The Tell-Tale Heart
Leniency Policy in Hub and Spoke Cartels
Rodrigo Londoño, Caroline Buts∗and Katharina Hilken
Vrije Universiteit Brussel (VUB), Department Applied Economics, Pleinlaan 2, 1050 Brussels, Belgium.
Work in progress
Abstract
We study a hub and spoke model considering a dominant supplier leading a
duopolistic downstream collusion. Implementing sub-game equilibria in a repeated
game, we introduce a leniency policy for tripartite cartels. The antitrust authority
designs a leniency strategy influencing both the retailers’ as well as the manufacturer’s
preferences. We conclude that specific leniency programs may balance the cartel
stabilization effect of a hub’s embargo strategy. Furthermore, we show the limits of
triangular cartels with a downstream competitive market and reward mechanism.
Keywords: Leniency policy, Hub and spoke cartels.
JEL-codes: L41; L42; K21
∗
Rodrigo Londoño is a PhD student. Katharina Hilken is a post-doctoral researcher and Caroline Buts
is assistant professor. All authors are at the Department of Applied Economics of the Vrije Universiteit
Brussel (VUB). Corresponding author, [email protected], T. +32 (0)2 629 1399.
Suggestions made by Aleksandra Szymanska are gratefully acknowledged.
1
1
Introduction
Detection and prosecution of cartels is currently one of the major challenges facing competition authorities. Horizontal agreements are detrimental to competition, while vertical
agreements can have both positive and negative effects. The effects of combining these kind
of agreements are ambiguous. An example is the case United States of America versus Apple Inc.1 : Orchestrated by its highest level executives, Apple, acting as a hub, used its
market power for the establishment of a vertical agreement with certain e-book publishers,
the spokes. Apple facilitated and executed communication between the publishers which
resulted in mutual horizontal agreements enforcing an increase in retail prices. As a result
of this hub and spoke cartel,2 the price of bestselling e-books rose from $9.99 to $14.99
(Baer, 2014). The court found the hub and spoke conspiracy unlawful, because it harmed
competition, raised prices and reduced output. It is long recognized that companies can be
tempted to avoid competition in order to increase their market power and maximize their
joint profits (Stigler, 1964). Hence, the need for building and enforcing an appropriate set
of rules against collusion and price fixing (Motta & Polo, 2003). Both the antitrust laws
themselves and leniency programs form an integrative part of this.
Leniency programs can be considered to consitute the most recent tool of antitrust
authorities in the fight against anti-competitive practices (Leslie, 2011). In contrast with
plea bargaining, a leniency policy carries four intrinsic factors which are its ex ante, ex
post, general and public nature (Spagnolo, 2006): leniency policies target colluders who
have not yet been detected or reported (ex ante), they apply to everyone in a certain
situation (general ) and they are transparent, i.e. available to all interested parties (public).
Also, prosecution is easier whenever information is given in exchange for reductions in
fines for self-reporting cartelists. These particularities of leniency programs should lead
to an increased deterrent effect as well as to enhanced detection of already formed cartels
1
2
United States of America versus Apple INC., case: 14-60, document 133, Final Brief
Hub and spoke cartels, or also known as ABC collusion, refer to multiple vertical cooperations between
a common supplier (the hub or B) and two or more retailers (the spokes or A and C) leading to unlawful
horizontal behavior on the downstream market (Van Cayseele, 2014).
2
(Brenner, 2009).
Competition authorities in both the European Union and the United States (see Section
2) prohibit certain anti-competitive agreements between undertakings. However, neither
antitrust federal statute makes a distinction between vertical and horizontal agreements
(Sahuguet & Walckiers, 2013). While horizontal agreements mostly harm competition,
vertical integration in the production chain might increase consumer and retailer welfare
(Rey, 2012, Rey & Vergé, 2005, Rey & Tirole, 1986, Jullien & Rey, 2007, Gaudet & Long,
1996). With regard to tripartite collusion, the economics literature is still incomplete,
especially when it comes to the evaluation of leniency policies. The majority of the leniency literature deals mainly with horizontal strategic relationships and does not consider
intrabrand competition (see, e.g. Hinloopen, 2003, Aubert, Rey, & Kovacic, 2006, Bigoni,
Fridolfsson, Le Coq, & Spagnolo, 2012, Chavda & Jegers, 2007, Hamaguchi, Kawagoe, &
Shibata, 2009, Park, 2014).
This paper’s objective is to theoretically explore the impact of leniency policy on triangular unlawful agreements. Grounding our work on a modern industrial organization
method, we aim to assess the incentives of both members of downstream and upstream
internal markets to act as a hub and spoke cartel. We combine leniency policy with horizontal and vertical relationships in a super-game strategic context. This combination into
one model contributes to the economic literature through both its novelty as well as its
actuality in the legal context. As an extension to the analysis, we highlight the market
conditions which characterize hub and spoke cartels.
The complexity of this topic is inextricably related with its bipolar nature, hub and
spoke cartels have indeed an ambiguous effect on consumers’ well-being due to the benefits generated by the vertical integration on one hand, and the competitive restraints of
downstream coordination on the other hand (Sahuguet & Walckiers, 2013). In addition, it
has been found that a hub will face an interest to distort the internal market competition
only under certain conditions (Van Cayseele & Miegielsen, 2013). Our findings will exacerbate this last assumption, moreover and in contrast with what has been found, we will
demonstrate the low likelihood of a triangular conspiracy creating an increase in consumer
3
welfare.
