The Relative Efficacy of Price Announcements and
Express Communication for Collusion:
Experimental Findings∗
Joseph E. Harrington, Jr.
Dept of Business Economics & Public Policy
The Wharton School
University of Pennsylvania
Philadelphia, PA USA
[email protected]
Roberto Hernan-Gonzalez
Dept of Economic Theory and History
Universidad de Granada
Granada, Spain
[email protected]
Praveen Kujal
Middlesex University
London, U.K.
[email protected]
14 August 2013
.
∗
We appreciate the comments of Cedric Argenton, Hans-Theo Normann, and participants at
"Cartels: A Conference in Honor of Robert F. Lanzillotti" (U. of Florida) and the 3rd MaCCI
Summer Institute in Competition Policy (Edesheim, Germany). This research was partly conducted
while the first author was visiting the Universidad Carlos III de Madrid as a Cátedras de Excelencia, and he would like to thank Banco Santander for funding and the faculty for providing a most
collegial and stimulating environment. For financial support, the first author thanks the National
Science Foundation (SES-1148129) and the second and third authors thank the Spanish Government (DGICYT-2012/00103/00) and the International Foundation for Research in Experimental
Economics (IFREE). The experiments were run when the second and third authors were visiting
the Economic Science Institute at Chapman University.
1
Abstract: Collusion is when firms coordinate on suppressing competition. Coordination typically requires that firms communicate in some manner. This study performs
an experimental analysis to determine what modes of communications are able to
produce and sustain collusion and how the efficacy of communication depends on the
number of firms and firm heterogeneity. We consider two different communication
treatments: non-binding price announcements and unrestricted written communication. Our main findings are that price announcements allow subjects to coordinate
on a high price but only under duopoly and when firms are symmetric. While price
announcements do result in higher prices when subjects are asymmetric, there is little
evidence that they are coordinating their behavior. When subjects are allowed to engage in unrestricted communication, coordination on high prices occurs whether they
are symmetric or asymmetric. By analyzing chat, we are also able to learn how they
are coordinating which helps shed light on why collusion with price announcements
is relatively ineffective when firms are different.
2
1
Introduction
For firms to successfully collude, they must coordinate their behavior, and coordination requires some form of communication. In practice, this communication can
involve tacking on a few digits to a multi-million dollar bid (FCC spectrum auction)
or announcing future intended prices (airlines) or unilaterally announcing a pricing
strategy (truck rental) or sitting in a hotel room and talking about prices and sales
quotas (lysine). While the last mode of communication is presumably the most effective, it is also the most clearly unlawful. Firms interested in jointly raising prices then
face a tension in that communication which is more likely to result in coordination
may also be more likely to result in prosecution. Hence, they may choose to more
indirectly communicate when it is sufficient to produce at least some collusion.
This trade-off raises two questions that we will examine here. First, what are the
various forms of communication that can produce coordinated collusive outcomes?
In particular, how indirect can communication be and still be reasonably effective?
This question is central to antitrust and competition law and, in spite of a legion of
legal cases that speak to what practices are and are not lawful, there remains a large
gray area where legality is unclear. Second, how does the answer to the first question
depend on the specifics of the market?
These questions are notoriously difficult to examine theoretically because the equilibrium framework cannot speak to the issue of how firms coordinate in moving from
one equilibrium to another which is exactly what is at issue here: What forms of
communication will result in firms coordinating a move from a static equilibrium
with competitive prices to a dynamic equilibrium with supracompetitive prices? Experimental methods offer a comparative advantage in that subjects engage in exactly
the dynamic process of coordination that we are trying to understand. While the
subjects are college students and not managers - and thus extrapolating from experiments to market behavior is always a precarious leap - experimental methods have
more promise than other methods for shedding light on the effectiveness of various
communication practices in producing collusion.
The specific form of those two questions are addressed here are as follows. In
practice, two commonly observed methods of communication for coordinating firm
behavior are advance price announcements (as arose in the ATPCO airlines cases)
and unrestricted communication using natural language (as practiced by all hard core
cartels; for example, lysine, vitamins, and fine arts auction houses). To assess the
relative efficacy of different modes of communication, the research plan is to compare
outcomes when sellers can make price announcements with when they cannot, and
to compare unrestricted communication (through online chat) with price announcements. When are price announcements effective at producing collusion? When is
unrestricted communication particularly effective in producing collusion relative to
price announcements? Answers to these questions will shed light on when we can expect firms to engage in the most egregious form of collusion - involving unrestricted
3
communication - and when they will instead choose less express methods. In considering the relative efficacy of these different forms of communication, the primary
variation in market structure is the extent of firm heterogeneity though the number
of sellers is also examined. While unrestricted communication is surely expected to
be more effective than price announcements, less clear is how the incremental value
of unrestricted communication depends on firm heterogeneity.
Our main findings are that firms are able to coordinate on a high price with
price announcements but only for duopoly and when firms are symmetric. While
price announcements do result in higher prices for an asymmetric duopoly, there is
only weak evidence that they are coordinating their behavior. When firms engage
in unrestricted communication, coordination on high prices occurs whether firms are
symmetric or asymmetric and regardless of the number of firms. We also investigate
how they are coordinating with unrestricted communication which helps explain why
collusion with price announcements is relatively ineffective when firms are different.
Section 2 provides a review of experimental work pertinent to the current study;
specifically, oligopoly experiments for which sellers can communicate and those for
which sellers are heterogeneous. For the reader who just wants the executive summary
of that literature and how it relates to the current study, s/he can jump to Section
2.3. Section 3 describes the theoretical model underlying the experiment and derives
equilibrium predictions, while the experimental design is provided in Section 4. The
results from the experiments are described and discussed in Section 5.
2
Literature Review
Pertinent to this study, we will review oligopoly experiments that speak to either
of two questions. First, in an oligopoly setting, what is the impact of communication among firms about price or quantity intentions on the frequency and extent of
supracompetitive outcomes? Second, what is the impact of firm heterogeneity on
the frequency and extent of supracompetitive outcomes? Our review will begin with
experiments pertinent to addressing the first question - which is quite voluminous and then discuss experiments that address the second question - which is relatively
sparse. There are no experiments that address the interaction of communication and
firm heterogeneity on outcomes, which is the primary focus of the current study.1 Recent reviews of the literature on communication of intentions in an oligopoly include
Cason (2008), Normann (2008), Haan, Schoonbeek, and Winkel (2009), and Potters
(2009).
1
With the exception of Harstad, Martin and Norman (1998), all studies that allow for communications among subjects have assumed identical firms. However, that study does not vary the extent
of asymmetries and thus cannot address the questions of the current study.
4
2.1
2.1.1
Communication of Intentions in Oligopoly Experiments
Experimental Design
Experiments that allow for communication of intentions differ in many features. These
differences pertain to the communication protocol (that is, exactly how subjects are
allowed to communicate), market features, and model features. Market features are
defined to be those that correspond to sources of variation in real world markets
and thus one could say that two experiment that differ in terms of market features
actually pertain to different real world markets. In contrast, model features concern
artificial elements of a model that, in practice, do not pertain to sources of variation
in real world markets.
In terms of market features, experiments have assumed subjects engage in a price
game (that is, prices are simultaneously selected and firms produce to meet demand),
a quantity game (and price is set to equate supply and demand), or a price game
with a maximal number of units (that is, a firm produces to meet its demand up
to the maximal quantity it selected). When price is selected, the market institution
is almost always posted price but there are a few experiments that have specified a
double oral auction.2 While most experiments assume two sellers (or subjects), some
allow for more (as many as eight) and may examine the impact of the number of sellers. Products may be either homogeneous or differentiated, and market demand may
be perfectly inelastic or responsive to price (using a linear specification). Subjects
interact in a single market with the exception of one study that has subjects compete
in three markets in order to create multi-market interaction (Cason and Davis, 1995).
Most experiments assume complete information (all profit functions are known to all
sellers) but a few allow for private information; for example, a seller’s cost is private
information and a buyer’s valuation is private information.3 Finally, a number of
experiments have investigated the effect of competition policy for cartels by introducing probabilistic penalties if subjects choose to communicate, as well as leniency
programs (in which case a subject can avoid a penalty by turning in the other subjects
involved in the communication).
Turning to model features, subjects may be given either a profit function or a profit
table. A profit function means a mathematical formula for calculating a subject’s
profit once inserting the actions (price or quantity) of all subjects; while a profit
table (for a two subject experiment) is a matrix in which rows are a subject’s own
action, columns are the other subject’s action, and an entry in a cell is a subject’s
profit. Experiments may also vary in terms of the size of the choice set. They range
from as few as two actions or prices (Andersson and Wengström, 2010) to as many as
101 prices (Fonseca and Normann, 2012). Demand can be either automated or live.
2
A double oral auction has sellers post prices at which they are willing to sell, buyers post prices
at which they are willing to buy, any seller can accept an outstanding buyer offer, and any buyer
can accept an outstanding seller offer.
3
In that case, communication can extend beyond intentions though it is still cheap talk.
5
Most common is an automated specification in that there is a deterministic demand
function that maps from prices for firms into the number of units for each firm. In
a few experiments, buyers are live in that they are also subjects. There are either 3
or 4 buyers who are endowed with a valuation and receive a monetary payment that
is proportional to the surplus received on a purchase; that is, the valuation less the
price paid.4
Finally, a key model feature to any experiment designed to explore collusion is
how the horizon is modelled. Theory predicts that collusion will not emerge in a
finitely repeated game in which the stage game has a unique Nash equilibrium. Most
experiments have assumed an indefinite horizon whereby the experiment runs for
some number of periods for sure (say, 20) after which, in each period, a random
device determines whether the experiment goes another period (for example, a role
of a die whereby the experiments end when 1 is rolled). That random process is
enacted in each period until termination occurs. However, some experiments assume
a long but finite number of periods. Though theory does not predict any collusion
in those experiments, there is ample experimental evidence that cooperation does
emerge. With that model feature, it is common to exclude the last few periods in
order to prevent conclusions being contaminated by endgame effects.
An alternative to having an explicitly repeated setting is to simulate it through
a two-stage design, as is done in Andersson and Wengström (2010) and Cooper and
Kühn (2011). In the first stage of Cooper and Kühn (2011), subjects play a price game
where there are three prices (Low, Medium, High). The unique Nash equilibrium is
both firms price Low and joint profit is higher if both were to price Medium and is
higher yet if both were to price High. After playing that game (just once), subjects
observe the stage 1 choices and then place a coordination game in stage 2. This
coordination game has three actions (L, M, H) and all are symmetric Nash equilibria.
These equilibria are Pareto-ranked and the payoff from (L,L) is (for some discount
factor) equal to the present value of playing (Low, Low) forever from the stage 1
game. Similarly, the payoff from (M,M) equals the present value of playing (Medium,
Medium) forever and the payoff from (H,H) equals the payoff from playing (High,
High) forever. Thus, if players go to (L,L) in stage 2, it can be interpreted as the
grim punishment (static Nash equilibrium forever), while going to (M,M) or (H,H) is
like collusion ad infinitum.5 It is an open question whether results for this two-stage
4
While this is listed as a model feature, one could argue that it is a market feature. Perhaps retail
markets with many small buyers can be thought as having automated buyers, and some intermediate
goods markets with a few buyers is better described by live buyers. However, the more substantive
difference is whether buyers can make counter-offers or must take price as given. Experiments
with double oral auctions (all of which involve live buyers) are better models of intermediate goods
markets with large buyers, while those with posted price (sellers make take it or leave it offers) are
a better representation of markets with many small buyers.
5
Analogously, Andersson and Wengström (2010) have two actions (L, H) in the stage 2 game and
both are symmetric Nash equilibria which are Pareto-ranked with the same relationship between
(L,L) and (Low,Low) forever and (H,H) and (High,High) forever.
6
design are similar to those for an indefinite horizon.
We conclude this summary of experimental design by describing the many different
communication protocols that have been used. We have partitioned them into four
categories: Simple Price Announcement, Iterative Price Announcement, Strategy
Announcement, and Chat. To be clear, in all of these cases the announcements are
non-binding. A Simple Price Announcement (SPA) protocol involves one or more
subjects announcing a price and possibly subjects responding to an announcement
by affirming or rejecting it. The canonical case of a SPA protocol is when all subjects
announce a price each period prior to then selecting a price (for example, this is
one of the protocols in Cooper and Kühn, 2011). The timing is a bit different in
Cason (1995) and Cason and Davis (1995) where, in one treatment (referred to as
Discrete), each subject chooses a price (and maximum quantity) for the current period
and announces a price (and maximum quantity) for the ensuing period. In their
Continuous treatment, subjects can announce as many prices as they like during
a one (or two) minute period where the last price announced is the actual price
charged.6 Harstad et al (1998) also allow for multiple price announcements but do
not place an upper bound on the length of the announcement phase; it goes until
there has not been a message for some specified length of time (initially, two minutes
and then 30 seconds in later periods). In addition to a treatment in which prices
are announced, they have a more structured communication treatment in which price
changes are announced (relative to the preceding period’s price) and where subjects
can respond with "match" or "no match" to any such announcement (again, nonbinding). A relatively structured protocol is also used in Holt and Davis (1990) where
one selected subject makes an announcement of the form: "$_ is an appropriate
price for the market for this period." and the other two subjects simultaneously and
independently reply with either "agree," "disagree and price should be lower," or
"disagree and price should be higher." Prices are then selected.
An Iterative Price Announcement (IPA) protocol has the property that the communication phase has multi-stages and the messages that were sent in an earlier stage
restrict the messages that can be sent in the current stage. In Bigoni et al (2012),
two subjects are asked to choose a "minimum acceptable price" from the price set
{0 1  12} which is then shared with the other subject.7 In round 2 of the communication phase, subjects again choose a "minimum acceptable price" but where the
selected price message must be at least as great as the lowest price message in the
previous round. This process applies to all rounds in the communication phase. Thus,
the message space weakly contracts during the communication phase which lasts for
30 seconds, after which price is chosen (unconstrained by what was conveyed dur6
This is the one protocol in which messages are not purely non-binding in that the final message
is the actual price. However, if it is clear what is the last moment at which a price can be selected
then that "last moment" is the "transaction price" phase and all preceding "moments" comprise
the "price announcement" phase.
7
Also see Bigoni et al (2013).
7
ing the communication phase). Hinloopen and Soetevent (2008) engage in a similar
process but, in addition, have a "maximum acceptable price" and consider the intersection of subjects’ sets rather than the union as in Bigoni et al (2012). Specifically,
three subjects announce a lower and upper bound to price (which could be the same
so that it is a single price). If there is a non-empty intersection of these three sets then
there is a second round in which again subjects announce lower and upper bounds
but now from that intersection. This process continues until there is a single price or
the intersection is empty or a minute transpires, whichever occurs first. In both of
these studies, the purpose for restricting communication in this manner is to make
the environment more amenable to producing collusion. As their primary objective
is to investigate the effect of fines and leniency programs, if the experiment produced
very little collusion then it would be difficult to assess the effect of these programs
with a reasonable number of runs. However, one wonders to what extent the properties of collusive outcomes are influenced by an artificially constrained communication
process.
The Strategy Announcement (SA) protocol is where subjects announce not a price
but a strategy for the game or, more generally, some set of contingency plans. This
protocol is only used in Andersson and Wengström (2010) and Cooper and Kühn
(2011) whose simple two-stage game structure with two and three actions, respectively, makes for a simple strategy space. Andersson and Wengström (2010) assume
a subject announces prior to stage 1 what action it will take in the stage 2 game
depending on the action chosen by the other subject in the stage 1 game. In Cooper
and Kühn (2011), strategy announcements prior to the stage 1 game are contingent
on both subjects’ actions in stage 1; specifically, subjects are prompted with: "if we
choose the preceding [actions I think should be chosen] in period 1, I think we should
choose the following in period 2" and "if we DO NOT choose the preceding [actions I
think should be chosen] in period 1, I think we should choose the following in period
2." (They refer to a period what we are calling a stage.) Another distinction between these two studies is that strategy announcements are simultaneous in Cooper
and Kühn (2011), while Andersson and Wengström (2010) impose a sequential structure in which one subject is randomly selected to send an initial message which the
other subject reads before sending a message (that sequential structure is enacted
only when both subjects choose to send messages). They rationalize this sequential
structure on the grounds that it helps to avoid miscoordination.
Finally, the Chat protocol allows for either oral or written communication using
natural language with only minimal restrictions such as no profane language, not
offering side payments, and not making threats. Friedman (1967), which is the first
oligopoly experiment to allow for unrestricted communication, had a limited number
of rounds of communication by virtue of the need to hand carry messages:8
A period consisted of each subject sending two messages to the other,
8
Friedman (1967), p. 385.
8
then each choosing his price. One subject was designated to send the
first message. The second would read and reply. A second round of
messages would ensue after which the first subject would choose a price,
then the second would do so. The messages were carried back and forth
by a project assistant. After collecting both prices, he would inform each
of the price charged by the other; then the next period would begin. If
someone wanted to send no message, he was instructed to write an X.
Some later studies - such as Issac and Plott (1981) and Issac, Ramey, and Williams
(1984) - moved to face-to-face communication. In those experiments, the subjects
gathered at a table between periods to engage in a time-constrained conversation
(four minutes in Issac et al, 1984). Subsequent studies have made the standard
chat protocol to be written and anonymity-preserving as in Friedman (1967) though
now it is conducted through computers in the form of instant messaging with the
requirement that subjects do not provide identifying information. Typically, there is
an upper bound on the chat phase of 1-3 minutes which generally proves ample as
revealed by a content analysis of chat. A unique feature of Anderson and Wengström
(2007) and Cooper and Kühn (2011) - again associated with their two-stage design is that they consider two Chat protocols. One protocol only allows communication
prior to the stage 1 game; thus, it provides an opportunity to coordinate. The second
protocol also allows for communication prior to the stage 2 game. Since the outcome of
the stage 2 game is intended to correspond to continued cooperation or a punishment
(in the event of non-compliance with the collusive outcome), communication prior to
it allows for the possibility of renegotiation which can then undermine the credibility
of any punishment discussed during the pre-play communication phase of the stage
1 game.
An additional dimension to any communication protocol is whether communication is free or costly. Most experiments assume it is free but a few involve a direct
or indirect cost. Using a SPA protocol, Anderson and Wengström (2007) assumes
one subject decides whether to propose a price and, if so, what price to propose; any
proposal incurs a cost to that subject. In the event there is a price proposal, the
other subject can, at a cost, either accept or reject the proposal, or it can not reply
which incurs no cost. Apesteguia, Dufwenberg, and Selten (2007), Hinloopen and
Soetevent (2008), Dijkstra, Haan, and Schoonbeek (2011), and Bigoni et al (2012) all
assume an indirect cost. In those experiments, a communication phase is preceded by
a pre-communication stage in which all subjects decide whether or not to engage in
the communication phase. If and only if all subjects choose to do so is there a communication phase, which involves an IPA protocol in Hinloopen and Soetevent (2008)
and Bigoni et al (2012) and a Chat protocol in Apesteguia, Dufwenberg, and Selten
(2007) and Dijkstra, Haan, and Schoonbeek (2011). Furthermore, if all subjects have
chosen to communicate then they all become liable for probabilistic monetary penalties. Thus, the cost is not per message - as in Anderson and Wengström (2007) - but
rather is an expected fixed cost associated with the decision to communicate. These
9
studies are interested in exploring the effect of competition policy - in particular, corporate leniency programs - and thus have created a model encompassing the illegality
of communication with its associated penalties.9
2.1.2
Results
Before describing results for when subjects can communicate, let us begin by stating
a robust finding from the voluminous literature on oligopoly experiments without
communication. These studies consistently find that prices are often above static
Nash equilibrium levels but only if there are two sellers. The evidence is overwhelming
that duopolies are able to tacitly collude. A recent study (Rojas, 2012) even showed
that tacit collusion can occur when demand is changing over time, and subjects prove
quite sophisticated in adjusting their behavior to the current state of demand.10
Summarizing the literature on collusion without communication, supracompetitive
outcomes are common when there are two subjects, very rare with three subjects,
and non-existent with four or more subjects; see, for example, Huck, Normann, and
Oechssler (2004) and the review paper of Engel (2007).11
In summarizing oligopoly experiments with communication that use a SPA protocol, Cason (2008) accurately states: "Although price signaling often increases transaction prices, this increase is very often temporary. [Steady-state] behavior may be
unaffected by non-binding price signaling in many environments." Allowing subjects
to announce prices does raise the average price but the effect largely occurs early on
as prices eventually decline. By the end of the experiment, price has often returned
to the no communication benchmark level though may also remain above it (which
could be an artifact of ending the experiment before this declining price path has converged). Subsequently, there have been only two papers using a SPA protocol; one of
which confirms this finding and the other does not (but, as will be described, makes
9
Apesteguia et al (2007) is singular in that it does not provide repetition of interaction (or
simulate it as in, say, Cooper and Kühn, 2011) and thus rely on collusion emerging in a one-period
structure. Specifically, they assume sellers simultaneously decide whether to form a cartel and, if
and only if all sellers choose to form a cartel, then they have unrestricted chat. Sellers then choose
price. If they did form a cartel, sellers then simultaneously decide whether to report the presence
of a cartel.
10
It is important to note that this occurs in a simple environment with only three actions in the
stage game.
11
Singular in the literature on oligopoly experiments, Friedman et al (2012) finds collusive outcomes regularly emerge with three subjects. They consider a repeated quantity game in which
subjects know the game is symmetric but do not know payoff functions. A unique feature of the
experimental design is that periods are only 4 seconds in length and paired interaction occurs for
400 periods; in comparison, 40 periods is a long horizon in other experiments. Consistent with
previous experiments with low information, they find that quantities lie between static Nash equilibrium (Cournot) and Walrasian (perfect competition) levels for the first 25 periods. However,
when interactions get into the range of 50 periods, quantities start falling and eventually are close
to monopoly levels for duopolies and lie between monopoly and Cournot levels for triopolies. Thus,
quite contrary to preceding work, collusive outcomes arise and persist with three sellers.
10
a substantive change in the structure). Recalling the two-stage design of Cooper and
Kühn (2011), they find this pattern either when subjects announce stage 1 prices
or announce strategies (prices for stage 1 and contingent actions for stage 2). With
the first protocol, around 37% of subjects choose the High price in the first round
(and recall that there are only three prices) - compared to 15% when there is no
communication - but that steadily falls to where it is under 5% after 8 rounds of the
experiment which is not far from under 2% for the no communication treatment.12
The High price is chosen more frequently when subjects announce strategies but
there is still the same deterioration of collusion though around 12% of subjects are
eventually choosing High, which is above that for when subjects are not allowed to
communicate. In sum, Cooper and Kühn (2011) finds, for a quite different experimental design, that experience tends to undermine collusion when subjects engage in
very restricted communication in the form of price announcements.
An exception to that finding is Anderson and Wengström (2007). Recall that
they assume one subject is randomly selected to propose a non-binding price (or say
nothing) and the other subject, in the event there is a proposed price, either accepts
or rejects or does not respond. These messages are non-binding and are costly. For
the no cost treatment, the usual pattern is observed with prices starting high and
then declining.13 When messages are costly (and there is a low cost and high cost
treatment), prices tend to start at around the same level as the zero cost treatment
but, by the end of the experiment, are not lower. When messages have a low cost,
prices initially decline but then recover. With the high cost treatment, prices initially
rise, then decline, and recover. It is difficult to interpret the pattern but it is clear
that making messages costly can allow price announcements to sustain prices higher
for a longer time compared to when messages are free. This result seems consistent
with the theory of forward induction in that those subjects who are more confident
about supracompetitive prices being coordinated upon will incur the cost of sending
messages. Thus, the messages themselves are more informative.
The general finding for experiments with a SPA protocol are roughly confirmed
by the two studies using an IPA protocol. Conditional on all subjects choosing to
communicate (so that there is a communication phase), both Hinloopen and Soetevent
(2008) and Bigoni et al (2012) find that prices start high and tend to decline over time.
A comparison with the prices for the no communication treatment is a bit precarious
because the communication treatment also comes with probabilistic penalties and
thus costly communication (though of a very different variety than Anderson and
12
It is important to point out that what "additional rounds" means in Cooper and Kühn (2011)
is different from other experiments with a repeated game structure. In other experiments, it means
more periods in which the same two subjects choose price. In Cooper and Kühn (2011), each round
involves the two-stage game which is designed to simulate an indefinite horizon game. Thus, multiple
rounds means multiple indefinite horizon games where, with each round, subjects are randomly
matched. The two features are related in that both involve more experience.
13
As there was no treatment without communication, we do not know whether price converged
to the level for when communication is not allowed.
11
Wengström, 2007). Nevertheless, prices do seem to converge to the levels for the
no communication treatment in Hinloopen and Soetevent (2008) and in Bigoni et al
(2012) except for one competition policy treatment.14
Finally, we come to results for the Chat protocol. Quite contrary to the other protocols, unrestricted communication between the subjects is shown to be extremely
effective at producing successful collusion. Supracompetitive prices are frequent, are
at a high level (though often below the monopoly price), and persist over time. This
finding is true for almost all of the studies including Friedman (1967), Issac et al
(1984), Davis and Holt (1998), Cooper and Kühn (2011), Dijkstra et al (2011), and
Fonseca and Normann (2012). While having more sellers tends to reduce prices - just
as with the no communication treatment - prices are still well above "no communication" levels even when there are as many as eight sellers (Fonseca and Normann,
2012).
Figure 1 from Fonseca and Normann (2012)
To observe the striking effect of unrestricted communication, consider Figure 1
from Fonseca and Normann (2012) which reports average price across experiments
with communication (Talk) and without communication (No Talk) and when the
number of sellers ranges from 2 to 4 to 6 to 8. Goods are identical, the monopoly
price is 100, and the static Nash equilibrium price is 0. Without communication,
prices are very close to the competitive price when there are 4, 6, and 8 subjects
but, when there are two sellers, prices are half way between the competitive and
monopoly price. This is consistent with the body of work on oligopoly experiments
without communication which finds that tacit collusion is common but limited to
14
The latter statement is based on private communication with Maria Bigoni (28 December 2012).
When a firm that reports a cartel is given a reward (in addition to avoiding the penalty) then prices
remain above levels for the no communication treatment.
12
the case of two sellers. When subjects can engage in unrestricted chat, prices are
vastly higher. Even when there are eight sellers, price has risen more than half of the
difference between the monopoly price and the price without communication.15
Davis and Wilson (2002) use a common metric to measure the impact of communication which is the Monopoly Effectiveness Index (MEI). MEI is defined as (realized
profit - competitive profit)/(monopoly profit - competitive profit), where competitive
profit is that associated with the static Nash equilibrium. MEI measures the fraction
of monopoly profit that is captured. By the end of the sessions in their study, the
MEI was .7 higher in the communication treatment than when communication was
not allowed. This large effect of communication is also reflected in the commonality
of prices. Without communication, identical prices from all four sellers are observed
in only 3 out of 40 periods (where data is used from the last 10 periods for the four
sessions run). With communication, prices are identical in 9 out of 10 periods in 3
out of 4 sessions.
Figure 1 from Cooper and Kühn (2011)
To compare Chat with price and strategy announcements (as well as when there
is no communication), Figure 1 from Cooper and Kühn (2011) is reproduced. Recall
that they have a two-stage design that simulates a repeated game setting. In each
round, subjects are randomly matched to play the two-stage game. Results are reported for rounds 10-20 where all subjects were engaged in the no communication
15
Fonseca and Norman (2012) interestingly find that the incremental value to communicating is
highest with 4 sellers. The incremental value is measured by the difference in price (and profit)
between the communication treatment and the no communication treatment. Though the price
with communication is highest with two subjects, it is also relatively high without communication.
However, when there are 4, 6, or 8 subjects, the no communication price is very close to the static
Nash equilibrium price. Thus, the incremental gain from chat is higher with 4 subjects than with
2 subjects. It proves to be higher with 4 than with 6 or 8 because the supracompetitive price with
communication declines reasonably fast with more subjects.
13
(N) treatment through round 10. Starting with round 11, new treatments were introduced: price announcements (P1), strategy announcements (P1C), chat prior to
stage 1 (Pchat), and chat prior to both stages 1 and 2 (Rchat). For each round, the
percentage of subjects who selected the High price in stage 1 (or period 1) is reported.
Price announcements initially involve higher prices (relative to the no communication
treatment) but then it steadily declines. When subjects can chat, prices start high
and generally remain high.
There are two studies - Issac and Plott (1981) and a particular treatment in
Davis and Holt (1998) - that do not find that unrestricted chat produces strong and
stable collusive outcomes, but both of them have unique features that a priori one
would suspect would make collusion more difficult. Both of these studies assumed
live buyers; for example, Davis and Holt (1998) had three sellers and three buyers. In
their treatment of three minutes of open chat (after which sellers would post prices),
Davis and Holt (1998) found sellers to price close to the monopoly level. Now modify
this design so that, after prices are posted, a seller can offer a discount to a buyer
and this discount is never observed by the other sellers. For 5 out of 6 groups, any
initial collusion collapses and prices end up approaching the competitive level. While
posted (or list) prices are close to the monopoly level, transaction prices are much
lower. That collusion is more difficult with those hidden discounts is not surprising
as the environment is now one of imperfect monitoring in that a seller’s past prices
are not publicly observed by all sellers.16 Issac and Plott (1981) assume a double
oral auction so both sellers and buyers make offers. Successful seller collusion was
not observed in that setting. Issac et al (1984) used the same experimental design
and compared prices with the posted price format (only sellers make offers which
buyers accept or reject) with those for the double oral auction and find that prices
are higher under the posted price format and that chat is effective at producing high
and sustained prices. It would then seem that the active role by buyers in the double
oral auction format made collusion by sellers difficult in spite of the availability of
unrestricted communication.
On a related issue, Andersson and Wengström (2010) and Cooper and Kühn (2011)
explore whether the opportunity to communicate before a possible punishment phase
makes collusion more difficult. This is a test of the theory that renegotiation makes
punishments less credible which then undermines the collusion that is erected upon
a threatened punishment. Interestingly, their findings are in conflict. Andersson and
Wengström (2010) compares outcomes for two communication protocols: 1) pre-play
communication prior to stage 1 in which each subject announces the action s/he will
take in stage 2 depending on what action the other subject chose in stage 1; and 2)
the preceding protocol augmented with pre-play communication prior to stage 2 in
16
They also find that collusion is more effective when the treatment is altered to allow sellers’ past
quantities sold to be public information. Now, cheating through private discounts can be partially
monitored by observing a firm’s quantity. As a result, 3 out of 6 groups had near-monopoly prices
but prices were still lower than in the original communication treatment without discounts.
14
which each subject announces an action for stage 2. They find that the frequency with
which the high price is chosen in stage 1 is greater when subjects cannot communicate
prior to stage 2. While this result is consistent with the theory that the possibility of
renegotiating a punishment undermines collusion, it is statistically weak. In contrast,
Cooper and Kühn (2011) find that communication prior to stage 2 does not make
collusion more difficult and, in fact, it seems to enhance collusion (compare Pchat and
Rchat in Figure 1 from Cooper and Kühn, 2011). As predicted by theory, the option to
communicate prior to performing a punishment does result in fewer punishments but
it does not harm collusion. It is notable that, contrary to the use of a SA protocol as
in Andersson and Wengström (2010), Cooper and Kühn (2011) allow for unrestricted
chat. Andersson and Wengström (2010) conjecture these different communication
protocols is the source of the difference in results because "even though renegotiation
is profitable in terms of actions," a player might be deterred by "the perceived cost
of a verbal punishment." (p. 16). This does raise an important design issue. While
unrestricted chat is more descriptively realistic of the type of communication that
occurs in cartels, it may also insert forces (such as chastisement and guilt) that could
be irrelevant for market settings.
2.2
Firm Heterogeneity
Within the repeated game oligopoly setting without communication, experiments
exploring the effect of firm heterogeneity have focused on differences in costs. Cost
heterogeneity may be modeled in terms of differences in constant marginal cost, the
steepness of a rising marginal cost curve, or differences in capacities (with a common
marginal cost below capacity). Though the number of studies is limited and the
results are mixed, the tentative conclusion to be drawn is that the presence of cost
heterogeneity (or greater heterogeneity) results in lower prices.
Mason, Phillips, and Nowell (1992) considers a quantity duopoly game with linear demand and heterogeneous constant marginal costs. There are three treatments:
both firms have low cost (LL), one firm has low cost and the other high cost (HL),
and both have high cost (HH). They find that, relative to the joint profit maximizing
supply, industry supply is higher when firms are asymmetric (HL) than when they are
symmetric (LL and HH). Thus, price is lower - relative to the joint profit maximizing
price - when firms are asymmetric. Furthermore, the observed quantities under asymmetry are close to the static Nash equilibrium quantities so there is little apparent
collusion. These findings are confirmed in Mason and Phillips (1997) when there is
private information so each subject knows only his own mapping from quantity pairs
into profit. This lack of information reduces collusion when firms are symmetric but
- given quantities are still close to Nash equilibrium levels when firms are asymmetric
- prices remain higher compared to when firms have different costs.
Consistent with this finding is Fonseca and Normann (2008) who examine a price
game with homogeneous goods. Firms have identical marginal cost but potentially
15
different capacities. Industry capacity is kept constant across the symmetric and
asymmetric treatments. They find that an asymmetric capacity distribution results
in lower prices. Dugar and Mitra (2009) also have a price game with homogeneous
goods but firms have different constant marginal costs and no capacity constraints.
All treatments involve firms with different marginal costs but they allow the degree
of asymmetry to vary. In particular, the cost of the low cost firm is kept the same
and the cost of the high cost firm is allowed to take one of three values.17 The average
price and average lowest price are found to be statistically indistinguishable across
cost treatments and, in the case of a low or medium gap in costs, are above the static
Nash equilibrium prices (so there is some collusion). In this case, more heterogeneity
did not seem to have an effect.
The one study to find that firm asymmetry might actually result in higher prices is
Argenton and Müller (2012). They consider a duopoly price game with homogeneous
goods, linear demand, and a cost function of the form  2 where  is allowed to
vary across firms. A key assumption is that a firm is required to produce to meet
all demand.18 As a result, there are multiple static Nash equilibria. In particular,
there is a range of prices above marginal cost that are equilibria because a firm that
undercuts the price experiences a near-doubling of its demand and thus is forced
to produce and sell many units at a price below its marginal cost. Prices above
the highest static Nash equilibrium price are commonly observed whether firms’ cost
functions are identical or different. There is no evidence that symmetry produces
higher prices and, in fact, there is some evidence that prices are slightly higher in
the asymmetric treatments. In contrasting this finding with the other studies, it is
important to keep in mind the very different structure as reflected in the existence of
multiple static Nash equilibria.
In sum, there are not that many studies that have explored the effect of firm heterogeneity on achieving collusive outcomes. Two studies clearly find that asymmetric
cost functions make collusion less common (that is, prices are lower), one study finds
no effect of increased asymmetry, and one study (with a very different modelling of
the market) finds weak evidence that firm asymmetry makes collusion more common.
2.3
Summary of Findings and Open Questions
The following results are distilled from the literature:
17
Given that the static Nash equilibrium price is the price just below the high cost firm’s cost (for
the parameter values used in the experiment), it would have been a better design to hold fixed the
cost of the high cost firm and vary the cost of the low cost firm for then the static Nash equilibrium
price would be the same across treatments. As demand is perfectly inelastic with a maximum
willingness to pay of 50, the monopoly price is independent of all firms’ costs.
18
While that is an optimal response when a firm’s marginal cost is constant (assuming price is at
least as high as marginal cost), it is not when marginal cost is increasing. As they note, there are
some market settings for which regulation requires firms to meet all demand.
16
1. Without communication, prices above static Nash equilibrium levels commonly
occur when there are two sellers but very rarely occur with more than two
sellers.
2. Compared to prices when sellers do not communicate, allowing sellers to announce prices results in initially higher prices but then prices decline to levels
mildly above or close to levels when communication is prohibited.
3. Making communication costly tends to raise price.
4. Compared to prices when sellers do not communicate, unrestricted chat produces significantly higher prices that persist over time.
5. Compared to when firms are symmetric, asymmetric costs (tentatively) result
in lower prices.
Pertinent to the current study, the literature has not addressed the following questions:
• What is the effect of firm heterogeneity on the efficacy of communication?19
• What is the effect of firm heterogeneity on the efficacy of unrestricted communication compared to price announcements?20
• Do price announcements allow firms (whether symmetric or asymmetric) to
effectively collude when there are more than two firms?21
3
Theory
In this section, the theoretical model underlying the experimental design is described
along with the predictions coming out of the equilibrium analysis.
19
The only experiment with communication and asymmetric firms is Harstad, Martin and Norman
(1998) but they do not explore the interaction between heterogeneity and communication.
20
This question is of a similar nature to one posed in Fonseca and Normann (2012) in that it
is looking at the interaction of an element of market structure with the relative efficacy of communication. They ask: What is the effect of the number of sellers on the efficacy of unrestricted
communication compared to no communication?
21
The only study with price announcements and more than two firms is Hinloopen and Soetevent
(2008) which has three firms and finds the rise in prices due to communication is temporary. But
they also assume probabilistic penalties and have a very structured communication protocol.
17
3.1
Model
The setting is a market with  ≥ 2 firms offering homogeneous products. Production
of one unit requires one unit of capacity. A firm has an unlimited number of units
of capacity at cost 0 and a limited number at units at a lower cost . These cost
levels are the same across firms but the amount of low cost capacity is allowed to
vary. Firm ’s cost function is then of the form:
½

