that corresponds to their
choice. The choice screen also contained three other pieces of information. The payoff
table is displayed in the lower left-hand corner. Subjects were informed that all other
group members observed the same payoff table and that this payoff table would not change
throughout the experiment. A history of actual decisions box is displayed in the upper
right-hand corner. This box is similar to the box on the message-sending screen, although
the box on the choice screen also contained the message sent by each player immediately
prior to their actual decision for that period. Thus, if a subject sent a message of IN for
period 10 immediately prior to making his decision for period 10, the message of IN for
period 10 would appear in the history of actual decisions box in period 11, regardless of the
messages sent for period 10 in periods 1-9. This information was included so that subjects
could determine if other group members were adhering to the signal they most recently sent
for that period. Finally, the messages sent by each subject in the group appear in the
lower right-hand corner of the screen. These messages were only for the most recent round
of messages sent. Screen shots of the message sending and choice screens are included in
Appendix B.
5
Results
The results of the experiment have been broken into entry decision results and individual
signaling results. Although the APM did not arise in any treatments, the treatments where
the innovation costs were implicitly added did reduce the number of times all players chose
to enter the market. The results from the signals sent by the subjects are particularly
interesting in that they shed light on the subjects thought process.
5.1
Entry Decision Results
Due to the binary nature of both the entry decision and signaling data, most of the results
presented rely on visually identifying patterns that appear within the data. While this
14
It should be noted that to the subjects the choices were A and B, not IN or OUT.
9
Table 1: Number of times a particular market structure was achieved
Session Group #Mon #Duo #Tri #Quad #Zero MEI
1
0
11
46
25
0
27.7
4N
2
2
22
37
21
0
34.9
3
0
4
32
46
0
15.5
4I
1
0
17
34
29
0
28.0
2
3
24
44
9
0
41.7
3N
1
6
44
31
−
1
33.9
2
7
29
46
−
0
27.8
3I
1
5
66
12
−
0
47.4
2
18
51
14
−
0
53.6
3IEXP
1
83
4
0
−
0
97.8
initial approach lacks statistical rigor, it should be noted that subjects in the experiment
must use the same approach when viewing the data if they are to coordinate on an APM,
without the added benefit15 of knowing to look for APM patterns. Thus, if the researcher
without time constraints specifically looking for APM patterns in the data cannot find them
while scanning the data, it is highly unlikely that time-constrained subjects will find those
same patterns.
While visually identifying patterns is a first step, it is possible for the researcher to find
cases that he believes show evidence of the APM but which are really random strings of data.
In an attempt to statistically quantify subjects decisions, two definitions of randomness are
used. The first definition of randomness can be described as whether or not subjects flipped
a coin to determine if they should enter or remain out in any given period. Given an
underlying population composed of two categories, the binomial sign test can be used to
determine if the proportion of observations in one of the two categories is equal to a specific
value. The second definition of randomness is based on the fact that a series of binary data
generated by a random process can be expected to have a certain number of runs. A run is
defined as a sequence within a series in which one of the alternatives occurs on consecutive
trials. If subjects are behaving in a nonrandom matter, then there will either be too few or
too many runs in the series of entry decisions. These tests will be described in more detail
when applied.
5.1.1
Group Results
Table 1 shows the number of times each of the market structures (monopoly, duopoly, triopoly, 4-firm oligopoly, and zero-firms) were achieved by each group. In the two sessions
with 4 subjects, the modal market structure is triopoly except for group 3 in the 4N session.
While the APM with all group members is never approached in these sessions, the fact that
the modal market structure is triopoly does suggest that some subjects are attempting to
15
Whether or not knowing to look for APM patterns can be considered a benefit to subjects participating
in the experiment is a difficult question to answer, as one may be inclined to dismiss possible rotation schemes
that are not precisely APM.
10
create an APM by staying out of the market during some periods16 . The introduction of
the innovation cost provides no clear-cut evidence in the 4 subject groups as to whether or
not the APM can arise. Although group 2 in session 4I was able to avoid reaching a market
structure with 4 subjects all but 9 times, group 1 in session 4I has market structure numbers
similar to those of groups 1 and 2 in session 4N. Since both the 4N and 4I sessions ran for
82 periods this difference cannot be due to a difference in number of periods.
In the two sessions with 3 subjects, the modal market structure is duopoly for all groups
except group 2 in the 3N session. However, note that triopoly was the market structure
in about 15% of the periods in the 3I sessions, whereas it was reached in about 46% of the
periods in the 3N sessions. Also, group 2 in session 3I had 18 periods of monopoly market
structure, which almost matches the total from the rest of the sessions combined, regardless
of cost structure and group size. This suggests that in the 3 subject groups the innovation
cost appears to play a larger role in fostering collusion, although it is not quite enough to
generate a true APM. Once again, there was not a large difference in the number of periods,
as the 3N and 3I sessions ran for 82 and 83 periods respectively. Although the bulk of the
discussion on experienced subjects is saved for the end of the paper, note that they reached
the monopoly outcome in about 95% of the periods.
The last column of table 1 provides the Monopoly Effectiveness Index (MEI)17 . Since
the payoffs differ between sessions, a straightforward comparison of the total payoffs received
by each group throughout the session would inherently favor those sessions without the
innovation costs. Let ΠM denote the total profit each group would have received in the
experiment if the market structure had been a monopoly each period, ΠC denote the total
profit each group would have received in the experiment if all the subjects in a group entered
each period, and ΠA denote the total profit actually received by each group throughout the
(ΠA −ΠC )
entire experiment. The MEI is then (ΠM −ΠC ) ∗ 100. This standardization allows more
accurate comparisons as to how well the subjects performed in capturing the monopoly
profits throughout the experiment.
In the 4N sessions the MEI values were 15.5, 27.7 and 34.9, while in the 4I sessions the
MEI values were 28.8 and 41.7. Although slightly higher in the 4I sessions, the MEI shows
that the introduction of the innovation cost did not significantly alter subjects ability to
capture available profits. However, when comparing the 3N and 3I sessions subjects are
able to capture a much larger share of the available profits. Subjects in the 3I session
capture about 50% of the joint profit maximization level compared to only 30% in the 3N
sessions. Thus, the introduction of a fourth subject seems to hinder cooperation. This is
not unusual, as similar results about the effect that increasing the number of subjects has
on the stability of collusive behavior can be seen in Isaac and Reynolds [18]. For now, note
that the MEI for the experienced group was 97.8%.
Another possibility is that the groups were learning to play the APM as time passed.
The plots of the market structures over time show results similar to [2] in that different
groups tend to follow different paths or in some cases no discernible path at all. Figures 1
16
It is possible that some of the exit decisions occur because subjects wish to “see what happens” when
they choose B instead of A. However, once subjects have made more than a few such decisions it can no
longer be viewed as “seeing what happens”.
17
This measure is described in [17].