This paper is structured as follows: the subsequent section briefly describes the existing
legal framework and the main divergences between the European Union and the United
States with respect to competition law. Section 3 presents the related literature for both
leniency programs and tripartite cartels. Our theoretical model is developed in Section 4.
Section 5 provides a discussion and recommendations. Section 6 concludes.
2
Legal framework
The two pioneers in both the adoption and revisions of their leniency antitrust laws are
the European Union and the United States (Hammond, 2004): the United States were the
first country to introduce antitrust laws with the adoption of the Sherman Act in 1890
(Watkins, 1928). The EU explicitly mentioned its basid prohibition of anti-competitive
agreeements under Article 85 of the Treaty of Rome in 1957 (Neven, 2006). Nowadays,
this article is known as Article 101 of the Treaty of the Functioning of the European Union
(TFEU). Although both EU and US competition laws are based on the principle that
agreements preventing, restricting or distorting competition are prohibited3 , their leniency
policies differ significantly. The next paragraphs shortly discuss the main differences and
similarities.
Leniency policy is applied by both the United States and the European Union to deter
cartel formation and to detect existing cartels. By offering self-reporting cartel members partial or full immunity from fines, an incentive is created to report the cartel. Leniency policy seems to be the most efficient for the detecting and succesful prosecuting
3
See the Sherman Act (The Sherman Antitrust Act, 1890): ”Every contract, combination in the form
of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several States, or with
foreign nations, is declared to be illegal, and Article 101 TFEU: ”The following shall be prohibited as
incompatible with the internal market: all agreements between undertakings, decisions by associations of
undertakings and concerted practices which may affect trade between Member States and which have as
their object or effect the prevention, restriction or distortion of competition within the internal market,
[...]. (European Union, 2008)
4
cartels (Spagnolo, 2006). However, the design of a leniency policy might have an effect
on its efficiency (Leslie, 2011). In addition, different sanctioning possiblities also impact
cartel members’ behavior. While the European Commission only punishes corporations
(European Commission, 2006), the US Antitrust Division distinguishes between the Corporate Leniency Program (Department of Justice, 1993) and the Individual Leniency Program (Department of Justice, 1994). In practice this means that the US apply penal
sanctions for individuals if they do not self-report and/or cooperate before information
about the cartel is reported to the antitrust authority by another source. Furthermore,
the individual is not granted immunity if he/she was the leader or originator of the illegal
activity (Blum, 2005).
Considering corporate leniency programs, the US antitrust authorities grant immunity to fines to the first-reporting corporation (under specific conditions set out by the
Department of Justice, 1993). The EU also grants full immunity to first-reporting corporations, and additionally accords a reduction in fines of up to 50% whenever subsequent
corporations come forward with information additional to the existing evidence (digressive
rewarding system, see for example Werden, Hammond, & Barnett, 2011). Both antitrust
authorities require the reporting corporation(s) to cooperate in the investigation by supplying evidence.
Hub and spoke cartels do not directly fall under the legislation of the competition laws
discussed in the previous paragraphs. The main reason for this is that vertical agreements
do not necessarily harm competition, in many cases, vertical agreements might even be
beneficial for retailers and consumers. This is in sharp contrast to horizontal agreements.
In consequence, when combining these two kinds of agreements, it is ambiguous whether
competition is distorted or not, and therefore whether the legal provisions apply or not.
The Federal Trade Commission explains the difficulty of distinguishing between vertical
and horizontal agreements in the following way:
“The antitrust laws, which aim to preserve and protect competition in economically sensible markets, have long drawn a sharp distinction between contractual
5
restrictions that occur up and down a distribution chain - so-called vertical restraints - and restrictions that come about as a result of agreements among
competitors, or horizontal restraints. Sometimes, however, it can be hard as a
matter of fact to be sure what kind of agreement is at issue.”
One exception in European legislation can be found in the United Kingdoms’ guidelines
on market restraints: aiming to expand antitrust laws to hub and spoke cartels, the British
Court of Appeal agreed that undertakings in this situation may be considered as member
of a single illicit agreement, in contrast to a multitude of separate vertical agreements.
An illicit agreement can be considered as horizontal also if a hub transmits information
regarding any aspect of cartel formation from one spoke to another (where the spokes are
horizontal competitors) (for the specific conditions see Odudu, 2011). As a reaction to
the 2003 Replica Football Kit case4 , the British Court of Appeal required independence of
strategies and policies applied by undertakings. The text remains quite broad, but clearly
introduces guidelines for the assessment of potential hub and spoke cartels.
3
Literature Review
This section briefly discusses (i) vertical and horizontal integration models, (ii) the literature on hub and spoke collusion and (iii) the economics literature on leniency policies. Our
model incorporates the economics of leniency policies in a situation of hub and spoke cartels, based on the industrial organization theory and the model presented by Van Cayseele
(2014).
Vertical and horizontal integration models Belleflamme and Peitz (2010) model
vertical supply chain integration with one supplier and one retailer. With marginal costs
sufficiently low, the equilibrium market price is lower, and total profits are higher, in the
4
Price-fixing of Replica Football Kit, OFT Decision No. CA98/06/2003, August 1, 2003.
6
the integrated compared to the non-integrated model (see Table 1)5 . Both firms benefit
from coordination between the upstream and downstream market and consumers pay a
lower price.
Table 1: Equilibrium outcomes of different market organizations with market demand
P (q) = a − bq.