if  ∈ [0  ]
 () =
0
 +  ( −  )
if   
where  ≥ 0 and 0 ≤  ≤ 0 .
 () is market demand when the lowest price in the market is . Consistent with
the experiments that we conducted, price comes from a finite set Ω ≡ {0 1   }
for some  Also, assume 0 ∈ Ω and 0   It is assumed that market demand
is decreasing in the market price when demand is positive. Define  to be the
monopoly price based on marginal cost of 0 and assume it is uniquely defined:
 = arg max ( − 0 )  () 
∈Ω
It is assumed that the number of low cost capacity units is sufficiently P
small so that
all units are used up at the joint profit maximum; specifically,  ()  =1   ∀ ≤
 22 This condition implies the joint profit maximizing price is   Though firms
may differ in terms of their low cost capacity, they have the same ordering over a
common price and, in particular, agree that  is the most preferred common price.
Firms simultaneously choose price and how much they are willing to supply at
that price. Thus, a pure strategy is a pair ( ) where  is a firm’s price and  is
its maximum quantity, and a firm produces to meet all demand up to . Firm ’s
residual demand is given by
 (1    ; 1    )
⎧
⎧
⎞
⎛
⎨
⎨µ 1 ¶
X
X
⎝ ( ) −
= min 0 max
 ⎠   ( ) −
 −
⎩
⎩ |Γ ( )|
∈∆( )
∈∆( )
X
∈Γ( )−{}
where
∆ (0 ) = { ∈ {1  } :   0 } is the set of firms pricing strictly below 0
Γ (0 ) = { ∈ {1  } :  = 0 } is the set of firms pricing equal to 0
By (1), when firm ’s price is the lowest in the market then its demand is
⎧
⎫
⎨µ 1 ¶
⎬
X
 ( )   ( ) −
max