11
Figure 1: Time series of total number of entrants for two 4-subject groups
12
Figure 2: Time series of total number of entrants for two 3-subject groups
13
and 2 show the plots of four groups, two 4-subject groups and two 3-subject groups, in the
experiment. For example, group 2 of session 4I tends to show an increase in the number
of participants per period over time. The market structure starts as a duopoly/triopoly,
then moves to a fairly stable triopoly, and finally results in a 4-firm oligopoly. Group 1 of
session 4N follows a slightly different pattern — it begins by fluctuating between triopoly and
4-firm oligopoly, then from periods 38 to 73 it fluctuates between duopoly and triopoly, and
finally returns to 4-firm oligopoly at the end of the session. Group 1 of session 3N begins
as a fairly stable duopoly for the first 26 periods, reaching triopoly status in only periods 3
and 6, and then essentially fluctuates between duopoly and triopoly for the remainder of the
game. Group 2 of session 3N begins quite erratic, enters a long period of triopoly behavior
from periods 24 to 50, then seems to fluctuate, although it comes close to reaching a fairly
stable duopoly at the end of the session. The remaining inexperienced groups have similar
patterns, and it appears that subjects do not learn to play the APM over time.
5.1.2
Individual Attempts at the APM
It is possible that the market structure results in the previous section are determined by
purely random actions and that no subject was attempting to play an APM. Looking at the
individual entry decisions of some of the subjects shows that this is untrue. For example,
subject 2 in group 1 of the 4I session began by playing a 4-subject APM for the first 28
periods of the experiment, followed by 32 periods of playing a 2-subject APM, and finishing
with 18 periods of always entering. Subject 1 in group 1 of the 3I session played a 3-subject
APM throughout the first 60 periods of the experiment and then followed that by playing
a 2-subject APM for the remainder of the experiment. Group 1 of session 3I is described
in more detail in the next section. Subject 2 of group 1 in session 3N also began with a
3-subject APM, and although she abandoned that strategy in round 28 would return to play
it later in the experiment. There are a few other examples that can be found scattered
throughout the data that show that some subjects were actually playing an APM strategy,
but that the other subjects either did not want to join, could not coordinate on how to join,
or did not understand how joining could increase one’s payoff.
Tables 2-5 show both the actual number of times an individual subject chose to enter as
well as the percentage of times that the subject entered. In the 4N session, subjects entered
an average of 65.75 times or about 80% of the time. Of the 12 subjects who participated
in the session, 4 of them entered in at least 90% of the periods. In the 4I session, subjects
entered an average of 58.9 times, which is 73.4% of the time. There were 2 of the 8 subjects,
one in each group of the session, who entered over 90% of the time. While the APM did
not arise in the 4I session, the added innovation cost appears to have increased efforts to
coordinate on an APM.
The results in the sessions with 3 subjects per group were similar to those with 4 subjects.
In the 3N session, subjects entered an average of 65 times, which is about 79% of the periods.
Only 1 of the 6 subjects entered over 90% of the time. In the 3I session, subjects entered
an average of 55.8 times, or 67.2% of the periods. Again, only 1 of the 6 subjects entered
over 90% of the time. The innovation cost reduces the number of periods in which subjects
enter, which is consistent with the hypothesis that subjects will attempt more coordination
in the innovation cost sessions. It is interesting to note that the percentage of players who
14
Table 2: Individual results for session 4N
4N Subj #Enter %Enter #Truth Binomial
1
62
75.6
40 4.64∗∗∗
Group 1
2
64
78.0
68 5.08∗∗∗
3
81
98.8
32 8.83∗∗∗
4
53
64.6
68 2.65∗∗∗
1
70
85.4
33 6.29∗∗∗
Group 2
2
42
51.2
76 0.11
3
52
63.4
66 2.32∗∗
4
77
93.9
46 7.84∗∗∗
1
75
91.5
42 7.40∗∗∗
Group 3
2
71
86.6
30 6.52∗∗∗
3
82
100.0
4 8.94∗∗∗
4
60
73.2
33 4.09∗∗∗
Runs Test
2.95∗∗∗
1.27
0.16
1.58
2.47∗∗
2.67∗∗∗
1.43
3.44∗∗∗
0.59
0.02
−
5.45∗∗∗
The asterisks refer to significance levels of a 2-tailed test
∗∗∗ is significant at the 1% level, ∗∗ at 5%, and ∗ at 10%
Table 3: Individual results for session 4I
4I Subj #Enter %Enter #Truth Binomial
1
70
87.5
40 6.71∗∗∗
Group 1
2
41
51.3
62 0.22
3
79
98.8
50 8.72∗∗∗
4
62
77.5
67 4.92∗∗∗
1
61
76.3
71 4.70∗∗∗
Group 2
2
75
93.8
45 7.83∗∗∗
3
61
76.3
45 4.70∗∗∗
4
22
27.5
65 4.02∗∗∗
The asterisks refer to significance levels of a 2-tailed test
∗∗∗ is significant at the 1% level, ∗∗ at 5%, and ∗ at 10%
15
Runs Test
0.78
1.36
0.16
0.94
1.26
1.38
1.87∗
1.95∗
Table 4: Individual results for session 3N
3N Subj #Enter %Enter #Truth Binomial
1
72
87.8
20 6.85∗∗∗
Group 1
2
51
62.2
74 2.21∗∗
3
64
78.0
80 5.08∗∗∗
1
81
98.8
44 8.83∗∗∗
Group 2
2
63
76.8
71 4.86∗∗∗
3
59
72.0
42 3.98∗∗∗
Runs Test
0.82
0.84
2.58∗∗∗
0.16
0.25
1.91∗
The asterisks refer to significance levels of a 2-tailed test
∗∗∗ is significant at the 1% level, ∗∗ at 5%, and ∗∗ at 10%
enter in at least 90% of the periods changes very little from session to session when group
size is held constant. This suggests that there may be some players who refuse to play any
strategy other than the dominant strategy Nash Equilibrium to the stage game. This topic
is explored in more detail in the next section.
Another possible factor that could hinder the development of the APM is the truthfulness
of the subjects. Recall that, in addition to the history of past decisions made by all other
subjects of the group, the choice stage screen also displayed the last signal sent for a particular
period, providing subjects with a gauge of the trustworthiness of others. The fifth column of
tables 2-5 show the total number of times each subject acted truthfully. A subject behaves
truthfully if he follows the last signal he sends for a period. For example, there will be
ten period 10 signals sent, one for each of the first ten periods including period 10. The
subject is marked as truthful if the signal he sent for period 10 during the period 10 signaling
stage is identical to his actual decision. All signals sent for period 10 prior to the period 10
signaling stage (the signals for period 10 sent in the first 9 periods) are ignored. It should be
noted that 100% truthfulness may not occur even if an APM would occur, as there may be
some periods early in the session where subjects intend to follow one decision for the period,
but upon seeing the signals of others reverse their decision. Comparing the 4N session to
the 4I session, subjects truthfully revealed their intentions an average of 44.8 times in the
4N session and 55.6 times in the 4I session. In the 3N and 3I sessions, subjects truthfully
revealed their intentions 55.2 and 64 times respectively. The innovation cost sessions show
movement towards more truthful revelation, an indication that at least some subjects are
responding to the incentives provided.
Note that the group that exhibited the least amount of truthful revelation, group 3 of
session 4N, achieved the lowest MEI at 15.5 and that the group with the greatest amount of
truthful revelation, group 2 of session 3I, achieved the highest MEI at 53.6. The correlation
coefficient between the percentage of truthful revelation by subjects in a group and the
group’s MEI is 0.86, suggesting a strong direct relationship. A t-test of the hypothesis that
the true correlation coefficient is equal to zero is rejected at the 1% level for both directional
and non-directional tests, as the t-statistic is 4.12. This relationship between MEI and
truthful revelation suggests that subjects were more willing to sacrifice profits in the current
period for profits in the future periods if the other members of their group could be trusted.