Number of firms
Vertically
Cartel
Cournot
non-integrated†
formation‡
oligopoly
n=2
n firms outside cartel
n firms
k firms inside cartel
p∗N C =
3a+c
4
∗
gN
C =
a+c
2
Equilibrium quantity
∗
qN
C =
a−c
4b
Profit
Upstream
Equilibrium price
∗
πN
C =
p∗C =
qC∗ =
†
a−c
b(n−k+2)
p∗OL =
a+nc
n+1
∗
=
qOL
a−c
b(n+1)
∗
=
πOL
(a−c)2
b(n+1)2
Inside cartel
(a−c)2
16b
πC∗ =
Downstream
∗
πN
C =
a+(n−k+1)c
n−k+2
(a−c)2
kb(n−k+2)2
Outside cartel
(a−c)2
8b
∗
πOU
T =
(a−c)2
b(n−k+3)2
Outcome of double marginalization, with the retailer (selling at price p) buying from the supplier
at wholesale price g.
‡
Vertical or horizontal integration outcome, or collusion, with 1 < k ≤ n.
While a purely vertical agreement is not to the detriment of the consumer, when it
occurs between two competitors (e.g. a horizontal agreement), it is considered as collusion.
Transposing static collusion into a dynamic game involves an intertemporal decision
component for the cooperating firms. First, firms cooprate and earn the collusive profit
in each period, πC . If one of the firms decides to defect, it will capture the whole market
and earn the defection profit for one period, πD . After this one period though, the other
5
Note that, for reasons of comparability, we use the methodology described by Belleflamme and Peitz
(2010), but we use the inverse demand function P (q) = a − bq as basis for the calculations.
7
firm will also defect and both firms earn the non-cooperative profit, πN C (this is called the
Grim Trigger strategy, see Friedman, 1971)6 . In this setting, firms can either choose to
comply with the tacit agreement and cooperate, or deviate from the agreement and defect.
Collusion is only sustainable if the gain from cooperation is larger than from defection,
VC ≥ VD . Using the expected discounted value of future payoffs leads to the following
condition on the disount factor, δ:
VC =
πC
δπN C
≥ πD +
= VD
(1 − δ)
(1 − δ)
δ ≥ δ min =
πD − πC
πD − πN C
(1)
(2)
Leniency policy is introduced by setting rewards, R, for first cartel reporters as well as
fines, F , (imposed with probability ρ) for all other firms (Aubert et al., 2006).7
VC0 =
1
δ
(πC − ρF ) ≥ πD + R +
πN C = VD0
(1 − δ)
(1 − δ)
R ≥ Rmin =
δ
[(πC − ρF ) − πN C ] − [πD − (πC − ρF )]
(1 − δ)
(3)
(4)
Intuitively, for the reward to be effective, it must fill the gap between the future punishment
and the immediate benefit from deviation. The level of reward might be negative (which
means that the firm receives partial immunity), whenever the deviation profit is larger than
the dicounted future losses from deviation. In this case, a reward equaling the level of the
fine (R = ρF ) is sufficient. However, when collusion is highly stable (the discount factor
is close to 1), the reward needs to be suffiently large to ouweigh the expected fine. This
model serves as a base for the development of several optimal leniency programs, such as
Spagnolo (2006) and Harrington (2005).
6
Note that this model assumes that πD > πC > πN C and that the collusive profit is the monopoly
profit divided by the number of (colluding) firms k, e.g. πC = k1 πM .
7
This model assumes that i) reports are useless after a successful audit of the antitrust authority; ii)
information received from the leniency applicant must be sufficient to prove the existence of the entire
cartel; and iii) hard information disappears after one period.
8
Hub and spoke collusion The literature on this specific kind of collusion is rather
scarce. Sahuguet and Walckiers (2013) develop a dynamic hub and spoke model with one
manufacturer (upstream firm) selling to two retailers (downstream firms). Retailers choose
whether to transmit information about the (stochastic) market demand to the manufacturer, who is then deciding on a wholesale price, and whether to collude with the other
retailer. In equilibrium, retailers provide information to the manufacturer and tacit collusion is always sustainable whenever demand is low. Because (future) deviation profits
with undercutting the competitors’ prices are higher when demand is high, collusionary
prices are frictioned.8 While retailers are not worse off with collusion, the manufacturer
is clearly better off when being able to adjust supply to market demand. Whether the
conspiracy has negative effects on consumer welfare crucially depends on the relative bargaining power of the hub and the spokes. Whenever the upstream firm has bargaining
power, double marginalization is reduced and the price-setting mechanism becomes similar
to the one under vertical integration. Whenever the downstream firms have the bargaining
power, the agreement between the firms approaches the horizontal collusion. While the
former might be beneficial for consumer welfare, the latter is not. Sahuguet and Walckiers
(2014) suggest on one hand that hub and spoke cartels might decrease coordination failures. On the other hand, hub and spoke cartels have the potential to distort competition.
In addition, firms creat negative welfare effects by trying to increase prices.
Van Cayseele and Miegielsen (2013) include the option for the upstream firm to threat
cutting off the downstream firms (the ‘embargo strategy’) in their dynamic hub and spoke
analysis. Their results suggest that the cartel becomes more stable whenever the upstream
firm is able to use the embargo threat compared to the price war outcome. The upstream
firm has an incentive to use the embargo threat under two specific circumstances: first, the
downstream firms have a low degree of differentiation, or put differently, the firms compete
fiercely. Second, the upstream firm has limited bargaining power, because only then it is
(credibly) willing to decrease the number of downstream firms. Otherwise the upstream
8
Note that this is dependent on the discount factor and the probability of high and low demand
occurring.