⎩ |Γ ( )|
⎭
∈Γ( )−{}
22
This assumption is satisfied by the parameters used in the experiment.
18

(1)
⎫⎫
⎬⎬
⎭⎭
so that it equally shares market demand among the lowest priced firms or, when it is
larger, it receives the residual demand after the other lowest price firms supplied the
market according to their maximal quantities. When firm ’s price is not the lowest
in the market then one first subtracts off the supply of the lower priced firms and, if
that is positive, then firm ’s demand is the larger of the remaining demand equally
divided among the firms setting the same price as firm  and the remaining demand
after subtracting off the supply of the other firms setting the same price as firm 23
A key assumption is that a firm’s share of market demand when all firms charge
a price of 0 is at least as large as its low cost capacity:  (0 )  ≥ max {1    } 
024 The key implication is that, in equilibrium, a firm’s residual demand when it
prices at 0 is at least as large as its low cost capacity. In equilibrium, if   0
then it is not optimal for firm  to supply more than  units since for each unit it
sells beyond  , it receives a price less than the cost of producing that unit. Thus, if
 = 0 and firm  is a lower-priced rival to firm  (  0 ) then firm  supplies  25
Thus, subtracting out the supply of firms pricing below 0 , the remaining demand is
X
 
(2)
 (0 ) −
∈∆(0 )
If  = 0 then firm ’s demand is at least (2) divided by the number of firms pricing
at 0 , which is |Γ (0 )|. Hence, firm  has demand at least as large as its low cost
capacity when
⎞
⎛
µ
¶
X
1
⎝ (0 ) −
 ⎠ ≥  
|Γ (0 )|
0
∈∆( )
which can be rearranged to
 (0 ) ≥
X
∈∆(0 )
 + |Γ (0 )|  
0
)
≥ max {1    } then this condition holds for all  ∈
 ∆ (0 ) and for all Γ (0 )
If (

and ∆ (0 ).26
3.2
Static Equilibrium
In the static game, a pure strategy is of the form ( ) ∈ Ω × <+ and a mixed
strategy is a probability distribution over Ω × <+  Let  () denote the maximal
23
In the experimental design, a firm’s expected residual demand equals (1) in that the demand of
firms that charge the same price is sequentially allocated among those firms.
24
This assumption is satisfied by the parameters used in the experiment.
25
0
Note that all firms pricing below
P  are setting their maximal quantity equal to their low cost
0
capacity which, given  ( )  =1  , means that all of them have residual demand exceeding
their low cost capacity.
26
It can be shown that there is not a weaker assumption than  (0 )  ≥ max {1    } that
ensures a firm’s demand at a price of 0 is at least as great as its low cost capacity.
19
quantity associated with firm  choosing price  (whether as part of a pure or mixed
strategy). Note that when   0   () is part of an optimal strategy as long as it
as least as large as residual demand (for all possible realizations of the other firms’
strategies). However, setting the maximal quantity at least as large as market demand
 () weakly dominates setting it below market demand. When  = 0 , a maximal
quantity at least as great as  weakly dominates setting it below  . We will focus
on Nash equilibria in which  () ≥  () when  ≥ 0 .27
Theorem 1 Consider a Nash equilibrium in which  () ≥  () ∀ ≥ 0 in the
support of firm ’s strategy, ∀. Then each firm assigns probability one to prices in
{0  0 + 1}.
It is straightforward to show that there are only two pure-strategy equilibria; one
in which all firms price at 0 and one in which all firms price at 0 + 1.
Theorem 2 Consider a pure-strategy Nash equilibrium (1    ; 1    ) in which
 ≥  ( ) ∀ Then either (1    ) = (0   0 ) or (1    ) = (0 + 1  0 + 1).
There are also mixed-strategy Nash equilibria in which firms randomize over
{  0 + 1}  To characterize them, define
0
 ≡ ³
(0 − ) 
´
∈ (0 1) 
(0 +1)
0 − ) 
+
(


The next theorem provides sufficient conditions for all firms to randomize.
Y
Theorem 3 If (  )−2 
   ∀ then there is a Nash equilibrium for which (   ) =
0
00
00
6=
0
( + 1  )  where  ≥  ( + 1)  with probability
⎛Y