The final two columns of tables 2-5 provide statistical tests for the two definitions of
randomness defined at the outset of the experimental results section. The first test statistic
16
Table 5: Individual results for session 3I
3I Subj #Enter %Enter #Truth Binomial
1
35
42.2
81 1.42
Group 1
2
83
100.0
27 9.11∗∗∗
3
55
66.3
65 2.96∗∗∗
1
47
56.6
73 1.21
Group 2
2
58
69.9
66 3.62∗∗∗
3
57
68.7
72 3.40∗∗∗
Runs Test
3.52∗∗∗
−
1.70∗
1.18
3.43∗∗∗
1.36
The asterisks refer to significance levels of a 2-tailed test
∗∗∗ is significant at the 1% level, ∗∗ at 5%, and ∗∗ at 10%
reported is for the binomial sign test. The binomial sign test is used if the underlying data
is comprised of two categories, such as the entry decision data, and it determines if the
proportion of observations in one of the two categories is equal to a specific value, π. The
null hypothesis of the test is that the proportion of the chosen category is equal to π. The
test statistic reported below is for π = 0.5. Of the 32 subjects spanning the 4 sessions,
there are only 4 subjects for whom the null hypothesis cannot be rejected. While these 4
subjects may appear to be flipping a coin to decide their entry decisions, further inspection
shows that they are actually those subjects who were most likely to be playing an APM
for a portion of the session. Playing the APM reduced the number of entry decisions by
the subjects to make it appear as if they were playing a 50/50 split. For the remaining 28
subjects, all but one had a proportion of entry decisions that was statistically greater than
50%. While these subjects were inclined to enter more often than not, it is still possible
that the pattern of entry decisions was random.
The second test statistic reported is for the single sample runs test18 . This test can be
used to determine if the distribution of a series of binary events in a population is random.
A run is defined as a sequence within a series in which one of the alternatives occurs on
consecutive trials. The single sample runs test takes the observed proportions from the
sample as the underlying proportions of the population and uses those proportions to calculate a distribution of runs that should occur if the data were generated randomly. Thus,
the null hypothesis is that the data is random. For large sample sizes, a normal distribution
approximation is used.
When reviewing the statistical significance of the test it is important to remember that
the observed proportion of the events is considered the true proportion. Thus, a subject
such as subject 1 of group 2 in session 3N, who is almost assuredly acting nonrandomly since
he entered in 81 of 82 periods, appears to have randomly distributed data. This is because
the expected value of the number of runs when the underlying proportions of the data are
98.8 and 1.2 and the number of trials is 82 is approximately 3. With only 1 decision to not
enter there are only two possible numbers of runs that can occur, 2 or 3, so that regardless of
when the subject made his decision to not enter he could never be very far from the expected
value of the number of runs. Of the 32 subjects, there are 12 subjects for whom the null
hypothesis is rejected, providing evidence that the remaining 20 subjects have too many or
18
Sheskin [26] provides a thorough review of both the binomial sign test and the single sample runs test.
17
Table 6: Payoffs to following an APM strategy given a specific number of simple Nash players
4-subj APM 3-subj APM 2-subj APM Cournot
Avg. Payoffs APM SN
APM SN
APM SN
4N Session
975
—
600
1600
500
900
576
4I Session
862.5 —
450
1150
275
450
126
3N Session
—
—
1267 —
850
1600
900
3I Session
—
—
1033 —
500
900
200
too few runs in their data.
While these statistical tests provide some measure of quantitative analysis I believe that
they should only be used as a complement to the evidence obtained from visual inspection
of the data. Recall that subject 2 in group 1 of the 4I session began by playing a 4-subject
APM for the first 28 periods of the experiment, followed by 32 periods of playing a 2-subject
APM, then 18 periods of always entering, and a final 2 periods of not entering. This appears
to be a very clear case of a subject playing the APM, yet both of the statistical tests suggest
that this subject was behaving in a random manner. However, if the single sample runs test
is used on only the first 60 periods of the session, then the resulting test statistic is 4.40,
which provides evidence that the subject was behaving in a nonrandom manner throughout
the first 60 periods of the experiment. This approach of breaking down the data into smaller
series is utilized in the next section.
5.1.3
Simple Nash Players
Throughout the sessions there were some players who were either unaware that dynamic
collusion could lead to greater profits or were otherwise predisposed to play the Nash Equilibrium of the stage game each period. Define any player who chose to enter in more than
90% of the periods as a simple Nash player. As described in the next paragraph, simple
Nash players can greatly impact the ability of an APM to form, particularly in the 4N and
3N sessions. However, removing these simple Nash players may reveal attempts at an APM
by less than the full amount of subjects in a session. Table 6 shows the average payoffs
subjects would receive if they followed a 3-subject APM in the face of an extreme simple
Nash player who entered every period.
In the 4N and 3N sessions, a single simple Nash player is almost enough to thwart any
attempt at any type of APM. In the 4N session, the average payoff to following a 4-subject
APM is 975. If one subject is a simple Nash player and the three remaining subjects
attempt to form a 3-subject APM then the average payoff for those 3 subjects is reduced to
600 ECUs. If 2 subjects are simple Nash players and the remaining 2 subjects attempt to
form an APM then the average payoff for those participating in the 2-subject is 500 ECUs.
Recall that the minimum payoff that a subject can receive is 576 ECUs if he enters. Thus, a
2-subject APM should not form in a group in the 4N session as it cannot raise profits above
the minimum payoff a subject will receive if he enters every time. A 3-subject APM may
be able to form in the 4N session, although the profit level received from participating in a
3-subject APM is just slightly above the one would receive from entering each period. The
payoffs per period of forming a 3-subject or 2-subject APM in the 3N session are 1267 and
18
850 respectively, while the payoff obtained from entering each time is at least 900. Thus,
one simple Nash player in a 3N group destroys any hope of an APM arising, and in a 4N
group there is only a slight possibility that a 3-subject APM might arise.
Simple Nash players should not have as much impact in the 4I and 3I sessions. The
payoffs per period to each subject average 862.5, 450, and 275 for a 4-subject, 3-subject, and
2-subject APM in the 4I session. The payoff to always entering is a minimum of 126, which
occurs if all subjects enter. In the 3I session, the payoffs per period average 1033 and 500
for a 3-subject and 2-subject APM. The payoff to always entering is a minimum of 200,
again occurring if all subjects enter. Thus, the likelihood of an APM arising in the 4I and
3I sessions increases due to the innovation cost.
There are 8 of the 32 subjects who qualify as simple Nash, and 4 of those 8 subjects
entered the market either every period or all but one period. All groups except for group 1
in the 3N session and group 2 in the 3I session had at least one player who could be classified
as a simple Nash player, although one subject in group 1 of session 3N barely misses the
90% cutoff. Group 3 of session 1 had 2 subjects that qualified as simple Nash players.
If the simple Nash players are removed from each group a few instances of the APM arise,
albeit with less than the full number of subjects for the group and without the structure
used to derive the conditions of the theory. Some of the more interesting APM results are
described in the following paragraphs.