9
firm would be losing sales by cutting of a downstream firm. In this model, deviation is
more costly to the downstream firms, which shows in cartel stability for lower discount
factors.
With his case studies in the United Kingdom and the United States, Odudu (2011)
emphasizes the challenges that competition authorities face with hub and spoke cartels. In
a similar vein, Bolecki (2011) reviews three Polish cases on hub and spoke collusion.
Leniency in economics Harrington (2005) studies the evolution of cartel prices in function of the probability of detection, and the size of the fine. The results show the difficulty
of detecting cartels as the effects are not necessarily visible for antitrust authorities. Leniency programs might constitute a solution, but their optimal design is not evident. We
will discuss the problems confronting antitrust authorities in the following paragraphs.
In an early economic analysis, Motta and Polo (2003) find that antitrust authorities
using leniency programs, and therefore decreasing the expected fine for a colluding firm,
face the problem that firms collude more ex ante. Although the first-best solution is not
to use leniency programs, this is crucially dependent on the resources availiable to the
antitrust authorities. If these are limited, the authors suggest the use of leniency policies
with a reduction of fines for all reporting firms, supporting ex post cooperation. Ellis
and Wilson (2003) find that self-reporting may bring two opposite strategic effects: (i)
it will decrease cartel stability, or it may enhance collusion by giving more credibility to
the deviation threat of an undertaking. Spagnolo (2005) similarly focuses on developing
an optimal leniency program. In comparison with a stochastic system of audits carried
out by antitrust authorities, leniency methods lead to a higher probability of undertakings
self-reporting. In contrast to Motta and Polo (2003), the authors find that the optimal
leniency policy should only allow for a reduction in fine for the first-reporting party to the
cartel, as it increases the expected gain from self-reporting. Harrington (2008) similarly
suggests total leniency for the first-reporting firm to be optimal. He also suggests that
no leniency should be provided whenever the probability of conviction is sufficiently high.
Furthermore, they suggest that the deterrence effect is large following the breakdown in
10
trust, or the increase in riskiness of a new cartel formation and might hence prevent future
cartel formation. Taking it one step further, Spagnolo (2000) proposes that non-reporting
members of a cartel should be fined to pay the reporting firm a reward, again increasing
the deterrence effect.
The distinction between individual and corporate sanctions continues to feed the debate
about national divergences with respect to leniency programs (see Section 2). By incorporating both penal sanctions and rewards into a dynamic model, Aubert et al. (2006)
show that using rewards makes the deterrence effect more pronounced than in the case of
reduced fines. This effect is even larger when used for individuals rather than for the firm.
Buccirossi and Spagnolo (2006) suggest that individual penalty schemes might be replaced
with equivalently efficient corporate leniency programs (with sufficiently high penalties) at
a lower cost.
In a natural experiment, Apesteguia, Dufwenberg, and Selten (2007) differentiate between four different frameworks for leniency programs: i) no cartels are possible, ii) cartels
are possible, but there is no leniency policy, iii) cartels are possible and the leniency policy
includes only fines, iv) cartels are possible and the leniency policy includes bonuses. In
contrast with theoretical findings, equilibrium prices are higher in a bonus system, as well
as without leniency, compared to the competitive outcome and when applying standard
leniency policies with only fines. Their model is static and hence the punitive effects by
cartel members as well as threats cannot be analysed in the context of future cartel formation and price development. As an extension to this experiment, Hinloopen and Soetevent
(2008) analyse repeated interaction with several changes to the model, better imitating
real life leniency policies.9 They suggest that leniency programs have a positive deterrent
effect. In addition, existing cartels have lower probabilities to survive. Bigoni et al. (2012)
experimentally test cartel formation and price development in a dynamic setting. The
reporting rate is highest in case of rewards, followed by the leniency program
9
10
. Also
In their leniency program, firms applying for leniency receive reductions in fine in the order of reporting.
Cartels which have been formed and are not reported have a chance to be detected and punished.
10
The experiment implements a theoretical leniency policy consituting of full immunity only for the first
11
future cartel formation is lowest in these two treatments. A counterproductive effect of
the leniency policy results in higher prices for surviving cartels and increased stability.
In an earlier experimental study, Hamaguchi et al. (2009) show that the chance of cartel
dissolution is higher for a growing number of cartel members. Using reward schemes again
increases the number of cartels dissolving. There is, however, no difference in leniency
policies for the first-reporting firm versus the digressive leniency system. Ringleaders are
not allowed to apply for leniency which is suggested to increase the number of cartels
forming and counterintuitively induces more firms to become ringleaders (Clemens & Rau,
2014). The number of reported cartels alone cannot serve as a sound measure for the effectiveness of leniency policies as it sometimes might stabilize existing cartels (Hamaguchi
et al., 2009, also see Hinloopen & Onderstal, 2014 for an auction design of cartels). An
explanation might be found in Harrington and Chang (2013) where the effectiveness of
the leniency program (measured as reducing the number of cartels) is positively dependent
on the magnitude of fines as well as on the possibility to direct resources towards nonleniency cases. Experimental analyses of these predictions might disentangle the earlier
contradictory results.
This brief analysis of the economics literature on leniency programs clarifies that an
optimal design is complicated. On one hand, leniency might destabilize cartels. On the
other hand, abuse of generous programs might have pro-collusive effects (Chen & Rey,
2013, Park, 2014). This paper intends to shed more light on the economics of leniency
programs in tripartite collusion.