1
⎞ −1
⎜ 6= ⎟
⎟
⎜
⎝  −2 ⎠

and (   ) = (0  0 ), where 0 ≥  (0 )  with probability
⎛Y
27

1
⎞ −1
⎜ 6= ⎟
⎟
1−⎜
⎝  −2 ⎠


The following theorems have not been shown to hold when  (0 ) ∈ [   (0 ))  That case has
some subtle challenges which have prevented us from delivering a characterization theorem.
20
The probability that firm  chooses 0 + 1 is decreasing in   and, given that 
is increasing in  , then the probability is decreasing in its low cost capacity. Y
Note
−2
that if 1 = · · · =  then 1 = · · · =  (= ) and the condition (  )


6=
simplifies to  −2  −1 which is always true given that  ∈ (0 1). By continuity,
the condition also holds when firms’ low cost capacities are not too different. In
addition, if  =Y
2 then the condition becomes 1    ∀ which again is always true.
−2

 holds for some but not all  then, it is conjectured, there is
When 
6=
a Nash equilibrium in which some firms choose 0 + 1 for sure and the other firms
randomize over {0  0 + 1}.
In summary, static Nash equilibrium (for which maximal quantities for prices at
or above 0 are at least equal to market demand) predicts each firm prices at 0 or
0 + 1 and, therefore, the market price is 0 or 0 + 1. For the non-degenerate mixed
strategy equilibrium, a firm’s expected price is decreasing in its low cost capacity but
the effect is small since, for all firms, expected price lies in [0  0 + 1].
3.3
Dynamic Equilibrium
With static equilibria, firms are predicted to price at either 0 or 0 + 1, and that
prediction does not depend on a firms’ level of low cost capacity. Variation in the
amount of low cost capacity does affect payoffs - a firm with one more unit of low cost
capacity can expect to earn an additional 0 −  - but does not influence the prices
that firms set or the quantities they sell (at least for pure strategy equilibria) because
all firms expect to produce at a common marginal cost of 0 . In this sub-section, we
explore how, when firms interact repeatedly, variation in their low cost capacities can
influence behavior.
Assume there is an indefinite horizon in which the probability of continued interaction in the next period is  ∈ (0 1)  In each period, a firm chooses price and a maximal
quantity; let (   ) denote the action pair for firm  in period  A history in period  is
composed of all past prices and maximal quantities selected and quantities sold by all
firms, and a firm’s information set is that
The¡focus will be on¢pure strategies
©  ªhistory.
∞
−1
→ Ω × <+ .
where a pure strategy is of the form  =1 and  : Ω × <+ × <+
Each firm acts to maximizes its expected profit stream and we will examine subgame
perfect equilibria.
To consider equilibrium outcomes in this setting, consider the  firms acting collectively - as a cartel - to result in payoffs that exceed static equilibrium payoffs.
Imagine the cartel choosing an outcome path that maximizes some cartel welfare
function subject to the path being implemented by a subgame perfect equilibrium. A
cartel welfare function can be thought of as a reduced form for firm bargaining. The
question is: For various specifications of the cartel welfare function (that is, preferences) and the subset of equilibrium outcome paths from which the cartel can choose
21
(that is, the choice set), how do the resulting outcome paths depend on a firms’ low
cost capacities? In particular, do firms equally share market demand? Or do firms
with more low cost capacity have more or less market share?
Let us initiate this exploration by considering a specific scenario. Suppose the
cartel welfare function is the objective from the Nash bargaining solution and the
choice set is the set of all stationary outcome paths implementable using the grim
punishment.28 Let us further limit our attention to firms choosing a common price
but possibly setting maximal quantities less than 1 of market demand (though
at least as great as their low cost capacities).29 Thus, the outcome path may have
firms with unequal market shares. If the bargaining threat point is the static Nash
equilibrium when firms charge a price of 0  the cartel’s problem is:
max
(1  )

Y
=1
[( − 0 )  + (0 − )  − (0 − )  ]
(3)
subject to ( 1    ) satisfying:
( − 0 )  + (0 − ) 
 (0 − ) 
≥ ( − 1 − 0 )  ( − 1) + (0 − )  +
 ∀
1−
1−

X
(4)
 =  () 
=1
As specified in (3), the Nash bargaining solution is the outcome that maximizes the
product of the difference between a firm’s profit and its threat point which means
maximizing the product of firms’ incremental gains from colluding. (4) ensures that
the outcome can be generated by a subgame perfect equilibrium in which deviation
from the outcome path results in a static Nash equilibrium price of 0 forever. The
presumption is that firms appropriately set maximal quantities to produce the vector
of quantities: (1    ) = (1    ).30 This problem can be simplified to:
max
(1  )

Y
=1
( − 0 ) 
28
This specification was used in Harrington (1991) for the duopoly case when 1 = 0 and 2 = ∞
(that is, constant marginal cost that differs between firms). Also see Thal (2011) where optimal
punishments are considered.
29
Restricting the analysis to a common price is for purposes of simplification. The result that
is to be derived holds as well if the collusive outcomes considered are allowed to have prices vary
across firms.
30
(4) considers deviations in which a firm undercuts the collusive price. A second type of deviation
is for a firm, which is producing below its demand, to set a higher maximal quantity and thereby
produce more while maintaining the collusive price. It can be shown that this deviation is inferior
to undercutting the collusive price and producing to meet market demand.
22
subject to:

X
( − 0 ) 
 =  () .
≥ ( − 1 − 0 )  ( − 1)  ∀; and
1−
=1
Given that the objective and constraints are independent of firms’ low cost capacities,
the solution must then be independent of those low cost capacities and, therefore, it
is symmetric. Hence, when the process by which firms select a collusive outcome
is described by Nash bargaining and the feasible equilibrium outcomes are those
sustainable by the grim punishment, firm heterogeneity does not matter and the
resulting outcome is symmetric.
While firms’ traits then need not affect collusive behavior, the preceding analysis has considered only one possible model of collusion. There are two general ways
in which asymmetry in firms’ traits could possibly translate into asymmetry in the
collusive outcome. First, firms may care about relative profits and not just absolute
profits. In particular, a firm may not agree to an outcome that has it earn a significantly lower level of profit than other firms. Given that a firm’s profit is increasing
in the amount of its low cost capacity, this would result in an inverse relationship
between a firm’s collusive market share and its low cost capacity share. Thus, firms
may need to coordinate in unequally sharing market demand in order for firms endowed with fewer units of low cost capacity to produce more and thereby reduce the
difference in firms’ profits.
A second way in which asymmetric outcomes could emerge is through the equilibrium constraints. If an equilibrium has, for all histories, all firms producing at least
as much as its low cost capacity then the equilibrium conditions are independent of
the amount of low cost capacity; the additional profit that a firm receives from having
more units of low cost capacity is realized whether it abides by the collusive outcome
or deviates from it. However, consider a strategy profile in which the punishment is
that the deviator produces zero for some number of periods and, after doing so, there
is a return to the collusive outcome. Now equilibrium conditions depend on a firm’s
low cost capacity because a firm with more low cost capacity foregoes more profit
when it produces zero. By affecting the set of equilibrium outcomes from which the
cartel selects, firms’ traits may then result in an asymmetric outcome.
To elaborate on this point, consider the following strategy profile designed to
support a collusive outcome in which all firms set a common price  and firm ’s
share of market demand  () is   If a firm deviates from the outcome path then
the punishment has the deviator choose ( ) = (0 + 1  (0 + 1)) and the nondeviators choose ( ) = (0   (0 )) for one period - so the deviator sells zero and
the non-deviators share market demand at a price of 0 - and then there is a return
to the collusive outcome. This punishment applies whether a firm deviates from the
original collusive path or the punishment path.
There are three equilibrium conditions. First, the equilibrium condition on the
23
collusive path is:
(1 + ) [( − 0 )   () + (0 − )  ] ≥ ( − 1 − 0 )  ( − 1) + (0 − )  ⇒
( − 1 − 0 )  ( − 1) −  (0 − ) 
 ≥
(1 + ) ( − 0 )  ()
(5)
A firm that undercuts the collusive price realizes an increase in profit from the increase
in its demand but then, as part of the punishment, realizes one period of zero profit.
Second, the equilibrium condition on the punishment path when firm  is the firm
that deviated is:
 [( − 0 )   () + (0 − )  ] ≥ (0 − )  ⇒
(1 − ) (0 − ) 
 ( − 0 )  ()
(6)
 (0 + 1) − 2 (0 − ) 
2 ( − 0 )  ()
(7)
 ≥
The deviator is tempted to price at 0  not 0 + 1 in order to have demand that allows
it to sell output from its low cost capacity and thereby earn (0 − )  . It is deterred
from doing so by the prospect of earning zero profit next period rather than collusive
profit. Third, the equilibrium condition on the punishment path when firm  is not
the firm that deviated (and  = 2) is:
¶
µ
 (0 + 1)
0
0
0
( − )  +  [( −  )   () + ( − )  ] ≥
+ (0 − )  ⇒
2
 ≥
When  = 2 a non-deviator can increase its current profit by raising price from
0 to 0 + 1 and sharing market demand with the deviator while still selling its low
cost capacity (now, at a slightly higher price). When  ≥ 3, a non-deviator loses
all demand when it raises price to 0 + 1 because there are other non-deviators still
pricing at 0 ; hence, (7) is absent when  ≥ 3 because compliance by a non-deviator
is automatic.31
In examining how a firm’s low cost capacity influences these equilibrium conditions, first note that (5) and (7) are less stringent when a firm has more low cost
capacity because the punishment from deviating from the outcome path is harsher
for that firm since it foregoes more profit by producing zero for one period. Specifically, if    then the punishment lowers profit more for firm  than for firm 
by an amount equal to (0 − ) ( −  ). By analogous logic, equilibrium condition
(6) is more stringent when a firm has more low cost capacity because the path has
it produce zero in the current period; thus, with more low cost capacity, it is more
31
The latter statement does require that the  − 2 firms pricing at 0 have sufficient capacity to
meet market demand.
24
tempted to lower price to 0 so that it has demand which allows it to sell the output
of its low cost capacity.
Evaluate these equilibrium conditions at the parameter values that will be used in
the experiment -  () = 150 −  0 = 54  = 10  = 8 - and set the collusive price
at the joint profit maximum:  =  = 102 The equilibrium conditions are now:
 ≥
(102 − 1 − 54) (150 − 101) − 8 (54 − 10) 
⇒  ≥ 55531 − 0084877
(1 + 8) (102 − 54) (150 − 102)
 ≥
 ≥
(1 − 8) (54 − 10) 
⇒  ≥ 0047743
8 (102 − 54) (150 − 102)
(150 − 54 − 1) − 16 (54 − 10) 
⇒  ≥ 02577 − 019097
16 (102 − 54) (150 − 102)
As long as  ≤ 41 the binding constraint is the first one which ensures a firm wants
to set the collusive price. Evaluating it at the asymmetric capacities to be used in
the experiment - (1  2 ) = (18 6) - this is an equilibrium if and only if 1 ≥ 403 and
2 ≥ 504 With equal market shares, the low cost firm is amply satisfied - it only
needs a market share of at least 40.3% to find it optimal to set the collusive price but the high cost firm does not have enough market share for it to find it optimal to
abide by the collusive outcome. Thus, if firms use a punishment in which the deviator
sells zero for one period then the joint profit maximizing price is sustainable if and
only if the firm with fewer units of low cost capacity is given more than 50% of market
share. While any amount between 50.4 and 59.7% will work, if, as discussed above,
relative profits are a consideration in the selection of an outcome then the market
share may need to exceed the minimum 50.4% that will ensure stability.
The conclusions of our analysis of dynamic equilibrium are imprecise but perhaps
informative nevertheless. First, there is a wide class of scenarios whereby the collusive outcome is symmetric even when firms have different cost functions (at least
as heterogeneity is modelled here). If firms focus on equilibria in which they always
produce at least as much as their low cost capacity (such as with symmetric equilibria constructed on the grim punishment) and the selection of an outcome does not
depend on relative profits (such as with Nash bargaining) then the prediction is that
the collusive outcome will involve equal market shares. Second, scenarios have been
identified whereby the collusive outcome has the firm with fewer units of low cost capacity assigned a higher market share, but scenarios have not been identified whereby
it is the firm with more units of low cost capacity that is favored. If the selection of
an outcome considers relative profits then the higher cost firm may receive a higher
market share in order to reduce the difference in profits. If the punishment used in
equilibrium has the deviator produce zero for some length of time (and non-deviators
meet demand at a lower price), it is the higher cost firm’s equilibrium condition that
is most stringent which means it may then require providing more market share to
the higher cost firm in order to induce it to set the collusive price. There could,
25
of course, exist punishments whereby it is instead the lower cost firm’s equilibrium
condition that is more stringent, but thus far they have not been found. In sum, the
theory is inconclusive as to whether the firm asymmetries modeled here should result
in symmetric or asymmetric outcomes but, if it does require asymmetric outcomes,
it seems likely to imply that the higher cost firm will receive a higher market share.
4
4.1
Experimental Design
Environment
The experiment consists of a multi-period posted offer market with fixed matching.
If the market has  sellers then  participants are matched and the match is kept
fixed throughout the session. Participants are told that the experiment will last for at
least 40 periods after which there is an 80% chance in each period of the experiment
continuing to the subsequent period. The shortest experiment ran for 40 periods
while the longest lasted for 53 periods. Sellers offer identical products and face
market demand  ( ) = 150 −  , and are informed that the buyers are simulated.32
Each seller’s cost function is a step-function with the low cost step equalling 10 and
the high cost step equalling 54. Seller  is assigned  low cost units and  high
cost units so the cost function is
ª
©
½
10
if  ∈ ©0 1  
¡
¢
ª
 () =
10 + 54  −  if  ∈  + 1   + 
In all treatments, industry capacity is fixed at 24 units of low cost capacity and 180
units of high cost capacity. Thus, market demand and the industry cost curve are as
depicted in Figure 4.1.
Figure 4.1: Industry Cost and Demand
32
There are then 150 computerized buyers with one buyer with a valuation of 150, one with a
valuation of 149, and so forth.
26
In each period, subjects simultaneously choose a price and a maximal quantity (to
be sold). A subject’s total number of units sold equals the minimum of its demand
and the maximal quantity it selected. Subjects are told that low cost units will
be sold first, and any excess demand will not be carried over to the next period.
Sellers only incur costs for the units sold. Subjects have 60 seconds to select a price
and a maximal quantity, and there is only one price-maximal quantity offer posted
by a subject in each period. If a subject choose not to post an offer then s/he
earns zero profits for that period. Once subjects post their price-maximal quantity
offers, the market clears using computerized buyers. Buyers first purchase from the
low price seller until demand or the low price seller’s maximal quantity is reached.
If there is any residual demand, the process is repeated for the next lowest price
seller. This process continues until all demand is met at the prevailing prices or
maximal quantities are achieved. Buyers only purchase units if the price is below
their valuation for those units. In case of a tie, the system alternates between sellers
buying a single unit from each seller (with identical prices) until all available units
are exhausted. Subjects are informed about the tie-breaking rule and that the buyers
are computerized. At the end of each period, each subject learns the price-maximal
quantity offers of all subjects as well as all subjects’ results in terms of units sold
and profit earned. They can also review the entire history at any point in time. The
environment that subjects face is common knowledge; in particular, they all know
market demand, the number of sellers, and each seller’s cost function. Subjects are
provided with a profit calculator where they can input price-maximal quantity offers
for all sellers and learn the resulting profits. They are told: "The profit calculator
allows you to estimate your (and others’) profits. To do so you can input your price
and quantity and make guesses for the other sellers." The calculator allows them to
try various combinations of offers and learn the effect on profits.
By the theory in Section 4, if maximal quantities are not binding then static Nash
equilibrium predicts that firms assign positive probability only to prices of 54 and/or
55. We will take 55 to be the "competitive price." An advantage of having the stepwise marginal cost function is that, contrary to when marginal cost is constant, the
static Nash equilibrium price is not weakly dominated. For example, if there are two
symmetric firms and both price at 55 (and set the maximal quantity at least as high
as 95) then each earns expected profit of
µ
¶
µ
¶
150 − 55
150 − 55
− 12 = 5755
55 − 10 × 12 − 54 ×
2
2
while profit is zero by pricing above 55 (as residual demand is zero) and profit is only
528 by pricing at 54 (and is even lower by pricing below 54).
4.2
Treatments
There are three sources of treatments - number of firms, seller cost heterogeneity,
and information. The number of firms varied between 2, 3, and 4. In the symmetric
27
treatment, all sellers have the same number of low cost and high cost units. The
asymmetric treatment - which was run only for the case of a duopoly - assumes
that both firms have total capacity of 102 units with firm 1 having 18 units of low
cost capacity and firm 2 having 6 units of low cost capacity. The market structure
treatment allows the number of sellers to vary between two, three, and four. The
various market structure and cost treatments are shown in Table 4.1.
Table 4.1: Market Structure and Cost Treatments
Symmetric
Asymmetric
¡  ¢ = 2
¡  ¢= 3
¡  ¢= 4
¡  ¢ = 2
   = (12 90)    = (8 60)    = (6 45) ¡1  1 ¢= (18 84)
2  2 = (6 96)
There are three informational treatments.
• No Communication: All information is common and sellers have access to the
entire history; specifically, sellers can observe all past price-maximal quantity
offers, transaction prices, quantities sold, and profits. Sellers cannot communicate in any form with their rivals. Sellers simultaneously choose price-maximal
quantity offers and have a maximum of 60 seconds to make a decision. If offers
are made earlier, the system goes directly to determining the market outcome
(that is, allocating demand according to the price-maximal quantity offers selected and calculating profit) and informing sellers of the outcome. Sellers also
have the option of not posting an offer by clicking on the “Do not send an offer”
button.
• Price Announcement: Sellers are informed that each period of the experiment consists of two stages. In the first stage (Price Announcement), sellers
simultaneously choose (or not) to make a single non-binding price announcement regarding the price they will select in the market competition stage. Thus,
communication between sellers is exclusively numeric and no additional information can be transmitted. If any sellers choose to announce a price, the announcements are simultaneously released to the other sellers. All sellers know
that all price announcements are non-binding, and that they can choose not to
make an announcement. The first stage lasts for 60 seconds, however, it moves
to the second stage if all announcements are made before the time limit. As in
the No Communication treatment, the second stage has them simultaneously
make price-maximal quantity offers. All information is common and sellers have
access to the entire history, including all subjects’ announcements.
• Chat: Sellers are informed that each period of the experiment consists of two
stages. In the first stage, they can participate in an online chat room where they
can communicate with the other seller(s) for 60 seconds. The communication
protocol is explicitly explained to the participants: “You are free to discuss
28
any aspects of the experiment, with the following exceptions: you may not
reveal your name, discuss side payments outside the laboratory, or engage in
inappropriate language (including such shorthand as ‘WTF’). If you do, you will
be excused and you will not be paid”. After the first stage chat session, they
simultaneously make price-maximal quantity offers. All information is common
and sellers have access to the entire history.
The No Communication treatment describes the usual environment in which firms
can only coordinate by signaling through their actual transaction prices. The Price
Announcement treatment captures a feature of some markets in which firms make
non-binding announcements about future prices. For example, advance price announcements have been deployed and argued to have produced coordinated supracompetitive prices in steel (Scherer, 1980), airlines (Borenstein, 2004), and diesel and
petrol fuel in Taiwan (Fair Trade Commission, 2004). In our experiments, price announcements can only affect seller behavior because buyers are simulated and, even
if buyers were live, they would be irrelevant to buyer behavior. It is then best to
think of the Price Announcement treatment as relevant to markets in which these
announcements are not received by buyers (for example, they occur through a trade
association) or where such information is of little value to buyers. We intentionally
did not allow firms to also announce maximal quantities because such quantity announcements are very uncommon though have occurred in the automobile industry
(Doyle and Snyder, 1999). The Price Announcement treatment is designed to give
firms an instrument by which to coordinate that is short of express communication.
The issue is whether price announcements are sufficiently informative to induce coordinated behavior. Finally, the Chat treatment models explicit collusion in that
firms can engage in unrestricted communications in order to coordinate on a collusive
outcome and engage in an exchange of assurances. The primary objectives of this
study is to assess how effective are price announcements (relative to no communication) for producing supracompetitive outcomes, how effective is chat (relative to price
announcements) for producing supracompetitive outcomes, and how the incremental
value of communication depends on firm heterogeneity.
There are three sources of variation in treatments: market structure (that is,
number of sellers), firm heterogeneity (that is, symmetric vs. asymmetric cost functions), and communication protocol. Table 4.2 summarizes the different combination
of treatments used in the experiments along with the notation we will use when
referring to the treatment. In [ ] is the number of experiments run with that treatment. Given the large number of possible combinations, the market structure-firm
heterogeneity treatments were chosen to make the best use of our budget by avoiding
treatments that were unlikely to provide new information. For example, if  firms
for a treatment yielded competitive results then we did not run the treatment with
29
more than  firms as it is likely to produce competitive results.
Table
Communication
Protocol
No Communication
Price Announcements
Chat
4.3
4.2: Experimental Treatments
Symmetric
Asymmetric
=2
=3
=4
=2
SNC2 [12] SNC3 [8]
ANC2 [13]
SAN2 [12] SAN3 [8] SAN4 [6] AAN2 [12]
SCH2 [12]
SCH4 [6] ACH2 [12]
Procedures
Our subject pool consisted of students from a major American university with a
diverse population. Participants were recruited by email from a pool of more than
2,000 students who had signed up to participate in experiments. Emails were sent
to a randomly selected subset of the pool of students. Subjects were recruited for a
total of two hours. The experiments took place in May 2011. In total, 242 students
participated in 73 duopoly, 16 triopoly and 12 quadropoly experiments.
The instructions were displayed on subjects’ computer screens and they were
told that all screens displayed the same set of instructions. They had exactly 20
minutes to read the instructions (see Appendix B). A 20-minute timer was shown
on the laboratory screen. Three minutes before the end of the instructions period,
a monitor entered into the room announcing the time remaining and handing out a
printed copy of the summary of the instructions. None of the participants asked for
extra time to read the instructions. At the end of the 20-minute instruction round,
the experimenter closed the instructions file from the server, and subjects typed their
names to start the experiment. The interaction between the experimenter and the
participants was negligible.
Average payoffs (including the show-up fee) varied from a low of $18.85 (which
was for triopoly with the No Communication treatment) to a high of $34.35 (which
was for duopoly with the Chat treatment).
5
Results
In this environment, a seller is trying to determine both the optimal price given the
other sellers’ anticipated prices, and what prices it should anticipate being set by
the other sellers. There appears to be a fair amount of learning of the first kind as
reflected in the experimental output and in the messages from the Chat treatment.
In the Chat treatment, even when sellers communicated their intent to maximize
joint profit, there was a lot of discussion about what price would actually achieve
that objective. Presumably, when there is no chat, an individual seller is also trying
to "figure out" the best price, given beliefs as to the other sellers’ prices. What
this suggests is that the experimental output in the early periods is a confluence of
30
learning, competition, and cooperation, while the output in later periods is more
representative of what we are interested in which is competition and cooperation.
Therefore, results will be reported for periods 1-20, 21-40, and 1-40 (recall that the
length of the horizon is 40 periods for sure and is then stochastically terminated).
5.1
Baseline: No Communication
For the No Communication (NC) protocol, Table 5.1 reports the average market price
for the symmetric duopoly (SNC2), symmetric triopoly (SNC3), and asymmetric
duopoly (ANC2).33 In examining these prices, recall that the competitive (static
Nash equilibrium) price is 54-55 and the monopoly price is 102. As reported in Table
5.1, average market price is at least 54 in all treatments so the transaction price is at
least as high as the static Nash equilibrium price. With a symmetric duopoly, average
market price is 66.7 over periods 1-40 and 69.5 for periods 21-40; while it is 61.5 and
63, respectively, for when firms are asymmetric. With a symmetric triopoly, average
market price is 58.5 over periods 1-40 and 56.3 for periods 21-40 which is very close
to the competitive level. Conducting a t-test for the hypothesis that average market
price exceeds a price of 56, it is soundly rejected for a triopoly and soundly accepted for
both symmetric and asymmetric duopolies.34 Examining the histograms in Figure 5.1
for market price, the price distribution has a peak around 55 for symmetric triopoly
and asymmetric duopoly, while the peak is closer to 60 for symmetric duopoly. As we
move from symmetric triopoly to asymmetric duopoly to symmetric duopoly, there
is a shifting of mass to higher prices.
Consistent with previous findings in the experimental literature, supracompetitive
prices occur with two sellers but not with three sellers. We also find for the case of a
duopoly that prices are higher when firms’ cost functions are identical though it is only
barely statistically significant (which is not surprising given only 12 observations). For
periods 1-40, prices are higher under symmetry by 8.5% (= (66.7 - 61.5)/61.5) with
a p-value of .103 (see Table 5.4), and are higher for periods 21-40 by 10.3% (with a
p-value of .128).35
Property 1: For the case of no communication, average market price exceeds the
competitive level in duopoly (symmetric and asymmetric) but not in triopoly
(symmetric).
33
The market price is the sum of firms’ prices weighted by the firm’s market share. The average
market price for a group is the market price averaged across all periods and is the unit of observation
for calculating the average, median, and standard deviation in Table 5.1.
34
In conducing this test, one group (that is, a matched set of subjects interacting for 40+ periods)
is an observation so there are 12 data points.
35
Keep in mind that the degree of asymmetry is rather mild in that firms only differ in the number
of low cost capacity units and, at any relevant symmetric outcome, firms are producing well beyond
their low cost capacities in which case they face the same marginal cost.
31
Property 2: For the case of duopoly and no communication, average market price
is higher when firms have identical cost functions than when they have different
cost functions.
5.2
Signaling: Price Announcements
Now we turn to the central part of the analysis which is assessing the effect of the
communication protocol on behavior and how the communication’s effect depends on
market structure. It is important to emphasize that our interest lies in determining
whether firms collude, and collusion is more than high prices; it is a mutual understanding among firms to suppress competition. Prices could be high, and yet subjects
are not colluding. For example, firms may periodically raise price with the intent of
coordinating on some supracompetitive outcome but never succeed in doing so. High
average prices are then the product of failed attempts to collude. Or sellers may
engage in randomized pricing that periodically results in high prices - thus producing
high average prices - but again there is not the coordination that we would associate
with collusion.36
In the ensuing analysis, sellers are said to be colluding when they achieve high and
stable prices. This could mean they consistently set identical prices, and equally share
demand. Or firms could set different prices with the firm with the lower (but still
high) price restricting its supply so that the firm with the higher price has residual
demand. Or firms could alternate over time with one firm selling to the market and
the other firm pricing itself out of the market or not participating. Recognizing the
different forms that supracompetitive outcomes can take, various measures will be
used in our analysis.
As an initial step let us focus on collusion that takes the form of firms setting
identical supracompetitive prices. To identify the extent to which price announcements make such collusion more common, we will report average market price and two
measures of coordination: the number of periods for which sellers set the same price
(Same) and the longest number of consecutive periods for which sellers set identical
prices (Duration). If sellers achieve a high average price and high measures of Same
and Duration, this is compelling evidence that they are colluding. If sellers achieve
a high average price and low measures of coordination than it could either be that
firms are not colluding or are colluding in a different manner.37
In going from the No Communication to the Price Announcement treatment,
Table 5.2 reports that the average market price under duopoly substantially increases,
whether firms are symmetric or asymmetric. Over periods 1-40, price rises from 66.7
to 76.2 under symmetry (though the p-value is .133, see Table 5.4) and from 61.5
to 67.5 under asymmetry (p-value = .004). For periods 21-40, price rises from 69.5
36
While such randomizing pricing is not predicted by the theory, it appears to fit the pricing of
some groups.
37
Of course, a low average price and high coordination is consistent with competition.
32
to 79.5 under symmetry (p-value = .273) and from 63.0 to 70.6 under asymmetry
(p-value = .017). While the increase in average price is actually larger when firms
are identical - compare 9.9 (or 14.2%) for symmetric firms with 7.6 (or 12.1%) for
asymmetric firms - the standard deviation is much larger under symmetry which may
be why the difference is statistically significant only for the asymmetric duopoly case.
We will return to this point later.
Having the ability to make price announcements proves insufficient to produce
collusion when there are more than two firms. For symmetric triopolies, average
price is 57.7 (periods 21-40) which is close to average price without announcements
(56.3) and to the competitive price (55). Similar results were found in six sessions
conducted with four symmetric firms. In sum, price announcements matter when
there are two sellers - whether symmetric or asymmetric - but not when there are
more than two sellers. The general finding in the literature - collusion in the absence
of communication is unlikely when there are more than two sellers - is robust to
allowing sellers to communicate by announcing prices.
While price announcements are producing distinctly higher average prices for
duopolies, is this collusion? Examining the coordination measures, the evidence is
compelling that symmetric duopolies are colluding, but that is not the case with
asymmetric duopolies. As shown in Table 5.3, there is almost a doubling in the number of periods in which firms in a symmetric duopoly set identical prices; it increases
from 8.3 to 16.1. It is even more impressive if we focus on periods 21-40 where the
frequency of identical prices rises from under 25% of periods (4.6 out of 20 periods) to
more than 50% (10.3 out of 20 periods). The Duration measure tells the same story;
the average maximal number of consecutive periods for which firms set the same price
goes from 2-3 to 8-10 periods. In contrast, price announcements do not produce any
change in the coordination measures when firms are asymmetric. Though, given the
small number of observations, the differences for symmetric firms are not statistically
significant by the usual standards (see Tables 5.5 and 5.6), the evidence is suggestive
that price announcements are producing more coordination.38
Of course, the lack of evidence for increased coordination in asymmetric duopolies
may just reflect the inadequacy of our measures. Same and Duration are designed to
