abl-02
Dieses Dokument ist Teil der Anfrage „Amtsblätter bis 2018“
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
2 2015 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 491
(Holt and Davis, 1990; Cason, 1995; Cason and Davis, 1995). More generally signaling is
associated with signaling games in which players use signals to reveal their type (Spence,
1974). Note that in this article we will refer to (price) signaling exclusively as implicit
communication through price setting behavior. We suggest that such price signaling is
facilitated by multimarket contact, because firms meeting in several geographic markets
can set different prices (distinct price signals) on each market. This allows multimarket
firms to signal prices more efficiently in contrast to single market firms, which only have a
single price (one price signal) at their disposal.
The main message of this article is twofold. First, in contrast to previous experimental
studies (e.g., Güth et al., 2010), we are able confirm under controlled laboratory conditions
that multimarket contact facilitates tacit collusion. Second, we show that price signaling
can facilitate tacit collusion under certain conditions—a theory that was also dismissed in
previous experimental studies (e.g., Plott, 1982; Davis et al., 2010). Hence, our results bear
important insights for competition policy by highlighting that limiting firms’ possibilities
to engage in price signaling can effectively mitigate the emergence of tacit collusion. This
is particularly relevant if collusion is suspected among firms that meet in several geograph-
ically distinct, but otherwise relatively homogeneous markets (such as telecommunications
or airline markets), where a uniform pricing constraint could therefore be an effective tool
to render price signaling ineffective, and hence, may undermine the process that establishes
collusion.
The remainder of this article is organized as follows. Section 2 reviews the related
literature and Section 3 provides the theoretical background of our study. Subsequently,
the experimental design and procedure is described in Section 4. Sections 5 and 6 present
the results and finally, Section 7 offers a discussion and policy implications.
3
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
492 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 2 2015
2 Related literature
Multimarket contact and collusion
Edwards (1955) was the first to link multimarket contact to incentives for cooperative be-
havior. According to his mutual forbearance hypothesis, multimarket contact reduces the
competitive intensity, because firms that meet in multiple markets fear to trigger a price
war across all markets if they undercut their rivals in any one market. The mutual forbear-
ance hypothesis has stimulated considerable empirical research on multimarket contact in
several industry contexts, including airlines (Evans and Kessides, 1994), cement (Jans and
Rosenbaum, 1997), telecommunications (Parker and Röller, 1997), hotels (Fernandez and
Marin, 1998), and media (Waldfogel and Wulf, 2006). See Yu and Cannella (2013) for a
recent and comprehensive overview. By and large, this research confirmed a relationship
between multimarket contact and tacit collusion. Scott (2008) reviews merger cases in
the US, especially over different geographic areas, and makes a strong case for considering
multimarket contact as a potential anti-competitive harm in conglomerate and horizontal
mergers. In their seminal article, Bernheim and Whinston (1990) explain theoretically un-
der which conditions multimarket contact may indeed facilitate tacit collusion. However,
the authors also establish an irrelevance result stating that multimarket contact may not
explain mutual forbearance in situations where identical firms experiencing identical and
constant returns to scale meet in identical markets. Therefore, to date “most researchers
assume that mutual forbearance requires asymmetric markets, rivals, and competitive po-
sitions” (Yu and Cannella, 2013, p. 77).
Price signaling and collusion
By contrast, we challenge the irrelevance result by Bernheim and Whinston (1990) from a
behavioral point of view and argue that multimarket contact may facilitate tacit collusion
4
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
2 2015 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 493
also when the irrelevance result holds, i.e., when identical rivals with identical constant
returns to scale technology meet in identical markets. More precisely, we conjecture that
price signaling may be used to coordinate on a collusive state and that multimarket contact
renders these price signals more efficient.
This conjecture on price signaling and collusion is not new per se. However, previous
research could not find any convincing evidence on the effectiveness of price signaling on
the emergence of tacit collusion (Plott, 1982; Davis et al., 2010; Potters and Suetens, 2013),
nor did it consider price signaling in the context of multimarket contact, i.e., what we will
refer to as signal efficiency.
Initial observations of signals in repeated price competition experiments have been
made by Hoggatt et al. (1976) and Friedman and Hoggatt (1980). Plott (1982) discusses
these early attempts to model the effect of signals and conjectures that price signaling
occurs, but has no clear effect on tacit collusion.2 Hoggatt et al. (1976) conduct oligopoly
experiments with repeated price decisions. They differentiate between pulses (“sequence of
two or three successive price changes which sum to zero”, Hoggatt et al. (1976, p. 263)) and
steps (“price change of unusually large magnitude”, Hoggatt et al. (1976, p. 263)). Only
the latter are found to have a temporary effect on the price development and to be more
probable in a positive (negative) direction, if a firm’s price is low (high). Comparably,
in an auction experiment, where information about losing bids is a treatment variable,
Dufwenberg and Gneezy (2002) find prices to be supra-competitive if bidders are informed
about the losing bids in previous periods. They hypothesize that this is due to signaling
behavior during repeated interaction.