4
4.1
Hub and Spoke collusion with Leniency
Basic model
In the present model, we consider two retailers’ (the spokes, Si , with i ∈ {1, 2}) decision
to create a cartel by communicating via their common manufacturer (the hub, H). The
reporter and no possible rewards for other cartel members
12
antitrust authority has the task to detect and to prosecute anticompetitive behavior. In
order to reach this goal, the antitrust authority can use a leniency policy which allows
the cartel members to report. The timing of the dynamic hub and spoke model can be
summarized as follows:
Stage 1 The antitrust authority decides whether to establish a leniency policy or not.
Stage 2 The spokes decide whether to communicate or not. If no communication
takes place, the game ends and the competitive equilibrium defines the market price,
p, the transfer price, g, and quantities supplied, qi , with i ∈ {1, 2}.
Stage 3 Communication takes place between the spokes via the hub and evidence of
cartel formation is created. At this stage, the hub might decide to use the collusionstabilizing threat of cutting off one spoke in case of deviation (the ‘embargo’ strategy).
Stage 4 The spokes repeatedly decide whether to deviate from the collusive agreement
(by self-reporting to the antitrust authority) or to comply with the agreement. The
Grim Trigger Strategy is played by both spokes - whenever one party defects, the
other spoke punishes during the remainder of the game.
Stage 5 When no self-reporting took place, the antitrust authority operates an audit
which successfully detects the cartel with the probability, ρ. It punishes the hub and
the spokes by imposing a fine F . Considering the hub as ringleader, the antitrust
authority has the alternative to reward the selfreporting spokes with the amount R.
Information exchange between the spokes takes place in the form of revealing sensitive
commercial information, such as pricing strategy, via their common supplier. By communicating, the spokes intend to distort market conditions. The receiving spoke is aware
of the circumstances, meaning that the origin of the information is known. The spokes
decide to use this information and to enter into a tacit collusive agreement, or not to use
the information and to compete in a Cournot setting.
13
The manufacturer can either choose to supply both retailers or to exclude one retailer
from its distribution chain. The hub and the spokes (whether operating under a collusive
agreement or not) negotiate a transfer price that will depend on their relative bargaining
power. The bargaining power of the spokes is denoted by the variable γ ∈ [0, 1]. If γ = 0,
the hub has full bargaining power. If γ = 1, full bargaining power is situated downstream.
The antitrust authorities’ aim is to maximize consumer welfare. To this end, it can
either impose the maximum fine or grant.
The indirect market demand is linear with i, j ∈ {1, 2} and i 6= j:
p(qi , qj ) = a − bqi − θbqj
(5)
The variable θ ∈ [0, 1] measures the degree of substitutability between the products
of the retailers. If θ = 0, products are entirely distinct and one retailer’s decision has
no impact on the other retailer’s strategy. If θ = 1, products are perfect substitutes and
retailers compete in a duopoly structure.
4.2
Static equilibria
We start by considering a static game where punishment of deviation from collusive agreements is not possible. An antitrust authority is not present (therefore this part concerns
stages 2 to 4). The hub decides which spoke he is willing to supply and produces at constant cost, c. It sells to the spokes at the wholesale price g. Players on the downstream
market are symmetric and do not incur any costs, except paying the wholesale price to the
hub. If the spokes cooperate, the division of the profit is equal. We refer to this as the
static hub and spoke model.
Lemma 1 The static hub and spoke model is characterized by equilibrium quantities that
decrease with the number of downstream members:
qin=2 =
(a − p)
(a − p)
2(a − p)
< qin=1 =
< 2qin=2 =
b(1 + θ)
b
b(1 + θ)
with i ∈ {1, 2}.
14
(6)
Proof. This result follows directly from the indirect market demand in equation (5). qin=2
represents the quantity produced by each firm in the duopoly. qin=1 constitutes the quantity supplied whenever one firm captures the whole market.
This result is intuitive and has been utilized in models relating to market expansion
effects with differentiated goods (see Madden & Rudkin, 2012). It has two important
consequences. First, the supplier has an incentive to deal with both retailers as demand
increases with the number of downstream clients. Second, the retailers face a trade-off: a
high degree of differentiation (low θ) means less direct competition, but also results in lower
demand whereas a low degree of differentiation (high θ) means higher direct competition,
and increased demand.
In the next paragraphs, we characterize the three possible outcomes in the static hub
and spoke model: i) the hub decides to work with one retailer only, creating a monopoly
market structure ii) the hub decides to deal with two competing retailers, iii) the hub transmits information from one spoke to another forming a triangular collusive market structure.
Our model parallels the one of Van Cayseele and Miegielsen (2013), but generalizes the
analysis and subsequently adds leniency policies into this hub and spoke setting.