detect coordination on identical prices. Perhaps, due to cost differences, asymmetric
duopolies collude with different prices and choose maximal quantities so as to allocate
market demand, or instead alternate in supplying the entire market. If firms have
settled down to such supracompetitive outcomes then this will be reflected in high
and stable industry profit.
Figures 5.2 and 5.3 report the mean and standard deviation of industry profit over
38
In identifying the presence of collusion, this finding highlights the importance of including
measures of coordination as well as price levels. For example, Fonseca and Normann (2012) find
reasonably supracompetitive prices with duopoly without communication but an examination of the
price series (made available to us by the authors) shows that there is very little coordination. There
is something going on but it is not a straightforward story of tacit collusion.
33
periods 21-40 for asymmetric and symmetric duopolies, respectively, and for both the
No Communication and Price Announcement treatments.39 Collusion is associated
with the northwest quadrant where industry profit is high with low volatility. Examining Figure 5.2, price announcements raise average industry profit for asymmetric
duopolies but there are no observations of high and stable profit (relative to when
firms are not permitted to make price announcements). Instead, price announcements
are causing higher and more variable profit. In contrast, price announcements result
in higher and less variable profit for symmetric duopolies. More specifically, there
are four groups in Figure 5.3 in which profit is high and the standard deviation is
lower than in any of the 12 groups in the No Communication treatment. In sum, we
find clear evidence that price announcements are significantly increasing the extent of
collusion for symmetric duopoly but little evidence that it is doing so for asymmetric
duopoly.
Property 3: When firms can make price announcements then - compared to no
communication - firms in a duopoly set higher prices whether they are symmetric or asymmetric, but firms coordinate more only when they are symmetric.
When there are more than two firms, price announcements do not result in
supracompetitive prices.
Let us make two comments regarding our measures of coordination. First, these
measures look at the mean and standard deviation for periods 21-40. A duopoly
could succeed in colluding late in the horizon and thereby fail to have a high stable
profit in this 20 period window. Inspection of the time series for all of the groups
reveals only two such cases: one symmetric duopoly (SAN2 group 4) and one asymmetric duopoly (AAN2 group 9). They are both examined below. Second, sellers
could be coordinating on an industry outcome with periodicity exceeding one period.
For example, firms could cycle between both setting the monopoly price and both
setting the competitive price which would produce reasonably high industry profit
but with a high standard deviation. Besides the fact that a multi-period cycle would
be both more difficult to coordinate upon and sustain and probably less profitable,
an inspection of prices, quantities, and profits shows no evidence of such a pattern.
There is a rather natural explanation for why price announcements are more effective in producing collusion when firms are symmetric. When sellers have identical cost
functions, a symmetric supracompetitive outcome is focal, and can be implemented
by coordinating on identical prices. However, when sellers have different cost functions, a symmetric outcome is no longer focal. An asymmetric division of industry
profit could be produced in a variety of ways but arguably the most straightforward
is for sellers to set identical prices and unequally allocate market demand, which is
what has been done with many cartels (see Harrington, 2006). For example, if sellers
39
Note that the monopoly profit is 3360, and when all firms set a price of 54 the industry profit
is 1056.
34
wanted to support the joint profit maximum and have the high cost seller receive
60% of market demand, both sellers could charge the monopoly price of 102, which
yields market demand of 48, and have the low cost seller set its maximal quantity
equal to 19, which will result in the high cost seller supplying the residual demand
of 29. However, this collusive outcome requires coordination of prices and quantities.
The difficulty in coordinating on equal prices and unequal quantities in the Price Announcement treatment is that sellers are only allowed to announce prices. Of course,
just because an asymmetric outcome may be the first-best collusive outcome for an
asymmetric duopoly, it does not imply that firms would try to coordinate on it. If it
is perceived to be too difficult then they may decide to go for a second-best solution
of coordinating on identical prices and equally sharing market demand; some collusion is better than competition. However, that is not what we are finding. Under
asymmetric duopoly, sellers are not coordinating on a common price and, with one
exception to be analyzed below, they are not coordinating on different prices either.
It is worth pointing out that, in contrast to other experiments that have allowed
sellers to make non-binding price announcements, the effect of producing more coordinated behavior persists over time.40 Indeed, the results are stronger for periods 21-40
than for periods 1-20. More informative to this point than the aggregate measures
we’ve provided are the price series from the 12 symmetric duopolies in Figure 5.4. In
five out of the 12 groups, sellers eventually had identical prices well above competitive
levels. In four out of those five groups (groups 3, 7, 8, 12), sellers set the same price
for the last 20 or so periods with price at or near the monopoly level for three of them
(it was around 75 for group 7). (Group 9 is also a candidate for inclusion in that set.)
In the other run (group 4), sellers’ prices were common but steadily rising in the last
15 periods as they climbed from the competitive level to the monopoly level. Only
in one group did sellers achieve reasonably stable, common, and supracompetitive
prices to then experience an unravelling whereby prices retreated back to competitive
levels (group 2). Thus, our results show that price announcements can be effective in
producing persistent collusive pricing.
Let us now return to the issue of the high standard deviation for average price for
a symmetric duopoly under the Price Announcement treatment (see Table 5.2). The
price paths in Figure 5.4 reveal that, generally, either sellers set high identical prices
(groups 3, 4, 8, 9, 12) or set prices near competitive levels with some unsuccessful
forays into supracompetitive territory (groups 1, 5, 6, 10, 11). (Group 2 does not fall
into either of those two bins, and group 7 would fall into the first bin except that price
is only 75.) This pattern can also be seen in the market price histograms in Figure 5.5.
For the symmetric duopoly, the distribution has a mode near the competitive price
and one near the monopoly price (both for periods 1-40 and 21-40). In comparison,
there is not this stark dichotomy when firms are asymmetric. The distribution in
40
Recall the assessment of the literature in Cason (2008): "Although price signaling often increases
transaction prices, this increase is very often temporary. [Steady-state] behavior may be unaffected
by non-binding price signaling in many environments."
35
Figure 5.5 for asymmetric duopoly is unimodal for periods 1-40 and far less bimodal
for periods 21-40 than under symmetry.
It is this dichotomy in outcomes for the symmetric duopoly which is producing
a relatively high standard deviation; either firms have great success in colluding or
very little success. Figure 5.6 nicely depicts this distinction between symmetric and
asymmetric duopolies. An observation here is a group’s average market price and the
number of periods for which firms set the same price. When firms are symmetric,
the observations form two clumps; one with low price and low coordination, and the
other with high price and high coordination (with the exception of group 2 which has
high price and low coordination). When firms are asymmetric, there is just one large
clump without any apparent relationship between average price and the frequency
with which firms set the same price.
Having found that collusion in symmetric duopolies is more common when sellers
can make price announcements, it is useful to examine the pattern of announcements
and prices in order to gain some insight into the underlying mechanism responsible
for this finding. It was with this objective in mind that we performed a statistical
analysis of announcements which, however, proved uninformative. This is not too
surprising given that announcements are cheap talk. (Even if announcements do
serve to coordinate behavior in some instances, any regularity could easily be lost
if many announcements are meaningless.) Instead, let us engage in some post hoc
analysis of seller behavior in a few groups, which is suggestive but speculative.
To frame our thinking, consider two hypotheses regarding how announcements
could produce collusion. The first hypothesis is that a seller believes there is mutual
understanding of a desire to collude and the only challenge is to coordinate on a
particular price. In that case, one might expect to observe a seller announce a high
price and, in anticipation that the announced price coordinates expectations, sellers
then price at the announced level. A second hypothesis is that a seller is uncertain
that there is mutual understanding regarding collusion and, therefore, acts cautiously
by announcing a high price but not pricing at that level until the other seller has
made the same announcement. If both sellers are thinking that way then we ought
to observe high prices only when both of them have announced high prices.41
Illustrative of the first hypothesis is group 12 from the symmetric duopoly treatment (see Figure 5.7). After some initial failed attempts at coordinating through
announcements, success occurred in period 24 when firm 1 announced a price of 102
and both firms priced at 102. Thereafter, they priced at that level and, with the
exception of one period, firm 1 preceded it with the same announcement.
Perhaps illustrative of the second hypothesis is group 9 from the symmetric
duopoly treatment. In period 13, firm 2 announced a price of 100 but firm 1 did
not make an announcement, and neither set a high price. Again in period 17, firm 2
41
This latter scenario corresponds with the ATPCO case whereby American Airlines would announce a future price increase and enact that price increase if and only if the other airlines also
announced a future price increase; otherwise, the proposed price increase would be retracted.
36
announced 100. Though firms did not raise prices, firm 1 did respond in periods 18
and 19 with an announcement of 95 though again there was no effect on prices. In period 20, firm 2 priced at 90 even though it made no announcement. Finally, in period
21, both firms announced high prices - firm 1 with 90 and firm 2 with 95 - and firms
coordinated on the lower announcement by pricing at 90. From that point onward,
announcements and prices steadily rose. What differs from the second hypothesis
is that firm 1 raised price in period 20 prior to the simultaneous announcements in
period 21. Thus, coordination of expectations could be due to the price increase in
period 20 and/or the price announcements in period 21.
Another symmetric duopoly, group 4, is interesting. During the first third of
the experiment, announcements were rarely used and, subject to some initially high
prices, prices settled down at competitive levels. Then, in period 15, there was an
attempt to coordinate on higher prices which ultimately failed. Firm 2 announced
and priced at 102 but firm 1 kept price low at 50. In period 16, firm 1 announced 102
but only raised price to 91, while firm 2 continued to price at 102. Firm 2 did not
give up, as it announced and priced at 102 in period 17; again firm 1 kept price below
that level. Prices then gradually declined. A second attempt to coordinate began in
period 25 which proved successful. Firm 1 announced 55 and priced at that level.
Though 55 is the competitive price, firm 1’s purpose may have been to signal to firm
2 that its announcement is an accurate predictor of its price. Firm 1 gradually raised
its announcement while always pricing at its announcement, as did firm 2. From
period 25 to 38, price gradually rose to 102. Every now and then, firm 2 would make
a different announcement but prices always followed firm 1’s announcement. Clearly,
firm 1 emerged as the market leader.
Turning to an asymmetric duopoly, group 9 initially had a lack of success in
coordinating - in spite of firms using announcements - but eventually one firm took
charge and collusion ensued. In period 21, firm 2 (high cost firm) announced 100
and priced at 62 but firm 1 priced at 54 and sold all units. In period 22, firm 2
continued to announce 100 but dropped price to 56. While firm 1 priced at 55, it
limited its supply to 18 units which left residual demand for firm 2; firm 1’s profit
was 810 and firm 2’s was 416. Starting with period 23, firm 1 began announcing. It
announced and priced at 57 and again limited its supply to 18 units, while firm 2
announced 100 but priced at 58. Firm 1’s profit was 864 and firm 2’s profit was 560.
From that point onward, firm 1 gradually raised its announcement, always priced at
its announcement, and always limited its quantity to 18. While firm 2 was pricing
above firm 1’s price, firm 2 always had residual demand due to the limited supply of
firm 1; in fact, firm 2 (who had higher cost) made higher profit along this path. The
steady-state was reached in period 33 and it was characterized by firm 1 announcing
and pricing at 99, firm 2 announcing and pricing at 100, and firms sharing market
demand with firm 1 selling 18 units and firm 2 selling 32 units. The steady-state
profit was 1602 for firm 1 and 1736 for firm 2. This group clearly colluded and was
able to coordinate on different prices and quantities.
37
Summarizing this section, we found that the ability to make non-binding price
announcements produces more collusion - as reflected in stable supracompetitive outcomes - only for symmetric duopolies. In contrast to previous experiments, collusion
persists until the end of the experiment. For symmetric duopolies, if price announcements are able to produce collusion then the collusion is typically considerable in that
sellers consistently set identical near-monopoly prices. While price announcements do
raise average prices for asymmetric duopolies, there is little evidence that sellers are
coordinating; they do not set common prices, and an examination of profit does not
support coordination on an asymmetric outcome (with the exception of one group).
5.3
Express Communication: Chat
Turning to the Chat treatment, collusion is rampant; Figures 5.8 (symmetric) and
5.9 (asymmetric) provide some representative price series. When they can expressly
communicate through written messages, sellers set high and identical prices most of
the time and in almost all groups. From Table 5.2 for the symmetric case, average
price is 91.2 over periods 1-40 (which is 77% of the gap between the competitive and
monopoly prices) and is 98.9 over periods 21-40 (93% of the gap). Even more impressive, the median price is the monopoly price of 102 (periods 21-40). Prices are just
as high when the duopoly has asymmetric firms: an average price of 91.2 for periods
1-40 and an average price of 99.5 for periods 21-40. From Table 5.4, the difference
in price between the Price Announcement and Chat treatments is highly statistically
significant with p-values of .022 under symmetry and .000 under asymmetry (periods
21-40).
We have already noted that, when sellers are symmetric, coordination is higher
with price announcements compared to when there is no communication, and they
are yet higher when sellers can chat. From Table 5.3, when sellers are symmetric, the
percentage of periods for which sellers set the same price (during periods 21-40) is less
than 25% with no communication, is more than 50% with price announcements, and
is more than 90% with chat; these changes are statistically significant. When sellers
are asymmetric, the percentage of periods for which sellers set the same price (during
periods 21-40) is 20-25% with either no communication or price announcements and
jumps to almost 60% with chat. For the case of asymmetric duopolies, the extent of
coordination that emerges with chat is even higher than what those numbers suggest.
As we describe below, some groups successfully coordinate on asymmetric collusive
outcomes. The power of chat for producing collusion is consistent with earlier work.42
Property 4: When sellers can engage in chat then - compared to either no communication or price announcements - sellers set higher prices and coordinate more,
42
We also ran the Chat treatment with four symmetric firms and found it very effective at producing coordinated supracompetitive prices. For five out of six groups, sellers eventually settled on
and persisted with identical high prices of 79, 102 (three groups), and 110.
38
whether they are symmetric or asymmetric. With chat, prices are often at or
near monopoly levels.
An examination of the messages conveyed during chat for asymmetric duopolies
shows, for some groups, a goal of equal profits which has sellers selling different
amounts by constraining demand through maximal quantities; prices may be the
same or different. Equality of profits requires the high cost firm selling more than
the low cost firm and/or selling at a higher price. In any case, the seller charging
the lower price would have to set its maximal quantity below its demand to leave
adequate residual demand for the other seller. To exemplify this point, here are some
communications from three of the 12 asymmetric duopolies.
In ACH2 Group 7, sellers initially seek to equate profit with different prices. In
period 5, the low cost firm is supposed to set a price of 61 and the high cost firm a
price of 72. The low cost firm would then have demand of 89 but it sets its maximal
quantity at 35 and thereby leaves residual demand for the high cost seller. (Note
that they incorrectly expect the high cost seller will have demand of 100 at a price
of 72; residual demand is actually 43.) Again in period 10 they are proposing to set
different prices while supplying the same amount. Later in the horizon (period 28),
they are proposing to set the same price of 98 and set maximal quantities so that the
high cost firm’s market share is 65%.
• ACH2 Group 7
— Period 5
∗ Low cost firm 1: "I got it. you sell 100 units for 72. I sell 35 for 61."
∗ High cost firm 2: "okay"
∗ Low cost firm 1: "so for it looks like i’ll get 1037 and then you get
1038"
— Period 10
∗ Low cost firm 1: "sell 33 for 83 and i do 33 for 67. we both get 1221.
i’ll look for a higher even. nice"
— Period 28
∗ Low cost firm 1: "You sell 37/98. And i sell 20/98. we both get 1672."
In the next group, sellers eventually reached a point at which they are setting identical
prices and allocating 60% of the market to the high cost firm.
• ACH2 Group 12 - Period 36
— High cost firm 2: "you sell 18 at 103 and i sell 28 at 103. itd be 1674 and
1636 respectively"
39
— Low cost firm 1: "okay cool"
— High cost firm 2: "its a little less for you and a little more for me"
The final case is especially interesting in that sellers persisted with different prices
and quantities with the stated objective of equating their profits. The high cost firm
is to price at 82 and the low cost firm at 90. Though the high cost firm has demand
of 68, it sets its maximal quantity at 42 so that it sells 42. This leaves residual
demand of 108 −  for the low cost firm who, by pricing at 90, is able to sell 18 units.
As they correctly calculated, each earns 1,440. Figure 5.10 reports the price and
maximal quantities (when they are binding) and shows that this collusive outcome
was sustained for the last 21 periods of the session.
• ACH2 Group 6
— Period 19 - Low cost firm 1: "do 42 and 82. ill do 18 and 90. we both
win"
— Period 20 - Low cost firm 1: "We will both get 1440 until the end of the
experiment if you follow my advice. Check it out on the calculator."
For the case of asymmetric duopoly, seven of the 12 Chat groups have sellers
eventually set identical prices equal to or very close to the monopoly price, and there
are three additional groups which coordinated on a supracompetitive outcome with
different prices. In the just examined group 6, sellers coordinated on unequal prices
(which are well above the competitive level) and implemented unequal sales quotas.
In two other groups, sellers took turns being the exclusive supplier. In one case, they
alternated between being the low and high priced sellers; in the other, they rotated
setting a price of 102 and not being in the market (that is, not posting an offer).43
Thus, 10 out of the 12 Chat groups with an asymmetric duopoly eventually colluded.
When firms are symmetric, collusion occurred in 11 out of 12 groups.
To pull together this discussion, consider Figure 5.11 which plots Average Market
Price and Same (number of periods for which subjects set identical prices) for the
various groups, and for all communication protocols (periods 21-40). We will focus
on the Chat treatment which are the triangles. A larger triangle means more observations at that point in the space; in particular, there are many observations with
the monopoly price of 102 and 20 periods of identical prices (8 groups in SCH2 and 2
groups in ACH2). Consider symmetric duopolies which is the top figure. 10 of the 12
groups have very high prices and very high coordination; the other two groups have
more moderate coordination and either moderately high or very high prices. By comparison, when firms are asymmetric, there are two clumps (see the bottom figure).
One involves high prices and high coordination - for which there are seven of the
43
A policy of taking turns as the lone supplier does not maximize joint profit because it results in
some low cost capacity not being used in each period.
40
12 groups - and the other has fairly low coordination and, depending on the group,
prices that are modestly high to very high. The presence of this latter group at least
partly reflects coordination without identical prices; specifically, subjects alternate
their prices or set different prices and restrict supply so as to allocate the market.
5.4
Regression Analysis
As a final analysis of the data, panel data regressions were conducted to measure
the effect on market price of the communication protocols and cost structures. The
empirical model is:
0
 =  + 
+ 
0
where  is the market price in group  in period  and 
are dummy variables for
each treatment. Similar to previous studies, we allow for serial autocorrelation of the
disturbance.44 The model was estimated for duopolies and for periods 1-20, 21-40,
and 1-40
Let us begin by assessing the effect of allowing price announcements relative to
the case of no communication. In Table 5.7, DAnn is a dummy variable that takes the
value 1 for the Price Announcement treatment (and value 0 for the No Communication
treatment), DAsym is a dummy variable that takes the value 1 for the asymmetric
cost treatment, and we also have an interaction term for the two treatments.
All estimated coefficients are highly significant. Confirming Property 2, the coefficient on DAsym is negative indicating that, when communication is prohibited, prices
are lower when firms are asymmetric. Permitting firms to make price announcements
raises price by 10 for symmetric duopolies and 7.64 for asymmetric duopolies (using
the estimated coefficients for periods 21-40). Of course, as previously argued, coordination is higher only with symmetric firms. The negative coefficient on the interaction
term DAnn x DAsym supports the claim that indirect communication through price
announcements is a more effective collusive device when firms are symmetric.
Table 5.8 reports estimates that allow us to compare the efficacy of communicating through chat with non-binding price announcements. Express communication
significantly raises price. When firms are symmetric, price is higher by 19.43 and,
when firms are asymmetric, the price increase is 28.71 (using the estimated coefficients for periods 21-40). The positive coefficient for the interaction term supports
the claim that direct communication through chat is a more effective collusive device
when firms are asymmetric, compared to price announcements. Thus, the incremental value to directly, as opposed to indirectly, communicating, is greater when firms
have different cost functions.
Property 5: Price announcements are more effective in producing collusion when
firms are symmetric compared to when they are asymmetric. Relative to price
44
See Mason, Phillips and Nowell (1992), Mason and Phillips (1997), and Argenton and Müller
(2012).
41
announcements, chat is more effective in producing collusion when firms are
asymmetric compared to when they are symmetric.
6
Concluding Remarks
The objectives of this project are to investigate: 1) the efficacy of non-binding price
announcements in producing collusion; 2) the efficacy of unrestricted communication
relative to price announcements in producing collusion, and 3) how the answers to
those first two questions depend on market structure in terms of the number of firms
and firm asymmetries. One main finding is that price announcements clearly increase
the frequency of collusion for a symmetric duopoly but do not facilitate collusion when
there are more than two firms or firms are asymmetric. Though price announcements
do raise average price with asymmetric duopolies, there is little evidence that they
are able to generate stable supracompetitive outcomes. Regarding the efficacy of
unrestricted communication, it is highly effective in producing collusion whether firms
are the same or different and regardless of the number of firms. For all cases, prices
and profits are significantly higher when sellers can engage in express communication
compared to when only price announcements are available. The incremental gain of
direct communication (through chat) compared to indirect communication (through
price announcements) is large for all market structures but especially when firms are
asymmetric and when there are more than two firms.
Our experimental evidence is consistent with the following two hypotheses. First,
indirect communication through price announcements is sufficient for producing collusion in symmetric duopolies. Supportive evidence is that collusion is commonly
observed when firms in a symmetric duopoly can make non-binding price announcements. Second, express communication is necessary and sufficient for producing collusion when firms are asymmetric and/or there are more than two firms. The evidence
for that hypothesis is that collusion is almost universally observed when firms could
engage in online chat, while price announcements rarely produce collusion when there
are more than two firms or firms have different cost functions. Of course, the validity
of these hypotheses remains open. Regarding the second hypothesis, there may be
forms of indirect communication other than price announcements which would produce collusion. Also, while price announcements produced little collusion for asymmetric duopolies, higher prices were observed which may indicate failed attempts at
colluding. Perhaps the addition of quantity announcements would be sufficient to result in collusion in that case. At the same time, the asymmetry in our experiment is
very mild so it is rather striking that price announcements are insufficient to produce
coordination.
In terms of future research, there is more to be done in terms of allowing for
different firm asymmetries and communication protocols. The cost asymmetry could
be more extensive by assuming it applies to all units. Other forms of asymmetry to
consider are capacity and product differentiation. It is especially important to inves42
tigate other types of non-express means of communication such as the announcement
by a seller of a strategy. Such messages were the basis for at least two Section 5
"invitation to collude" cases pursued by the U.S. Federal Trade Commission in recent years. Finally, some experiments have allowed for probabilistic penalties when
sellers choose to engage in online chat in order to simulate the penalties imposed by
antitrust and competition law. Our design could be modified to make online chat
an option. Sellers could then seek to "legally" collude through price announcements
or "illegally" collude through online chat. We could then assess the types of market
structures for which sellers opt for express communication.45
43
7
Appendix A: Proofs
Proof of Theorem 1. Let us first show that 0 is a lower bound on the support of
a Nash equilibrium strategy. Let  denote the lower bound of firm ’s support and
suppose, contrary to the theorem, that, for some    0 and, wlog,  ≤  ∀ 6= .
It is immediate that equilibrium requires  ≥  Given that   0 then firm  sets
´
³
 =  and realizes profit of  −   . Alternatively, consider it pricing at 0  All of
those firms that price lower than 0 will, in equilibrium, set their maximal quantity
equal to their low-cost capacity. Hence, firm ’s demand at a price of 0 is at least
⎞
⎛
¶
µ
X
1
⎝ (0 ) −
 ⎠ 
(8)
|Γ (0 )|
0
∈∆( )
0
)
≥ max {1    } implies (8) is at least as large as  .
The assumption that (