Perhaps the clearest example comes from group 1 of session 3I. Subject 2 was a simple
Nash player who entered every time period. As discussed above, subject 1 played a 3-subject
APM for about the first 60 rounds of the experiment. Subject 3 always chose “IN” until
round 27, when he began exiting whenever subject 1 would enter. In round 61 subject 1
switched to playing a 2-subject APM, and by round 67 subjects 1 and 3 were in sync and
alternated entering and exiting the rest of the game. Table 5 shows that the null hypothesis
of the runs test is rejected for both subjects, although subject 3’s test statistic is barely
significant at the 10% level. When the first 21 periods are removed from subject 3’s data,
his test statistic rises to 3.18. This is the cleanest APM that arose, and it may in fact have
been because subject 2 was so attracted to the simple Nash strategy that he never disrupted
the attempts of the other two players to lock into a pattern.
In session 3N, subject 2 in group 1 was playing a 3-subject APM from the beginning of
the experiment. In period 7, subject 3 picked up on this and began exiting whenever subject
2 would enter. This lasted until period 27, when subject 3 entered during one of subject
2’s time slots. Using the single sample runs test for subject 2 over the first 27 periods of
the session we find that the null hypothesis can be rejected at the 10% level. For subject 3,
the null hypothesis of the single sample runs test is rejected at the 5% level for the string of
entry decisions from periods 7-26.
In group 2 of the 3N session subjects 2 and 3 play what is essentially a 2-subject APM
from periods 67-82. This APM arises even though the average payoff to the 2-subject APM
(850 ECUs) is less than the minimum payoff the subjects would be guaranteed to receive if
they entered (900 ECUs). Both subjects have identical amounts of entry and exit decisions,
9 and 7 respectively, and numbers of runs, 14. The number of runs is too large to be
considered as generated from a random process.
Group 1 of the 4N session provides some interesting patterns involving subjects 1, 3, and
4. From periods 20-26 subjects 2 and 4 settled on a 2-subject APM. Subject 2 breaks
19
the pattern in period 27, possibly realizing because he realized that he would be guaranteed
to earn more if he always entered. In period 38, subjects 1 and 4 begin a 2-subject APM
that lasts until period 43. The breakdown in the 2-subject APM may be due to subject 3
attempting to join the APM, as subject 3 had been entering every period from 26-42. Subject
4 attempted to start a 3-subject APM when he realized that subject 3 might be interested in
joining, but discontinued his pursuit of the 3-subject APM in period 51. An unusual APM
for periods 62-73 evolved between subjects 1 and 4 where one subject would enter the market
for 3 periods while the other subject remained out. The subjects were able to settle on this
rotation for 12 periods until endgame effects took hold and both subjects began entering
every period. Unfortunately, while these partial APM schemes are interesting, the sample
sizes are too small to perform runs analysis.
Over the last 7 periods of play for group 2 in session 4N, subjects 1, 2, and 3 develop a
slightly more complex method of extracting profits in excess of 576 ECUs. Although it is
only 7 periods, its development can be seen in the previous 7 periods, and likely would have
continued had the experiment continued. Subject 2 attempted to coordinate a 3-subject
APM, where the subjects would each earn 600 ECUs. Subjects 1 and 3 both entered in
the periods in which subject 2 sat out. The result was that subject 2 averaged 600 ECUs
per period during this time, while subjects 1 and 3 averaged 633 ECUs. Near the end of
session 4N, subject 4 of group 3 attempted to start a 4-subject APM. Perhaps realizing this,
subject 2 exited during those periods in which subject 4 entered. Once again, while this
partial APM is interesting, the sample size is too small to perform a runs test.
These results show that some subjects, while not able to obtain the benefits from an APM
in which full group participation occurred, were able to increase their payoffs by coordinating
on a smaller-scale APM. Most of this behavior occurred in the sessions with innovation costs
which were more conducive to fostering smaller-scale APMs. Thus, while the availability
of multi-period binary signals may not have been able to generate collusive behavior for the
full set of subjects within a group, it may have fostered collusive behavior among a subset
of those subjects.
5.2
Signal Usage
The signals that the subjects sent can be used to determine the degree to which they are trying to communicate with other members of the group. Since there are 1024 distinct signaling
strings that can be sent, and only 80-83 periods per session, most of the signal combinations
will not be sent by each subject. However, several important signal combinations can be
pinpointed and the frequency with which those signals were sent can be observed. I have
broken these important signal combinations into two categories — combinations in which the
subject is signaling one of the APM patterns and what I will call simple signal combinations.
It should be noted that for 29 of the 32 subjects, each subject’s modal choice of signaling
combination is included in one of these two categories19 .
19
Of the remaining 3 subjects, one had a modal sequence choice that can be explained as a variant of an
APM strategy, one subject had a sequence of signalling strings that seemed almost entirely random, and the
third subject had an “abbreviated” 2-subject APM, where the subject signalled in for periods 1 and 3 and
out for the remainder of the periods.
20
Table 7: Signals sent indicating recognition of the APM for session 4N
4N Sub 4-subj 3-subj 2-subj %APM
1
0
5
0
6.1
Group 1
2
0
0
0
0.0
3
1
0
1
2.4
4
9
0
1
12.2
1
4
2
33
47.6
Group 2
2
16
17
18
62.2
3
6
15
18
47.8
4
0
0
1
1.2
1
0
0
0
0.0
Group 3
2
34
1
5
48.8
3
0
0
0
0.0
4
11
0
1
14.6
Table 8: Signals sent indicating recognition of the APM for session 4I
4I Sub 4-subj 3-subj 2-subj %APM
1
0
1
0
1.3
Group 1
2
28
0
30
72.5
3
0
0
0
0.0
4
0
0
0
0.0
1
0
0
1
1.3
Group 2
2
0
0
1
1.3
3
11
12
14
46.3
4
45
0
0
56.3
5.2.1
APM Signals
The APM signaling combinations are quite complex. For instance, a subject participating
in a 4 subject group session may send any of the following sequences of binary signals in an
attempt to communicate desire to participate in a 4-person APM: 1000100010, 0001000100,
0010001000, and 0100010001. The amount of times that the subject sent ANY one of
those signals is counted as an attempt to signal a 4-subject APM. Similar counts have
been calculated for signaling combinations which communicate a desire to participate in a
3-subject or 2-subject APM. While these tables will not capture all of the attempts at
coordination20 , they do provide some measure of the ability of the subjects to realize that a
higher payoff can be obtained through intertemporal collusion.
Tables 7 and 8 show the amount of times each subject sent signals corresponding to one
of the APM sequences. There is not much difference in the signals sent by the subjects in
session 4N or 4I, despite the fact that the payoff to each subject when all four subjects chose
to enter the market was only 126 ECUs in session 4I, and was 100 ECUs if a subject stayed
20
See the note on group 2 of session 4N in the discussion of simple Nash players in the previous section.
21
Table 9: Signals sent indicating recognition of the APM for session 3N
3N Sub 4-subj 3-subj 2-subj %APM
1
3
2
1
7.3
Group 1
2
0
38
0
46.3
3
0
0
0
0.0
1
2
7
6
18.3
Group 2
2
0
5
0
6.1
3
0
2
18
24.4
Table 10: Signals sent indicating recognition of the APM for session 3I
3I Sub 4-subj 3-subj 2-subj %APM
1
0
61
15
91.6
Group 1
2
0
1
0
1.2
3
0
7
52
71.1
1
0
71
0
85.5
Group 2
2
0
10
9
22.9
3
0
0
2
2.4
out of the market for a particular period. In fact, it could be said that the subjects in the
4I session showed less understanding as to how payoffs could be increased by intertemporal
collusion. For instance, even though subject 2 of group 1 in session 4I sent 60 periods of
signals suggesting either a 4-subject APM or 2-subject APM, there is only one other signaling
string between the other 3 subjects of that group that matches any version of the APM. The
lack of attempted coordination in the 4-subject innovation cost treatment is puzzling given
6
that only 10
of a penny is given up if one stays out of the market and the other 3 subjects
enter.