Vertical integration between the hub and one spoke (double monopoly outcome) When the hub decides to deal with just one spoke, vertical integration of the
supply chain is beneficial for both parties (see Section 3). Instead of the non-cooperative
equilibrium, the hub and the spoke decide to cooperate which results in a monopoly
market structure. With the indirect market demand (equation (5)), monopoly profits
S
π2M
= (p − g)q are maximized under the following equilibrium price and quantity and
dependent on the transfer price:
p2M (g) =
a+g
2
(7)
q2M (g) =
a−g
2b
(8)
15
To determine the transfer price which maximizes joint profits, we take the relative
bargaining power into account:11
S
S
g2M = argmaxg V = [π2M
(g) − 0]γ [π2M
(g) − 0](1−γ)
(9)
With profits for the spoke and the hub respectively:
(a − g)2
4b
(10)
(a − g)(g − c)
2b
(11)
S
(g) =
π2M
and
H
π2M
(g) =
Lemma 2 Vertical integration of the supply chain with two parties results in the following
equilibrium profits for the spoke and the hub, respectively:
1
[(a − c) + γ(a + 3c)]2
16b
(12)
1
(1 − γ)(a − c)[(a − c) + γ(a + 3c)]
8b
(13)
S
π2M
∗ =
H
π2M
∗ =
Proof. Consider the case when the spoke has all bargaining power, e.g. γ = 1. The
transfer price is set as low as possible, at g = c. Next, assume that the hub has the entire
bargaining power, e.g. γ = 0. The transfer price is now set as high as possible, at g = p.
In both cases one of the parties has zero profits. As a consequence, the transfer price g lies
between c and
a+c
2
= p:
g2M ∗ =
(a + c)(1 − γ)
+ cγ
2
(14)
The transfer price is decreasing with the bargaining power as long as a > c12 . The equilibrium price and quantity are, respectively:
11
12
Note that the outside option in a monopolistic setting is zero.
Note that this result parallels the one of Van Cayseele (2014) for a = 1 and c = 0. If a < c, the
supplier will not produce anything.
16
1
p2M ∗ = a(3 + γ) + c(1 + γ)
4
(15)
1
a(1 + γ)c(1 − 3γ)
4b
(16)
q2M ∗ =
Profit equilibria are affected by several factors, which can be divided into two general
types: i.e. direct and indirect effects. By fragmentation, the direct effect is driven by
(a − c) which varies with consumers’ willingness to pay, the elasticity of demand and
the production costs. An indirect effect results from the level of relative bargaining power.
Intuitively, and tempered by the classical factors of demand and cost, the level of bargaining
power has a negative effect on the hub’s profit, and a positive one on the spokes’ profit.
Competitive duopoly with a common hub In this competitive duopoly model with
two retailers, the manufacturer benefits from a higher demand. Additionally, the transfer
price g is lower as in the monopoly case as a consequence of downstream competitive
pressure. As there exists no exclusive deal, both retailers will face a higher aggregate
demand, however, they will compete on prices and negotiate the manufacturing price more
fiercely (as a cost disadvantage could result, at best, in a wide margin loss, and at worst,
in a zero profit gain). To find the equilibrium, bost retailers maximize profits as a best
response, facing a higher demand, such that qin=2 (pi , pj ) =
pj −pi
b(1−θ2 )
+
a−pj
b(1+θ)
with i, j ∈ 1, 2
and i 6= j. Bargaining power, γ, and product substitutability, θ, are endogenised. The best
response function, maximizing profits with respect to p, is then for both retailers (due to
symmetry):
piBR (pj ) =
1
[a − θ(a − pj ) + gi ]
2
(17)
Substitutability, as well as the transfer price, play an important role in the companies’
strategies. If products are differentiated, θ = 0, each player will behave independently.
However, when products are perfectly substitutable, prices are positively related. This
17
means that an increase in pi will affect pj upwards. Substituting the best response functions
into the equilibrium quantities gives the following outcome:
qin=2 (gi , gj ) =
(2 − θ2 )(gj − gi )
a − gj
+
2
2
b(1 − θ )(4 − θ ) b(1 + θ)(2 − θ)
(18)
To derive the optimal transfer prices gi and gj , we again have to take the relative
bargaining power of the hub and the spokes into account. The manufacturer, in contrast
to the earlier considerations, has the choice between doing business with both retailers
(and to earn (qi gi ) + (qj gj )) or, dealing exclusively with one retailer and earn the monopoly
H
outcome. The outside option of the hub is therefore not equal to zero, but to πM
(gj ). This
results in the following bargaining problem:
S
H
H
(1−γ)
giN C = argmaxgi Vi = [πN
Ci (gi , gj ) − 0]γ [πN
C (gi , gj ) − πM (gj )]
(19)
Lemma 3 The situation with one hub and two spokes, that gain from a vertically integrated
value chain, results in the following profit equilibrium:
∗
S
πN
C∗
(a − g N C )(1 − θ)
=
b(1 + θ)(2 − θ)2
(20)
and
H
πN
C∗ =
(a − gN C ∗ )(gN C ∗ − c)
b(1 + θ)(2 − θ)
(21)
with
g
N C∗
(1 − γ)[a(2 − θ + θ2 ) + c(4 − b(2 + θ − θ2 ))]
=
+ cγ
8 − b(4 − 2θ + 2θ2 )
(22)
Proof. First consider the case when the spokes have all bargaining power, and hence
γ = 1. The transfer prices will be set at gi,j = c to maximize the spokes’ profits. When all
the bargaining power is situated at the hub, and γ = 0, the bargaining problem reduces to
the following:
18
maxg
(a − bg)(g − c)
(a − g)(g − c)
−
2
b(1 + θ)(2 − θ)
2b
g=
a(2 − θ + θ2 ) + c(4 − b(2 + θ − θ2 ))
8 − b(4 − 2θ + 2θ2 )
(23)
and solves for
(24)
The optimal g therefore lies between c and equation (24).
Considering a situation with substitutability equaling one or zero renders our analysis
substantially less complicated.