Durham et al. (2004) observed signaling behavior in pricing decisions in an extensively
repeated posted offer market experiment. According to Durham et al. (2004, p. 155), “a
price signal is defined as any price submitted by any firm that is greater than or equal
2
Surprisingly, price signaling has not been addressed again until 20 years later.
5
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
494 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 2 2015
to the lowest posted price that failed to attract buyers in the previous period”. Using
this measure there is heavy signaling in all experimental treatments, especially in those
with sunk fixed cost. Price signals are found to elicit higher prices in the subsequent
period, but the authors do not test for an overall effect of price signaling on tacit collusion.
Furthermore, the presence of fixed cost has a significantly positive effect on prices. As the
presence of fixed cost assures firms a loss if they play the Nash equilibrium, subjects face
a behavioral incentive to collude. It cannot be excluded that this drives the already little
effect of price signals on prices in the immediately following period.
Davis et al. (2010) explicitly address this open issue of an overall effect of price signaling
on tacit collusion. Therefore they combine past price choices (baseline treatment) with
non-binding price announcements (forecast treatment). The latter are based on cheap-talk
and, als noted above, also sometimes referred to as price signals in the literature (Holt
and Davis, 1990; Cason, 1995; Cason and Davis, 1995).3 Recall that in this study we
focus on price signals based on past price choices that do not require any means of explicit
communication. Davis et al. consider a market with Bertrand-Edgeworth competition
among three firms. The experiment comprises two successive sequences. Firms first play
the baseline treatment and, after regrouping, they play the forecast treatment in which
firms are additionally provided with the other firms’ expectations on the maximum price
in the next period. Thereby, a price signal can be identified as a firm’s price that is
higher than its forecast on the rivals’ price choices. Hence, the baseline treatment serves
as a benchmark and price signaling may only occur in the forecast treatment. Market
prices are found to be supra-competitive throughout, but not different between the two
treatments. Moreover, the authors find frequent signaling activity in the forecast treatment
raising prices in the immediately following period, but no overall effect on tacit collusion.
Recently, Horstmann and Krämer (2013) found in a comparable laboratory experiment
3
Cason and Davis (1995) study non-binding price communication in a multimarket environment. How-
ever, they do not compare their findings to a single market context.
6
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
2 2015 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 495
with symmetric firms and markets that firms compete less intensely under multimarket
contact than under single market contact. However, the study does not consider price
signaling, and hence, cannot provide evidence why multimarket contact facilitates tacit
collusion.
3 A conjecture of price signaling under multimarket
contact
The distinct strategic feature of multimarket contact is that firms are able to discriminate
prices across the different markets. Conversely, if all firms are restricted to choose the
same price across all markets (uniform pricing constraint), then this removes the strategic
options arising from multimarket contact, and hence, it effectively renders the markets
to be one single market. It will therefore often be convenient to think of single market
contact as a uniform pricing constraint. Consequently, in the following we will refer to price
discrimination and multimarket contact as well as to uniform pricing and single market
contact synonymously, respectively.
In order to exemplify this, consider two identical markets with N consumers each.
Here, multimarket contact means that each firm faces a total demand of 2N , but can set a
different price in each market. In reverse, single market contact means that each firm also
faces a total demand of 2N , but must set the same uniform price in both markets. Clearly,
the latter is strategically indistinguishable from a situation in which each firm faces a total
demand of 2N in a single market.
Our main conjecture is that price signaling can be conducted more efficiently in an
environment where the same competitors meet in several small markets, rather than one
large single market. Thereby, signal efficiency refers to the ability of a price signal to evoke
an increase in market prices, relative to the intensity at which the signal was sent. More
7
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
496 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 2 2015
precisely, under multimarket contact a price signal can be sent in only one market (low
intensity) or in both markets (high intensity). Under single market contact or likewise,
under a uniform pricing constraint, firms can only send price signals in both markets,
i.e., of high intensity. Obviously, any type of price signaling is costly because the signal-
sending firm will incur an inevitable loss in demand due to its price increase. However,
in a multimarket environment a firm can decide to send a price signal in only one, small
market (low intensity price signal), which incurs a comparably lower opportunity cost than
if the price signal would be sent across all markets (high intensity price signal). However,
as the same competitors meet in all markets, a price signal that is sent in only one market
may be just as effective in raising prices in all markets as a signal which is actually sent
in all markets. Consequently, we hypothesize that signal efficiency may be higher due to
multimarket contact, which in turn facilitates the emergence of tacit collusion.