Tables 9 and 10 show the signal usage in the 3N and 3I sessions respectively. Although
it should not arise, I have included the 4-subject APM strings for completeness. There does
not appear to be much difference in the APM signals sent between subjects in the 3N session
and those in either 4N or 4I. However, it is possible that some subjects, particularly one such
as subject 2 in group 1 of session 3N, realized that while a 3-subject APM would raise profits
a 2-subject APM would actually reduce profits. Subjects in the 3I session were particularly
savvy, with three of the six subjects sending either the 3-subject or the 2-subject signaling
string over 70% of the time. A fourth subject, number 3 of group 2, consistently sent signals
where he proposed exiting for 1 round and entering for 2. Also, when the signaling data is
looked at, it appears that subject 3 in group 1 of session 3I may have convinced subject 1
to abandon his strategy of using the 3-subject APM in favor of a 2-subject APM.
In all, 4 of the 32 subjects sent signals for one version of the APM in at least 70% of the
periods and an additional 7 subjects sent signals for a version of the APM between 45%-65%
of the periods. Thus, about one-third of the subjects displayed some recognition of the APM
and actively chose to signal this recognition to the other members of the group. For the
remaining two-thirds of the subjects it is impossible to distinguish whether subjects lacked
22
understanding of how payoffs could be increased by the APM or if they simply chose not
to signal the APM. It is quite possible that those subjects who did not signal the APM
behaved by sending random signal combinations, which would inhibit the development of
the APM. This claim is investigated in the following section.
5.2.2
Simple Signals
In order to investigate whether or not subjects were randomly submitting signal combinations
I have tabulated counts for three strings of signals. I will call these simple signal combinations. Those three strings are a sequence of 10 zeros (the no periods signaling string),
a sequence of a 1 followed by 9 zeros (first period only signaling string), and a sequence of
10 ones (the all periods signaling string). The no signaling string has two interpretations.
The first interpretation is the literal interpretation of the signaling combination, that the
subject intends to remain out for the next 10 periods. A second interpretation is that, since
the no signaling string was the default string, the no signaling string could also be used by
subjects attempting to hide their intentions21 . It is possible that subjects may have viewed
this sequence as a “no information” sequence. The 1st period signaling combination is essentially the same as simple one-period, pre-period communication and does not provide any
information as to the subject’s understanding of dynamics. I have included the all periods
signaling combination as a simple signal, although some subjects may use the all periods
signaling combination as a threat to others. Also, although the endpoint of the session
was randomly determined, some subjects were susceptible to end-game effects, and signalled
their desire to enter every round in the late rounds. The columns in tables 11-14 contain the
total number of times a particular signaling combination was sent, as well as the percentage
of periods in which those signaling combinations were sent. Since the all periods signaling
combination may be viewed as a sophisticated strategy, I have included two columns for the
percentage of total rounds in which a simple signal was sent, one with and one without the
all periods combination.
Tables 11 and 12 show the simple signal combinations for subjects in sessions 4N and
4I. Note that 7 of the 12 subjects in session 4N and 4 of the 8 subjects in session 4I sent
signaling combinations of no signal or 1st period at least 50% of the time. Also, every group
except for group 2 in session 4I had at least one person send no signal or 1st period at least
90% of the time. Whether these signals were meant to be strategic or simply demonstrated
a lack of understanding of the dynamics of the problem is unknown. It is highly unlikely,
however, that coordination among 4 subjects would occur without the use of the signaling
device, particularly since coordination can only occur intertemporally.
Tables 13 and 14 show the simple signaling combination results for sessions 3N and 3I.
In the 3N sessions there was still one subject in each group who signalled either no period
or 1st period about 50% of the time. While this is less than the 90% levels that were seen
in the 4-subject groups, it still demonstrates either an inability to see or an unwillingness to
cooperate on a more profitable strategy. The 3I sessions, however, show a stark improvement
in that the number of no period and 1st period signals sent falls below 10% for all subjects.
21
One subject privately asked how he could choose to “not signal”. My response was that the software
was going to send either a zero or a one for each signal depending on how he chose, and he promptly pressed
the submit button sending a string of all zeros.
23
4N
Group 1
Group 2
Group 3
Table 11: Simple Signals Table for session 4N
Sub
# No
# 1st % No sig
# All % No, 1st
signals period & 1st per periods & All per
1
42
0
51.2
0
51.2
2
26
56
100.0
0
100.0
3
7
1
9.8
2
12.2
4
22
19
50.0
9
61.0
1
18
0
22.0
8
31.7
2
8
8
19.5
2
22.0
3
13
20
40.2
7
48.8
4
37
37
90.2
3
93.9
1
43
37
97.6
1
98.8
2
23
1
29.3
3
32.9
3
78
0
95.1
1
96.3
4
56
2
70.7
1
72.0
Table 12: Simple Signals Table for session 4I
4I Sub
# No
# 1st % No sig
# All % No, 1st ,
signals period & 1st per periods & All per
1
40
25
81.3
2
83.8
Group 1
2
18
0
22.5
0
22.5
3
26
42
85.0
1
86.3
4
27
53
100.0
0
100.0
1
1
0
1.3
1
2.5
Group 2
2
32
10
52.5
11
66.3
3
28
1
36.3
11
50.0
4
18
0
22.5
0
22.5
24
Table 13: Simple Signals Table for session 3N
3N Sub
# No
# 1st % No sig
# All % No, 1st ,
signals period & 1st per periods & All per
1
8
0
9.8
0
9.8
Group 1
2
13
26
47.6
0
47.6
3
1
19
24.4
0
24.4
1
13
6
23.2
9
34.1
Group 2
2
5
0
6.1
21
31.7
3
38
9
57.3
1
58.9
Table 14: Simple Signals Table for session 3I
3I Sub
# No
# 1st % No sig
# All % No, 1st ,
signals period & 1st per periods & All per
1
0
0
0.0
2
2.4
Group 1
2
6
1
8.4
3
12.0
3
5
2
8.4
9
19.2
1
0
0
0.0
12
14.5
Group 2
2
6
0
7.2
1
8.4
3
1
0
1.2
12
15.7
Additionally, while the number of all periods signals increases, especially in group 2 of
session 3I, most of these all periods signals were sent near the end of the game, indicating
that endgame effects had likely taken hold. Subject 1 sent 7 of her 12 all periods signals after
period 76 while the other 5 were sent consecutively from periods 37-41, possibly suggesting
a punishment if the others failed to cooperate. Subject 3 sent 11 of his 12 all periods signals
after period 68. The decrease in simple signals sent in the 3-subject groups suggests that the
dynamic collusive possibilities are more obvious in the 3-subject groups, particularly when
the costs of non-participation in the APM increase.