The triangular collusive relationship In this typical hub and spoke structure, retailers are supplied by the same hub and agree on non-competitive behavior. This has two consequences. First, competitors will be more likely to accept higher transfer prices, because
competition in the downstream market is relaxed by a common supplier’s threat. Second,
retailers have a larger profit margin, because they face a higher demand (qin=2 =
(1−p)
)
b(1+θ)
than in the monopoly case. As this model reflects the collusive outcome, the price of
finished goods is the same for both spokes. Also the transfer price is equal. Spokes maximize their profits πCS with respect to prices, resulting in the following quantity and price
equilibrium:
(a + g)
2
(25)
a−g
2b(1 + θ)
(26)
pC (g) =
qC (g) =
19
The hub and the spokes again face a bargaining problem to determine the transfer
price:
(1−γ)
γ gC = argmaxV = πCS (g) − 0 πCH − 0
(27)
Lemma 4 The profit equilibrium for companies in a hub and spoke cartel is defined as
follows:
πCH∗ =
(1 − γ)(a − c)[(a − c) + γ(a + 3c)]
4b(1 + θ)
(28)
[a(1 + γ) − c(1 − 3γ)]2
16b(1 + θ)
(29)
(a + c)(1 − γ)
+ cγ
2
(30)
and
πCS ∗ =
with
gC ∗ =
Proof. When the hub has no bargaining power and γ = 1, the transfer price is set at
g = c. On the contrary, when the hub has all bargaining power, the transfer price equals:
gC ∗ =
(a + c)
2
(31)
The optimal g therefore lies between c and equation (31).
The resulting equilibrium price and quantity then are, respectively:
pC ∗ =
a(3 + γ) + c(1 + γ)
4
(32)
qC ∗ =
a(1 + γ) + c(1 − 3γ)
4b(1 + γ)
(33)
20
4.3
Static analysis
This part focuses first on the comparison of equilibrium prices and quantities obtained in
the previous section. Next, we compare equilibrium transfer prices. Third, profit equilibria
are more closely examined.
In all three regimes, the transfer price has a positive effect on equilibrium prices and
a negative one on equilibrium quantities. Facing an increase in production costs, retailers
pass this on through higher prices (direct effect), diminishing final demand (indirect effect).
The other variables that influence the equilibrium are the willingness to pay of the consumer
and the inverse demand-price elasticity. A higher willingness to pay makes the industry
better-off. Conversely, a larger demand-price elasticity reduces quantities. For the exclusive
dealing regime, the substitutability of products does not appear in the equilibrium as there
is only one spoke. Prices and quantities in both exclusive dealing and triangular collusion
are very similar, i.e., prices are equal and quantities differ by the denominator term (1 + θ).
This trivial result stems from the intrinsic aim of a cartel to reach the monopoly outcome.
Focusing on the competitive case where retailers compete on quantities, the substitutability
of products has an effect on both prices and quantities. This factor clearly endogenizes the
distinction between two competing spokes. As a result we obtain qM ∗ = qN C ∗ = qC ∗ and
pM ∗ = pN C ∗ = pC ∗ when θ is considered equal to zero (products are completely distinct).
Under the most fierce competition, where θ = 1, both non-collusive price and quantity
outcomes are reduced. Interestingly, non-cooperating retailers will earn zero profit. This
result is similar to the classic Bertrand-Nash equilibrium outcome.
Lemma 5 If transfer prices are kept equal, product substitutability is the determining element of difference between the three equilibria.
In addition, focusing on the quantity denominators, the elasticity of demand can have
both positive and negative effects on the equilibria. When the elasticity is smaller than
one, quantities increase in b. When the elasticity is larger than 1, quantities are decreasing
with the elasticity of demand. This relationship simply highlights consumer preferences
21
Table 2: Equilibrium outcome for different market regimes
Vertical integration
Equilibrium price
p2M ∗ =
a+g2M ∗
2
gN C ∗ =
Equilibrium quantity
q2M ∗ =
Competitive duopoly
pN C ∗ =
Triangular collusion
a(1−θ)+gN C ∗
2−θ
pC ∗ =
a+gC ∗
2
a−gN C ∗
b(1+θ)(2−θ)
qC ∗ =
a−gC ∗
2b(1+θ)
a+c
2
a−g2M ∗
2b
qN C ∗ =
when facing differences in price. In our model with a duopolistic downstream market, the
elasticity of demand is assumed to be smaller or equal to one. Intuitively, as there are
only two competitors, the choice for the consumer is limited. Moreover, the elasticity will
increase with product differentiation. In other words, a change in substitutability directly
translates into an altered elasticity.
Lemma 6 When consumers face a competing duopolistic market, e.g. θ ∈ [0, 1], the demand elasticity is always equal to or smaller than one (relatively unelastic).
Proof.
qin=2 =
pj − pi
a − pj
+
2
1−θ
b(1 + θ)
ε=−
ε=
δqin=2
δpi
=
(34)
1
1−θ2


0 if
θ=1

1 if
θ = 0.
(35)
Analysing transfer prices gives us more insight into the price and quantity equilibria.
Bargaining power plays an important role. When the downstream market has full bargaining power, γ = 1, transfer prices are equal to c. Both price and quantity equilibria would
22
depend only on product substitutability, the marginal profit, (a − c), and the demand elasticity. This situation reflects the positive impact of a vertically integrated market. With
vertical integration, the transfer price mechanism disappaers, resulting in lower prices for
consumers and higher consumer welfare. This is considered to consitute the main explanatory factor for possible ambiguous effects of a hub and spoke cartel. Considering the other
extreme, i.e., all bargaining power rests in the upstream market (γ = 0), transfer prices are
at their marginal level. Note the intersting similarities in equilibria between exclusive dealing and the collusive regime. Willingness to pay as well as the retailers’ production costs
influence the level of g to the same extend. Focusing on the non-cooperating regime, willingness to pay varies negatively with product substitutability. When γ = 0 and θ ∈ [0, 1],
the marginal effect of the willingness to pay on transfer prices equals:
When γ = 0, the maximum transfer price equals
a+c
2
δgN C ∗
δa
=
2−θ+θ2
.