0
Hence, if firm  prices at   it can expect to sell at
³ least ´ units which means its
0
profit is ( − )  . Given that this profit exceeds  −   from pricing at  , it
contradicts  ( 0 ) being part of an equilibrium strategy. We conclude that a Nash
equilibrium must have  ≥ 0  ∀. (Note that this property did not use the condition
that  () ≥  () ∀ ≥ 0  ∀.)
Next let us show that 0 + 1 is an upper bound on the price support. For this
purpose, let  denote the upper bound to the support of firm ’s price strategy and
suppose   0 + 1 and, wlog,  ≥  ∀ 6= . Let  denote the probability that all
firms (other than ) price at  . Note that equilibrium requires   0 for if  = 0
then firm ’s payoff from a price of  is zero, when it could earn positive profit of
(0 − )  by pricing at 0 . The expected profit from firm  pricing at  is
¸
¶
∙µ
 ( )
0
0
(9)
( −  ) + ( − )  


In deriving (9), firm ’s demand is positive at  iff all rivals price at  because
 () ≥  () ∀ ≥ 0 and  ≥ 0  ∀ 6= , so that there is no residual demand if the
lowest price of the other firms is below   In comparison, the expected profit to firm
 from pricing at  − 1 is at least
 [ ( − 1) ( − 1 − 0 ) + (0 − )  ] 
(10)
This is a lower bound because it ignores when the lowest price of other firms is  − 1.
If (10) exceeds (9) then a price of  − 1 is more profitable than a price of  which is
the case when
¶
µ
 ( )
0
 ( − 1) ( − 1 −  ) 
( − 0 ) 
(11)

45
We would like to thank Massimo Motta for suggesting this idea.
44
Given that  ( − 1)   ( ) then (11) holds when
µ
¶
 ( )

0
( − 0 ) ⇒  ≥
+ 0
 ( ) ( − 1 −  ) ≥

−1

which is true since −1
≤ 2 and  ≥ 0 + 2 by supposition (recall that the price set
is a subset of the positive integers). We conclude that a Nash equilibrium in which
 () ≥  () ∀ ≥ 0  ∀ must have  ≥ 0  ∀.
Proof of Theorem 2. Let us first show that there are no pure-strategy equilibria
in which firms set different prices. Consider an asymmetric price vector in which all
prices are at least as high as 0 (which, by Theorem 1, is a necessary condition for
Nash equilibrium). Suppose firm ’s price is not the minimum of all firms’ prices. As
it is assumed  () ≥  () for all  in the support of firm ’s price strategy then firm
’s demand is zero and its profit is zero by pricing above the lowest price. However,
it could earn positive profit of (0 − )  by pricing at 0 . Thus, there does not exist
a pure-strategy Nash equilibrium (with  ≥  ( ) ∀) in which firms set different
prices.
For the remainder of the proof, consider symmetric price vectors. By Theorem 1,
there are only two candidates for equilibrium: 0 and 0 + 1. First consider all firms
pricing at 0  Given all rival firms price at 0 , the payoff for firm  is ( − )  for all
 ∈ {  0 } (assuming  is optimally set at  for   0 ), and is zero for all   0
because  ≥  (0 ) ∀ 6=  results in zero demand. Hence, a price of 0 is optimal so
(0   0 ; 1    ) is a Nash equilibrium when  ≥  (0 ) ∀
Next consider all firms pricing at 0 + 1 Given rivals price at 0 + 1, a price of
0 + 1 yields profit for firm  of
¶
¶
¶
µ
µ
µ
 (0 + 1)
 (0 + 1)
 (0 + 1)
0
0
( + 1) −  −
−   =
+ (0 − )  



A price of  ∈ {  0 } - along with optimal  () =  for   0 - yields lower profit
of (0 − )   while a price of   0 + 1 yields zero profit. Hence, a price of 0 + 1 is
optimal so (0 + 1  0 + 1; 1    ) is a Nash equilibrium when  ≥  (0 + 1) ∀
Proof of Theorem 3. Consider a mixed strategy profile whereby firm  chooses
(0  0 )  where 0 ≥  (0 )  with probability 1 −  and (0 + 1 00 )  where 00 ≥
 (0 + 1)  with probability   Given its rivals act according to this mixed strategy profile, firm ’s payoff from the pure strategy (0  0 ) is (0 − )  , and from the
pure strategy (0 + 1 00 ) is
¸
Y ∙µ  (0 + 1) ¶
0
+ ( − )  