The simple signals tables show that most subjects were not sending signals in a random
manner. The APM signaling combinations represent 9 of the possible 1024 signaling combinations that could be sent while the simple signal combinations represent 3 of those possible
1024 signaling combinations. Call these 12 signaling combinations the “favored signaling
combinations”. The favored signaling combinations comprise a little more than 1% of the
total number of signaling combinations that could have been sent. Of the 32 subjects, 20
subjects sent a favored signaling combination in at least 75% of the periods, with 12 of those
20 subjects sending a favored signaling combination in 90% or more of the periods. Subject
1 in group 2 of session 4I had the lowest percentage of favored signals sent at 3.8%. The
next lowest percentage was 13.2% by subject 2 in group 1 of session 3I.
Although it seems highly unlikely, it is still possible that the underlying distribution of
12
favored signaling combinations and 1012
nonfavored signaling combinations generated the
1024
1024
22
observed data. The binomial sign test can be used to determine if the observed proportion
22
The test statistics are calculated using a correction for continuity.
25
12
of the favored signaling combinations is equal to 1024
. For subject 1 in group 2 of session 4I
(the subject with only 3 favored signaling combinations sent), the test statistic that results
from choosing 3 favored signaling combinations in 80 periods is 1.62. The binomial sign test
is evaluated with the normal distribution, and we fail to reject the null hypothesis at the 10%
level. For the subject with the second lowest percentage of favored signaling combinations
sent, subject 2 in group 1 of session 3I, the test statistic is 9.72. Thus, we reject the null
hypothesis at standard significance levels. The remaining 30 subjects have test statistics
greater than 9.72. These tests show that it is highly unlikely that subjects were choosing
their signaling combinations randomly.
5.3
Experienced Subjects
A fifth session (3IEXP) was conducted using only experienced subjects who had previously
demonstrated a willingness to participate in the APM either through signaling or through
actual play. The recruitment email indicated to the subjects that only those subjects who
had previously participated in a particular type of experiment would be able to participate,
although subjects were not told which type of experiment was being conducted23 . The
session was conducted using the parameters of the 3I treatment. While there was only one
group of 3 subjects, the subjects were not allowed to talk prior to or during the experiment,
and they were visually isolated by dividers at the computer monitors. This session lasted
for 87 periods.
The results from this session heavily favor the development of the APM. From periods
1-81 the subjects played the APM perfectly, with each subject entering 27 times and gaining
the monopoly profit each time. From periods 82-87, subject 1 decided to enter each period,
possibly succumbing to endgame effects. Thus, the monopoly outcome was reached 83 times,
with duopoly accounting for the remaining 4 periods. This generated an MEI of 97.8%.
The signaling strings sent by the subjects were almost flawless, with each subject sending
a 3-subject APM signaling string every period except for one24 . The null hypothesis of the
single sample runs test is rejected for all 3 subjects, with t-statistics of 2.99, 4.70, and 4.45
for subjects 1, 2, and 3 respectively. Subjects 2 and 3 were truthful every time period, and
subject 1 was truthful in each of the first 82 periods, until he began entering each period.
These results suggest that the combination of subjects inclined to play the APM and the
signaling device is enough to generate a collusive outcome even if the subjects are not allowed
to openly discuss such a strategy.
6
Conclusion
The main result of the study is that a multi-period signaling device serves as a useful collusive
device but appears unable to educate subjects on how to collude intertemporally. Previous
studies have shown that intertemporal collusion schemes tend to arise when subjects are
23
There were several different experiments run in the summer of 2004 at the XE/FS laboratory at Florida
State University.
24
In the 72nd period, subject 1 failed to send a 3-subject APM signaling string. This failure can be traced
to the subject failing to send a message of "IN" for the 77th period. It was likely a mistake.
26
allowed free-form verbal or written communication, but not when one-period ahead signaling
is used, particularly when more than 2 subjects are involved. The experiments in this study
provide evidence that free-form communication may be necessary to educate those subjects
who fail to understand the underlying dynamics of intertemporal collusion, as the multiperiod signaling device used is unable to generate collusive outcomes when inexperienced
subjects participate in the experiment. However, experienced subjects are able to use the
multi-period signaling device as a means of communication and are able to generate a highly
collusive outcome.
These results pose an interesting problem for antitrust authorities concerning the preannouncement of product releases. If the CEOs are assumed to understand the dynamics of
the product release problem, then pre-announcement could lead to firms forming the APM;
however, the assumption of understanding is a difficult one to make. Also, there may be
beneficial aspects of pre-announcement that have been ignored in this study. Ultimately,
the benefits of pre-announcement must be weighed against the collusive possibility of preannouncement.
There are a variety of extensions that could be pursued to enhance the results. One
possibility is to break from the Cournot payoff function and make the monopoly payoff
an even larger multiple of the payoff each firm receives when all firms enter. A second
possibility is to incorporate costly signaling in the experiment, which can be done in at
least two manners. The first is to require that subjects who wish to send signals must
pay some amount of ECUs, such as taking out an advertisement to announce a product
release. It is possible that other subjects may pay more attention to these signals since
they are costly. A second possibility is to make deviating from the signals sent costly,
particularly when the time period for which the signals are sent is close to the current time
period. This may more accurately reflect real-world effects of changing product release dates
as delaying a product release may anger some customers and cause a loss in revenue, while
releasing a product without announcing the release may cause the product to go unnoticed
by consumers, decreasing revenue. Finally, a direct test between the APM and the ESM
needs to be performed.
References
[1] Jamie Brown-Kruse, Mark B. Cronshaw, and David J. Schenk. Theory and Experiments
on Spatial Competition. Economic Inquiry, 31:1:139—165, 1993.
[2] Lluis Bru, Rosario Gomez, and Jose M. Ordonez. Information in Repeated Experimental
Cournot Games. In Research in Experimental Economics, volume 9, pages 191—216.
Elsevier Science, 2002.
[3] Timothy Cason and Douglas Davis. Price Communications in a Multi-Market Context:
An Experimental Investigation. Review of Industrial Organization, 10:6:769—787, 1995.
[4] Russell Cooper, Douglas DeJong, Robert Forsythe, and Thomas Ross. Selection Criteria
in Coordination Games: Some Experimental Results. American Economic Review,
80:1:218—233, 1990.
27
[5] Douglas Davis and Charles Holt. Conspiracies and Secret Discounts: Initial Laboratory
Results. Economic Journal, 108:1—21, 1998.
[6] Douglas Davis and Bart Wilson. Collusion in Procurement Auctions: An Experimental
Examination. Economic Inquiry, 40:2:213—230, 2002.
[7] John Dickhaut, Margaret Ledyard, Kevin McCabe, and Arijit Mukherji. Pareto Optimal
Allocations from Multi-period Coordination: The Catalytic Role of Communication,
2002. Working Paper.
[8] John Duffy and Nick Feltovich. Do Actions Speak Louder Than Words? An Experimental Comparison of Observation and Cheap Talk. Games and Economic Behavior,
39:1—27, 2002.
[9] Ido Erev and Amnon Rapoport. Coordination, Magic, and Reinforcement Learning in
a Market Entry Game. Games and Economic Behavior, 23:146—175, 1998.
[10] Urs Fischbacher. z-Tree: Zurich Toolbox for Readymade Economic Experiments, 1999.
Zurich University.
[11] Lawrence Fouraker and Sidney Siegel. Bargaining Behavior. McGraw-Hill, USA, 1963.
[12] Drew Fudenberg and Eric Maskin. The Folk Theorem in Repeated Games with Discounting or with Incomplete Information. Econometrica, 54:3:533—554, 1986.