To elaborate on our conjecture of signal efficiency we adopt the most simplistic setting
that is covered by Bernheim and Whinston’s irrelevance result, i.e., where alternative
explanations why multimarket contact facilitates tacit collusion can be ruled out. As before,
consider two identical markets X = {A, B} with N consumers each. Moreover, consider
two identical firms i = {1, 2} that each offer a homogeneous product with marginal cost of
c in each market. Under the assumption of Bertrand competition, each firm sets a price
pX
i,t in period t = 1, ..., T in market X and receives the full market demand of N if and only
if it offers the lowest price in market X. Otherwise, if both firms offer the same price, they
split the market demand equally. For expositional clarity, assume that in t − 1 firm 1 sets
the current market price (lowest price) in market X, i.e., pX X X X
t−1 ≡ min{p1,t−1 , p2,t−1 } = p1,t−1
and that this price is above marginal cost. Therefore, according to the logic of Bertrand
competition, firm 1 receives full market demand. Evidently, in this situation the myopic
best response by firm 2 in period t is to undercut the rival’s price of the previous period
slightly or, if this would incur a loss, to match the rival’s price. In any case, from a
8
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
2 2015 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 497
theoretical point of view firm 2 is not expected to maintain its price, or even to raise it, in
period t.4
If such price setting behavior occurs nevertheless, it is considered a price signal by which
firm 2 wishes to implicitly communicate to firm 1 that it wants to coordinate on a higher
market price, rather than to engage in a price war. More formally, firm i is said to send a
price signal in period t > 1 if the price pX
i,t is greater than or equal to the maximum posted
price in the previous period and greater than the market price in the previous period.5
Hence, the indicator function of a price signal sX
i,t in market X by firm i in period t is
1 if pX X X X X
i,t > pt−1 and pi,t ≥ max{pi,t−1 , p−i,t−1 },
sX
i,t = (1)
0 otherwise.
Furthermore, we can now define the efficiency of a price signal as
s
(pA A B B A
t+1 − pt−1 + pt+1 − pt−1 ) · max{si,t , si,t }
B
ηi,t = . (2)
(pA A A B B B
i,t − pt−1 ) · si,t + (pi,t − pt−1 ) · si,t
Intuitively, signal efficiency is the ratio between the market price reaction to the price
signal (as measured by the change in market price before and after the period in which
the price signal was sent) and the intensity of the price signal (as measured by how much
a firm raises its price above the market price of the previous period). More precisely, the
signal efficiency measure’s denominator denotes the signal intensity, i.e., by how much firm
i raised its price in period t above the market price in period t − 1. Whereas the latter is
positive by definition, the signal reaction may be either positive or negative. Hence, signal
efficiency is positive if the market price increases in t + 1 upon a price signal sent in t and
4
As pX X
1,t = p2,t = c constitutes the unique Nash equilibrium of the Bertrand stage game (neglecting
price increments), this is also the unique subgame perfect equilibrium (Selten, 1975) and the unique weakly
negotiation proof equilibrium (Farrell and Maskin, 1989) of the finitely repeated Bertrand game.
5
Note that our price signal definition coincides with that by Durham et al. (2004) for the case of two
firms.
9
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
498 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 2 2015
it is negative if the market price decreases. Thus, a signal efficiency of 0.5 implies that the
signal reaction in t + 1 is half as large as the intensity of the price signal sent in t, i.e., the
market price increased by half of the delta between the signaled price in t and the initial
pre-signal market price in t − 1.
In case of multimarket contact (price discrimination), a firm can choose whether it
sends a price signal in only one market or in both markets. Conversely, in case of single
market contact (uniform pricing constraint), the same price signal is always sent in both
markets. Therefore, the maximum efficiency of one price signal can, in theory, be twice as
large under multimarket contact – both for positive and negative values. However, signal
efficiency is not higher under multimarket contact per se. With identical price paths in all
markets, signal efficiency is indeed exactly the same under multimarket contact as under
s
single market contact. If the absolute value of signal efficiency exceeds one, i.e., if |ηi,t | > 1,
the signal is overcompensated, i.e., the absolute value of the signal reaction is higher than
s
the signal intensity. Note that this may occur in a positive direction (ηi,t > 1) if both firms
simultaneously increase their prices above the signaled price. Conversely, this may occur in
s
a negative direction (ηi,t < 1) if one of the firms lowers its price below the initial pre-signal
market price, e.g., because a firm does not understand the signal or the signal-sending firm
intends to punish its rival after a longer duration of signaling.