6=
where firm  has zero demand except when all other firms price at 0 + 1. Using the
argument in the proof of Theorem 1, one can show that pricing at 0 + 1 is superior
45
to pricing above it, and that pricing at 0 is superior to pricing below it. Hence,
a necessary and sufficient condition for it to be an equilibrium to randomize over
{(0  0 )  (0 + 1 00 )} is that the expected payoffs from those two pure strategies are
equal:
¸
Y ∙µ  (0 + 1) ¶
Y
0
0
( − )  =
+ ( − )  ⇒  =

 
(12)

6=
6=
Note that
Y




6=
= Y ⇒
=
⇒  =




µ


¶

(13)
6=
Using the expression from (13) in (12),
Y
Y µ  ¶
Yµ 1 ¶
−1 −1
 =
 ⇒  =   
⇒
 ⇒   =


6=
6=
6=
1
Y
⎛ Y ⎞ −1


⎜ 6= ⎟
6=
⎜
⎟
−1
=
⇒

=


⎝  −2 ⎠
−2


The last property to check is that  ∈ (0 1) which is true iff
Y

 
 −2

6=
and that holds by assumption.
8
Appendix B: Instruction Summary (Asymmetric Firms and Price Announcement)
Complete instructions for all treatments are available at
  
Here we provide an overview of the instructions for the treatment with asymmetric
duopoly and price announcements.
• You will be matched with the same person during the length of the experiment.
There are two sellers in each market.
• Today’s experiment will consist of a number of trading days.
46
• In the first stage, you will make an announcement regarding the price you
propose to offer. This announcement is not binding.
• In the second stage, you will choose a price and quantity offer in the subsequent
stage. Both the quantity and price can be changed in the following trading days.
• In today’s experiment one seller will have a Unit Cost of 10 and 54 for the first
18 and 84 units. The other seller, meanwhile, will have a Unit Cost of 10 and
54 for the first 6 and 96 units. Unit Costs are the same in all trading days.
• You will be paid 1 U.S. dollar for every 2500 “experimental units (dollars)” you
earn in the market. Your total earnings for today’s experiment will be the sum
of your earnings in the experiment, plus your appearance fee.
• The experiment will continue at least till period 40. After period 40, and in
every subsequent period, the continuation of the experiment will be determined
with the draw of a number between 0 and 100. If a number lower than 20 is
chosen the experiment ends.
• The trading day proceeds as follows:
— Each seller first makes a price announcement.
— After the announcement, each seller offers to sell certain units (or none)
at a certain price on any trading day. While choosing the quantity you
should keep in mind that,
∗
∗
∗
∗
∗
∗
∗
You earn profits only by selling units at a price above Unit Cost.
If you sell at a price below cost you will lose money.
The low price seller gets to sell first.
You earn zero if you sell nothing.
Your EARNINGS = Revenues -Total Cost.
Your demand in the experiment is: Q=150-P.
Your unit cost for the first 12 units is 10 cents, and is 54 cents for the
remaining 90 units.
47
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50
TABLE 5.1: Average Market Price (No Communication)
Periods
1-40
1-20
21-40
Standard
t-test (T>56)
Treatment
Average
Median
Deviation
(p-values)
SNC2
66.7
63.4
11.8
0.005
SNC3
58.5
56.8
8.1
0.206
ANC2
61.5
57.8
10.9
0.047
SNC2
64.0
61.3
11.7
0.018
SNC3
60.7
56.0
15.9
0.216
ANC2
60.0
56.6
12.4
0.135
SNC2
69.5
64.1
17.1
0.010
SNC3
56.3
55.6
2.2
0.352
ANC2
63.0
56.9
14.3
0.052
SNC2 – Symmetric, No Communication, Duopoly
SNC3 – Symmetric, No Communication, Triopoly
ANC2 – Asymmetric, No Communication, Duopoly
Table 5.2: Average Market Price
Average (Median) [Std. Dev] Market Price
Periods
1-40
1-20
21-40
No
communication
Sym2 Asym2
66.7
61.5
(63.4)
(57.8)
[11.8]
[10.9]
64.0
60.0
(61.3)
(56.6)
[11.7]
[12.4]
69.5
63.0
(64.1)
(56.9)
[17.1]
[14.3]
Announcements
Sym2
76.2
(72.6)
[17.6]
72.9
(64.5)
[18.1]
79.5
(76.5)
[20.2]
Asym2
67.5
(65.7)
[5.9]
64.4
(64.3)
[7.3]
70.6
(72.8)
[9.4]
Sym3
58.0
(55.7)
[21.5]
58.3
(56.1)
[5.3]
57.7
(55.8)
[4.3]
Chat
Sym2
91.2
(92.7)
[12.5]
83.5
(83.8)
[18.4]
98.9
(102.0)
[8.6]
Asym2
91.2
(90.4)
[17.6]
82.7
(83.5)
[20.2]
99.5
(99.8)
[17.2]
Sym4
89.6
(94.7)
[17.1]
85.7
(87.2)
[16.8]
93.4
(102.0)
[18.5]
Sym2 – Symmetric Duopoly
Asym2 – Asymmetric Duopoly
Sym3 – Symmetric Triopoly
Sym4 – Symmetric Quadropoly
Table 5.3: Coordination Measures (Duopoly)
Number of periods
with equal price
Duration of Price
coordination
Periods
1-40
1-20
21-40
1-40
1-20
21-40
No
Price
Communication Announcements
Sym
Asym
Sym
Asym
8.3
8.3
16.1
7.5
3.7
3.9
5.8
3.4
4.6
4.4
10.3
4.1
2.8
2.9
10.5
2.5
1.4
1.6
3.6
1.5
2.5
2.2
8.3
1.9
Chat
Sym
31.7
13.1
18.6
27.1
10.2
17.9
Asym
20.4
8.6
11.8
14.0
6.4
10.4
Table 5.4: Average Market Price - MWW Tests
p-values for the test that average market price is the same across two treatments,
periods 1-40 (1-20) [21-40]
SAN2
SCH2
SNC3
SAN3
SAN4
SCH4
ANC2
AAN2
ACH2
SNC2
.133
(.184)
[.273]
.001
(.008)
[.001]
.045
(.488)
[.009]
.037
(.355)
[.025]
.349
(0.999)
[.092]
.015
(.019)
[.031]
.103
(.828)
[.128]
.326
(.564)
[.248]
.001
(.006)
[.001]
SAN2 SCH2 SNC3 SAN3
SAN4 SCH4 ANC2 AAN2
.057
(.184)
[.022]
.004
(.007)
[.002]
.009
(.031)
[.006]
.039
(.454)
[.011]
.134
(.134)
[.092]
.008
(.030)
[.019]
.525
(.453)
[.419]
.074
(.225)
[.065]
.016
(.025)
[.006]
.793
(.599)
[.726]
.039
(0.999)
[.011]
.002
(.019)
[.001]
.000
(.017)
[.000]
.001
(.004)
[.000]
.003
(.019)
[.001]
.925
(0.999)
[.758]
.000
(.002)
[.000]
.001
(.004)
[.000]
.564
(.817)
[.231]
.916
(.674)
[.529]
.302
(.245)
[.699]
.005
(.014)
[.002]
.311
(.562)
[.426]
.004
(.037)
[.001]
.000
(.009)
[.000]
.699
(.366)
[0.999]
.005
(.007)
[.005]
.515
(.612)
[.612]
.003
(.064)
[.003]
.000
(.002)
[.000]
SNC2 – Symmetric, No Communication, Duopoly
SNC3 – Symmetric, No Communication, Triopoly
SAN2 – Symmetric, Price Announcement, Duopoly
SAN3 – Symmetric, Price Announcement, Triopoly
SCH2 – Symmetric, Chat, Duopoly
SCH4 - Symmetric, Chat, Quadropoly
ANC2 – Asymmetric, No Communication, Duopoly
AAN2 – Asymmetric, Price Announcement, Duopoly
ACH2 – Asymmetric, Chat, Duopoly
.003
(.005)
[.007]
.025
(.011)
[.019]
.708
(.454)
[.638]
.004
(.211)
[.017]
.000
.000
(.002) (.008)
[.000] [.000]
Table 5.5: Same (Coordination) Measure - MWW Tests
p-values for the test that the number of periods with firms setting the same price is the
same across two treatments, for periods 1-40 (1-20) [21-40]
SAN2
SCH2
SNC3
SAN3
SAN4
SCH4
ANC2
AAN2
ACH2
SNC2
.269
(.883)
[.128]
.000
(.002)
[.000]
.877
(.726)
[.877]
.015
(.021)
[.239]
.239
(.005)
[.887]
.024
(.021)
[.021]
.681
(.847)
[.783]
.663
(.657)
[.862]
.040
(.071)
[.022]
SAN2 SCH2 SNC3 SAN3 SAN4 SCH4 ANC2 AAN2
.008
(.020)
[.003]
.131
(.459)
[.141]
.005
(.017)
[.016]
.048
(.002)
[.219]
.146
(.144)
[.128]
.199
(.869)
[.074]
.111
(.929)
[.037]
.370
(.210)
[.352]
.001
(.004)
[.000]
.000
(.001)
[.000]
.002
(.001)
[.001]
.672
(.851)
[.372]
.000
(.002)
[.000]
.000
(.002)
[.000]
.053
(.118)
[.013]
.289
(.146)
[.315]
.745
(.043)
[.897]
.033
(.027)
[.051]
.772
(.532)
[.799]
.969
(.576)
[.641]
.053
(.074)
[.095]
.744
(.161)
[.512]
.033
(.022)
[.027]
.035
(.001)
[.306]
.040
(.001)
[.508]
.011
(.003)
[.013]
.036
(.020)
[.035]
.252
(.001)
[.894]
.451
(.001)
[.814]
.024
(.001)
[.042]
.022
(.030)
[.017]
.024
(.021)
[.019]
.301
(.324)
[.252]
.891
(.843)
[.848]
.041 .032
(.074) (.069)
[.016] [.017]
Table 5.6: Duration (Coordination) Measure - MWW Tests
p-values for the test that the maximum number of consecutive periods for which firms
set the same price is the same across two treatments, for periods 1-40 (1-20) [21-40]
SAN2
SCH2
SNC3
SAN3
SAN4
SCH4
ANC2
AAN2
ACH2
SNC2
.170
(.344)
[.155]
.000
(.002)
[.000]
.936
(.870)
[.968]
.408
(.024)
[.775]
.626
(.010)
[.922]
.024
(.019)
[.024]
.637
(.852)
[.622]
.879
(.446)
[.928]
.038
(.021)
[.025]
SAN2 SCH2 SNC3 SAN3 SAN4 SCH4 ANC2 AAN2
.004
(.016)
[.002]
.269
(.342)
[.182]
.089
(.008)
[.123]
.142
(.004)
[.181]
.157
(.074)
[.165]
.113
(.326)
[.056]
.171
(.150)
[.115]
.334
(.177)
[.428]
.001
(.005)
[.000]
.000
(.001)
[.000]
.001
(.001)
[.001]
.481
(.814)
[.343]
.000
(.001)
[.000]
.000
(.001)
[.000]
.026
(.200)
[.008]
.703
(.189)
[.745]
.743
(.073)
[.895]
.044
(.027)
[.042]
.849
(.747)
[.701]
1.000
(.964)
[.905]
.078
(.071)
[.066]
.895
(.298)
[.947]
.031
(.019)
[.026]
.669
(.011)
[.970]
.467
(.019)
[.781]
.023
(.001)
[.026]
.036
(.020)
[.035]
.749
(.003)
[.892]
.773
(.004)
[.886]
.030
(.002)
[.043]
.025
(.018)
[.016]
.023
(.016)
[.018]
.259
(.347)
[.275]
.602
(.466)
[.691]
.025 .025
(.013) (.005)
[.010] [.018]
Table 5.7: Duopoly Market Price - No communication vs. Price Announcements
Regression 1
Regression 2
Periods:
1-20
21-40
Constant
64.00***
69.47***
(3.05)
(1.03)
DAnn
8.93***
10.00***
(2.86)
(1.66)
DAsym
-4.04***
-6.46***
(1.06)
(0.78)
DAnn x DAsym
-4.48***
-2.36*
(1.52)
(1.35)
N
980
980
*p -value<.10, ** p-value<.05, and *** p-value<.01.
Driscoll-Kraay standard errors in parentheses.
Regression 3
1-40
66.74***
(1.98)
9.46***
(1.92)
-5.25***
(0.75)
-3.42***
(1.07)
1960
Table 5.8: Duopoly Market Price - Price Announcements vs. Chat
Regression 1
Regression 2
1-20
21-40
Constant
72.93***
79.47***
(1.48)
(0.71)
DChat
10.38*
19.43***
(5.59)
(0.64)
DAsym
-8.51***
-8.83***
(1.25)
(1.54)
DChat x DAsym
7.85***
9.28***
(2.16)
(1.59)
N
953
959
*p -value<.10, ** p-value<.05, and *** p-value<.01.
Driscoll-Kraay standard errors in parentheses.
Periods:
Regression 3
1-40
76.2***
(1.27)
14.97***
(3.32)
-8.67***
(1.06)
8.53***
(1.37)
1912
Figure 5.1: Market Price Histogram (No Communication)
Periods 1 to 40
Periods 21 to 40
Figure 5.2: Mean and Standard Deviation of Profit - Asymmetric Duopoly
(No Communication and Price Announcement Treatments)
Figure 5.3: Mean and Standard Deviation of Profit - Symmetric Duopoly
(No Communication and Price Announcement Treatments)
Figure 5.4: Price Series for Symmetric Duopoly with Price Announcements
Figure 5.4: Price Series for Symmetric Duopoly with Price Announcements (continued)
Figure 5.5: Market Price Histograms
Periods 1 to 40
Periods 21 to 40
Figure 5.6: Average Market Price and Coordination (Same)
Price Announcement: Symmetric and Asymmetric Duopolies
Figure 5.7: Some Price and Announcement Series for Duopoly
Figure 5.7: Some Price and Announcement Series for Duopoly (continued)
Figure 5.8: Some Price Series for Symmetric Duopoly with Chat –
Coordination with Common Prices
Figure 5.9: Some Price Series for Asymmetric Duoploy with Chat –
Coordination with Common Prices
Figure 5.10: Asymmetric Duopoly with Chat:
Collusive Outcome with Different Prices and Quantities
Figure 5.11: Average Market Price and Coordination (Same)
Symmetric firms
Asymmetric firms