[13] David Grether and Charles Plott. The Effects of Market Practices in Oligopolistic
Markets: An Experimental Examination of the Ethyl Case. Economic Inquiry, 22:4:479—
507, 1984.
[14] P. Jean-Jacques Herings and Ronald Peeters. Stationary Equilibria in Stochastic Games:
Structure, Selection, and Computation, 2000. Meteor Research Memorandum 00/031,
University of Maastricht.
[15] P. Jean-Jacques Herings, Ronald Peeters, and Maarten Pieter Schinkel. Intertemporal
Market Division: A Case of Alternating Monopoly, 2001. Working Paper.
[16] R. Mark Isaac and Charles R. Plott. The Opportunity for Conspiracy in Restraint
of Trade: An Experimental Study. Journal of Economic Behavior and Organization,
2:1:1—30, 1981.
[17] R. Mark Isaac, Valerie Ramey, and Arlington W. Williams. The Effects of Market
Organization on Conspiracies in Restraint of Trade. Journal of Economic Behavior and
Organization, 5:2:191—222, 1984.
[18] R. Mark Isaac and Stanley Reynolds. Two or Four Firms: Does it Matter? In Research
in Experimental Economics, volume 9, pages 95—119. Elsevier Science, 2002.
[19] R. Mark Isaac and Vernon Smith. In Search of Predatory Pricing. The Journal of
Political Economy, 93:2:320—345, 1985.
28
[20] R. Mark Isaac and James Walker. Information and Conspiracy in Sealed Bid Auctions.
Journal of Economic Behavior and Organization, 6:2:139—159, 1985.
[21] Anthony Kwasnica and Katerina Sherstyuk. Collusion via Signaling in Multiple Object
Auctions with Copmlementarities: An Experimental Test, 2002. Working Paper.
[22] Amnon Rapoport, Darryl Seale, Ido Erev, and James Sundali. Equilibrium Play in
Large Group Market Entry Games. Management Science, 44:1:119—141, 1998.
[23] Amnon Rapoport, Darryl Seale, and Eyal Winter. An Experimental Study of Coordination and Learning in Iterated Two-Market Entry Games. Economic Theory, 16:661—687,
2000.
[24] Amnon Rapoport, Darryl Seale, and Eyal Winter. Coordination and Learning Behavior
in Large Groups with Asymmetric Players. Games and Economic Behavior, 39:111—136,
2002.
[25] R. Selten and W. Guth. Equilibrium Point Selection in a Class of Market Entry Games.
In Games, Economic Dynamics, and Time Series Analysis, volume , pages 101—116.
Physica-Verlag, 1982.
[26] David Sheskin. Handbook of Parametric and Nonparametric Statistical Procedures.
Chapman and Hall, USA, 2004.
[27] James Sundali, Amnon Rapoport, and Darryl Seale. Coordination in Market Entry Games with Symmetric Players. Organizational Behavior and Human Decision
Processes, 64:2:203—218, 1995.
[28] John Van Huyck, Raymond Battalio, and Richard Beil. Tacit Coordination Games,
Strategic Uncertainty, and Coordination Failure. American Economic Review, 80:1:234—
248, 1990.
[29] Arthur Zillante. Spaced-Out Monopolies: A Theory of Alternating Product Release
Time, 2003. Working Paper.
Appendix A. Instructions for the Experiment
This appendix includes a sample of the instruction script that subjects were read in the
experiment. This particular script is the one used on May 26th , 2004.
Script for AZ 5/26/04 Experiment
Thank you for participating in today’s experiment. I will read aloud from this script to
ensure that all sessions of this experiment receive the same information. However, if you
have any questions please do not hesitate to ask myself or one of the other experimenters.
At this time I ask that you refrain from talking to any of the other subjects. If you violate
this rule then the experimenter reserves the right to remove you from the experiment and
you will receive only your $7 show-up fee.
29
How are groups determined?
In today’s experiment the computer has randomly placed subjects into 3 groups of 4.
Your decisions and those of the members of your group will determine your payoff. The
exact method in which your payoff will be determined will be described momentarily. It
is important to note that although the members of the groups will remain anonymous, the
other subjects in your group will remain the same THROUGHOUT THE EXPERIMENT.
How are payoffs determined?
At this point in time it should be noted that all currency amounts will be denoted in a
fictitious currency, called Experimental Currency Units (or ECUs). ECUs will be exchanged
at the rate of 50 ECUs = $0.01, or 50 ECUs = 1 penny. Thus, 5000 ECUs = $1. The only
number that is not transformed is your $7 show-up fee, which remains fixed at $7 US dollars.
Stages
There are 3 stages in this experiment. The three stages are called:
1.
Message sending
2.
Choice
3.
Payoff display
Although the “Choice” stage is the 2nd stage in the actual experiment I will discuss it
first as the choice stage determines your payoff for a period.
Please turn your attention to your computer screen now, but do not hit any buttons at
this time. In the center of the “choice” stage it has your subject ID number for your group.
You will retain this identification (P1, P2, or P3) throughout the experiment. Also, your
overall subject number is noted, but you can disregard this number — it is essentially there
for my benefit as I walk around. Also note that the current period and the remaining time
for the particular stage are indicated in a header along the top of the screen.
Upper-left
The upper-left corner of the “Choice” stage contains two buttons, A and B (although
in the demo only B is a button — in the actual experiment both A and B are buttons). In
today’s experiment you will be asked to decide between choosing option A and choosing
option B in the “Choice” stage of each period. You make this choice by pressing the button
in the upper left corner of your screen that corresponds to the choice you wish to make for the
current period. You will have 30 seconds to make this decision. Once you have made your
choice you will be asked to wait patiently until all other subjects have made their choices.
This ensures that all groups proceed at the same pace so that one group does not end up
finishing the experiment prior to another group. Your choice, as well as the choices made by
the other members of your group, will determine your payoff for that period.
Lower-left
Your payoff is a function of how many members of the group choose option A and how
many choose option B. The table in the lower left corner of your computer screen shows
your payoff schedule based on your choice and the choices of the other members of your
group. You should note that ALL members of your group (as well as all members of the
experiment) see the SAME payoff schedule. The payoffs will NOT change throughout the
30
course of the experiment. Please recall that all payoffs are denoted in ECUs and that 5000
ECUs = $1. Note that any time you choose option B you receive 100 ECUs, regardless of
what your fellow group members chose. Your payoff table shows that if only 1 subject in
your 4-subject group chooses option A within a particular period then ONLY that subject
will receive 3600 ECUs for that period. If exactly 2 subjects in your group choose option A
within a particular period then EACH subject who chose option A will receive 1600 ECUs
for that period. If exactly 3 subjects in your group chose option A then EACH subject who
chose option A will receive 900 ECUs for that period. This is how your decisions and your
group member’s decisions determine your payoff.
Note that when you make a choice of A or B it is ONLY for the CURRENT period, and
you may change from choice A to choice B as frequently or infrequently as you like from
period to period.