The intensity of price signals is averaged across markets.6 Thus, if a price signal is sent
in only one market, it is considered to be less intense than a comparable price signal that is
sent in both markets. The nominator of our signal efficiency measure denotes the average
increase in market price from period t − 1 to period t + 1 across both markets in response
to a price signal that was sent in any one of the two markets, i.e., when max{sA B
i,t , si,t } = 1.
Obviously, in case of a uniform pricing constraint the prices and price signals of any one
firm need to be the same across both markets. This precludes the possibility to signal only
6
As both the nominator and the denominator represent averages across the two markets, it is sufficient
to consider the sum of the values.
10
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
2 2015 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 499
in one market and thereby to economize on signaling cost. Thus, if our conjecture is true
that it is sufficient to signal in one market to evoke a price change across all markets, then
signal efficiency should be higher under multimarket contact. Otherwise, if firms set prices
under multimarket contact symmetrically in both (identical) markets, signal efficiency is
the same as under single market contact.
4 Experiment
In the following we will test whether multimarket contact increases signal efficiency and
thereby facilitates tacit collusion by means of an economic laboratory experiment. Note
that the above outlined conjecture of signal efficiency was explicitly developed in the con-
text of identical firms and markets, i.e., for a market environment that was previously
shown to be irrelevant by Bernheim and Whinston (1990) for the emergence of tacit col-
lusion due to multimarket contact. In order to exclude alternative explanations for the
emergence of tacit collusion under multimarket contact, we therefore deliberately consider
a market setting with two identical firms that meet in two identical markets, i.e., exactly
the same market environment that was used above to exemplify our definition of signal
efficiency.
Design
The experimental setup considers two identical markets with N = 10000 consumers each.
In each of the two markets the same two rival firms offer a homogeneous good and compete
in prices (Bertrand competition).7 Each consumer has a valuation of v = 50 M U (monetary
units) for the homogeneous good of both firms. The firms each have marginal cost of
production of c = 10 M U in each market. The two firms interact for a total of T periods,
7
Note that the markets are independent of one another and there is no cross-market demand link (cf.
Garcıa-Gallego and Georgantzıs, 2001).
11
Bonn, 28. Januar 2015
Amtsblatt der Bundesnetzagentur
für Elektrizität, Gas, Telekommunikation, Post und Eisenbahnen
500 – Mitteilungen, Telekommunikation, Teil A, Mitteilungen der Bundesnetzagentur – 2 2015
where T is uniformly distributed on T ∈ [45, 50]. Hence, participants know that the
experiment lasts at least 45 periods but no more than 50 periods. This termination rule
resulted from a trade-off between the length of the experimental sessions and the effort
to mitigate end-game effects.8 Note that the probability for an end of the experiment in
period 45 is the same for all experimental sessions. Thus, we only use periods 1 to 45 for
our statistical analysis.
We study two different treatment scenarios: In the multimarket contact (M M ) treat-
ment firms may differentiate prices between both markets. By contrast, in the single
market contact (SM ) treatment firms have to choose the same price in both markets,
i.e., a uniform pricing constraint is imposed. As discussed above, the uniform pricing
constraint strategically connects the two (otherwise independent) markets and effectively
renders them a single market.
Note that standard economic theory does not expect any differences in price setting
behavior between the two treatments as the two firms and markets are identical. This is
also why the irrelevance result by Bernheim and Whinston (1990) holds in this context.
Consequently, in the unique strict Nash equilibrium of the repeated Bertrand stage game,
both firms choose a price of 11 M U in all markets and periods in the SM treatment and
the M M treatment, respectively.
Procedure
The experiment was computerized using z-Tree (Fischbacher, 2007) and conducted be-
tween December 2012 and March 2013. Participants were students of economic fields at
the Karlsruhe Institute of Technology, and recruited via the ORSEE platform (Greiner,
2004). There were five sessions with ten subjects and four with twelve subjects, totaling
8
Such a random ending rule is widely used for closing auctions in financial stock markets to prevent
large changes in auction prices in the last moment. See e.g. the auction plan of the Frankfurt Stock
Exchange (Deutsche Börse, 2011).
12
Bonn, 28. Januar 2015