Upper-right
The box in the upper right-hand corner of the “choice” screen is the “history of play”
box. As of right now, the box contains a header row with Period, P1, MesP1, P2, MesP2,
P3, and MesP3. Period corresponds to the period in which the decision was made and the
columns beneath P1, P2, and P3 correspond to the decisions actually made by that specific
subject in your group for that period. As an example, if P1 chooses A in period 1, when you
see the choice screen in period 2 you will see the number one, “1”, appear in the cell of the
history box that corresponds to column P1 and Period 1. If P1 chose B in period 1, then the
number zero, “0”, will appear in the cell of the history box that corresponds to column P1
and Period 1. It is important to remember that A = 1 and B = 0 throughout the experiment.
In the demo it is period 1 and it is as if all the players chose B in period 0. You will be able
to observe the decisions made by every member of your group for every completed period of
the experiment. Again, note that you will only be able to see their decisions in the periods
following the current period (you will only be able to see period 1 decisions once we have
moved to period 2, you will see period 1 and period 2 decisions when we have moved to
period 3, etc.). Eventually a scroll bar will appear that will allow you to scroll up and down
the history box — when this occurs you will initially see the most recent periods of play at
the bottom of the box, and then you may scroll up to view the prior periods of play.
The MesP1, MesP2, and MesP3 columns will be explained after I explain the “messages
sent” box in the lower right corner of the screen.
Lower-right
Finally, the lower right-hand corner of your screen is the “Messages Sent” box. In this
experiment you will be able to send binary (0 or 1) messages to your fellow group members.
These messages are able to be sent 10 periods in advance for each message — I will explain
how the messages are sent momentarily. Note that the messages sent box contains the labels
period, P1, P2, and P3. Each cell in the messages sent box corresponds to the most recent
message sent by that player for that period. For example, if a 0 appears in the messages
sent box corresponding to period 4 and subject P3, this means that subject P3 has sent a
message that he or she INTENDS to choose B in period 4. If a 1 appears in the messages
sent box corresponding to period 4 and subject P2, this means that subject P2 has sent a
message that he or she INTENDS to choose A in period 4. It is important to note that these
messages are non-binding, which is why I stressed the word INTENDS — thus neither you
nor the other subjects in your group have to follow the messages sent.
31
Again, you will see messages for the next 10 periods, including the current period (the
message sending screen, to be described shortly, actually comes first in the experiment).
Also, your payoff does NOT depend on the messages that you have sent, nor does it depend
on the messages the other members of the group have sent. Your payoff ONLY depends on
the actual choices of A and B made by the group members during each period.
Finally, return to the history box. When you see MesP1 this shows the message that
was sent IMMEDIATELY prior to the actual choice made by that player. As an example,
consider period 10. There will be 10 period 10 messages (one for each period from 1-10) that
will be sent by each subject prior to the actual choice of A or B for period 10. The message
that appears in the history box corresponds to the period 10 message for period 10. That
is, if player 1 chooses to send a message of A (or 1) for period 10 prior to making his actual
choice for period 10, then when the choice screen appears for period 11 that message of 1
will be recorded under MesP1 for period 10, regardless of the messages sent by player P1 for
period 10 in periods 1-9.
Note that you will have 25 seconds to reach a decision in the choice stage — if you do not
reach a decision within 25 seconds a red “please reach a decision” will flash in the upper-right
corner of your screen (it should be flashing now). Although you will never be forced off of
the screen, it is asked that you make your decisions in a timely manner so that we can finish
all of the intended periods. Throughout the first few periods of the experiment I will allow
some excess time as you familiarize yourself with the interface, but after 5-10 periods I will
ask that you try to adhere to the 25 second clock.
To exit the choice stage, simply click on the button that corresponds to the actual decision
that you wish to make for the current period, A or B. In the demo only B is a button — in
the real experiment both A and B are buttons. If you have no questions about the choice
stage please click on B now to move to the next screen. Note that you will not receive any
payment for the choice made in this demo.
Message sending stage
PRIOR to entering the choice stage you will see the “Message Sending Screen”. In this
stage you have the ability to send messages about the option you plan on choosing in each of
the next 10 periods of the experiment. Again, the top of the screen contains a header with
the current period as well as a countdown clock.
The first column contains the labels for each row: Period, Choose A, Choose B, Current
Choice, and Last Round. The row for “period” corresponds to the period for which you are
sending a message. The rows for “Choose A” and “Choose B” will contain buttons in the
actual experiment (although they are only boxes now), that will allow you to send a message
of A or B for the upcoming periods. Pressing the button that corresponds to Period 1 and
Choose A will change the number in the “current choice” row under period 1 to a 1, and
pressing B will change the number back to a 0. Remember, a 1 corresponds to a message
that you INTEND to choose option A in a particular period, while a 0 corresponds to a
message that you INTEND to choose option B in a particular period. It is important to
note that when a new period begins the “Current Choice” will always reset to all zeroes.
Is everyone clear on how to send messages for the upcoming 10 periods?
The row corresponding to “last round” shows the message that you sent last round for
that period. Suppose that it is period 1 and you sent a message of 1 for periods 2 and 9.
32
When the period 2 message sending screen appears, the period labels at the top will shift
one spot to the left (so that period 1 is now where period 0 is), as period 0 drops off and
period 10 appears. The “Last round” row will also shift, so that if you wish to send the
same messages that you sent the previous period you merely need to look below the column
to see which message you sent for the last period — you do NOT need to keep track of which
periods you sent which messages in, as the software does that for you. Thus, if you sent a
message of 1 for periods 1 and 9 you would see a 1 in the first and next to last “last round”
columns in period 2, rather than the second and last columns. You WILL need to change
your messages from zeroes to ones IF you wish to send the same message for each period.
Also note that the cell for “last round” under Mes10 will always be a zero, as you will never
have sent a message for that period before.
When you have finished making your message selections you can submit your messages
by pressing the “Submit” button in the lower right-hand corner of your screen. You will
NOT be allowed to change your messages once you have pressed the submit button, but
you are allowed to change messages prior to pressing the submit button. When you submit
your messages you will see the “Waiting Screen”, which asks you to wait patiently until all
subjects in the experiment have finished submitting their messages. Again, note that these
messages are non-binding and that they do NOT affect your payoffs in any way.
There is a 45 second countdown clock in the upper right-hand corner of your screen. Once
45 seconds have passed, a message will flash in red asking you to please reach a decision.
Although the program will not force you to the next stage, it is asked that you make your
message sending decisions in a timely manner so that we can finish all of the intended periods
for this session. Again, due to the complexity of the interface I will allow a little excess time
during the first few periods.
The last piece of information is the history of play box. It is identical to the history of
play box in the choice stage except that it only contains the actual decisions by the subjects
in your group.
If you have no questions about the message sending screen, please hit the submit button
to exit the stage now.
Payoff display screen
The payoff display screen simply shows your payoff for the just completed period as well
as your total payoff from all the previous periods, including the one just completed. Both
the current payoff and the total payoff are denominated in ECUs. You can leave this screen
by pressing the OK button in the lower right-hand corner. The timer is set for 7 seconds for
this screen — you will exit the screen if 7 seconds elapses.
Length of the experiment
The experiment is intended to run for at least 80 periods. After the 80th period there
is an 85% chance that the experiment will continue for an additional period. This endpoint
has been previously determined by a random number generator and has been embedded into
the software.
Questionnaire
33
Once the experiment finishes you will be asked to fill in your first and last name for record
keeping. This facilitates the payment process for me. Once you have input your name press
the “OK” button and please wait patiently until your name is called.
Are there any questions?
Appendix B. Experiment Screen Shots
Message Sending Screen
34
Choice Screen
35