8−4b+2bθ−2bθ2
with θ = 1 for all of the regimes. The
possible set of values that transfer prices can take therefore varies between g ∗ ∈ [c, a+c
].
2
By consequence, transfer prices in the competitive duopoly (gN C ∗ ) equal both gM ∗ and
gC ∗ only if θ = 1 and γ = 0. This situation means fierce competition between retailers
and maximum upstream bargaining power. The same result is obtained when θ = 0 and
γ = 0. However, such level of product substitutability refers to completely differentiated
products and is outside the scope of this study as retailers do not have an incentive to
collude. This first insight confirms that the hub’s preferences tend towards a tripartite
collusive outcome. When bargaining power does not fully rest in upstream market, high
substitutability is preferred by the hub. Higher downstream competition (θ → 1) faciliates
negotiations for the hub.
Lemma 7 Considering a competing downstream market, the transfer price will always be
lower in a non-cooperative regime:
gN C ∗ < gM ∗ = gC ∗
with θ ∈]0, 1].
23
(36)
Proof.
g
N C∗
(1 − γ)[a(2 − θ + θ2 ) + c(4 − b(2 + θ − θ2 ))]
(a + c)(1 − γ)
=
+ c ≤ g2M ∗ = gC ∗ =
2
(8 − b(4 − 2θ + 2θ ))
2+c
(37)
maximum level of
gN C ∗ =
(a + c)
2
(38)
with θ = 1 and γ = 0.
Third, and following our basic objective, examining the profit equilibrium with respect
to the hub shows that transfer prices and product differentiation are decisive elements in
hub preferences. Transfer prices have an ambiguous effect on the resulting profit. On one
hand, it soars the hub profit level proportionally to consumer willingness to pay and costs.
On the other hand, it indirectly decreases the hub profit through its negative impact on
final demand. Passing the change in production costs through their final price, retailers
diminish the demand when facing increasing transfer prices. In other words, downstream
competition increases supplier bargaining power which results in higher transfer prices and
a decrease in final demand. Therefore, it would be inferred that a maximum transfer price
does not per se coincide with the hub’s preference. Hence, even with full bargaining power,
the supplier maximizes its profit by keeping g ∗ =
(a+c)
,
2
as opposed to g ∗ = 1.
Lemma 8 As a result of a negative impact on final demand, a maximum transfer price
does not necessarily mean profit maximization for the hub.
Table 3: Equilibrium hub profits under different market regimes
Vertical integration
H
Profits π2M
∗ =
(a−g2M ∗ )(g2M ∗ −c)
2b
Competitive duopoly
H
πN
C∗ =
(a−gN C∗ )(gN C∗ −c))
b(1+θ)(2−θ)
Triangular collusion
πCH∗ =
(a−gC∗ )(gC∗ −c)
b(1+θ)
In order to shape hub preferences, profit equilibria are compared with different levels of
bargaining power and product substitutability. Under lemma 5-8 we demonstrate that and
24
are the key elements determining profit equilibria. Through this process the assumption
that hub incentives are part of a triangular cartel is tested. It is assumed that the hub
faces higher margin profit when it has full bargaining power (γ = 0) and when products are
substitutable (θ = 1). Conversely, and as is explained in the transfer price maximization
(for each regime), all hub profits are equal to zero in all equilibria when γ = 1. That
is, when the supplier does not have any bargaining power at all. Keeping other variables
constant (a = 1, c = 0 and b = 1), we found that, under lemma 1-4, hub preferences are
reflected by high incentives to collude. Our results show that even when the supplier has
high bargaining power (γ → 1), regardless of the product substitutability level, collusive
profit is still higher than the two other ones. Remaining interesting points to underline are
(i) that the supplier obtains, in a collusive system, a higher margin profit when product
are not differentiated, and (ii) that the profit gap between a collusive situation and the
two other ones is decreasing in both θ and γ. Corresponding to the basic assumption, the
following proposition highlights the existing benefit for a hub to operate under triangular
collusion when the downstream market entails competing retailers.
Proposition 1 When a supplier faces a competitive duopolistic downstream market, i.e.
with 0 < θ < 1 and 0 < γ < 1, the supplier will always have an incentive to form a hub
and spoke cartel.
To conclude the static analysis and introduce the dynamic one, a discussion of retailer
preferences is warranted. It seems reasonable to suppose that spokes prefer both collusive
or monopoly situations rather than the competitive outcome. Moreover, as the monopoly
case represents a market with an exclusive manufacturing contract (no downstream competition), it is also reasonable to assume that a retailer will always prefer a monopolistic
position over a collusive one. However, we find that a retailer will have an interest in
taking part in a tripartite conspiracy when it has substantial bargaining power. Important
insights may be drawn from Figure 2. First, higher substitutability between products enhances the competition between retailers and widens the gap between the exclusive dealing
and the collusive profits. The cooperative situation then becomes less profitable. Second,
25
a, θ = 0
b, θ = 0.25
c, θ = 0.5
d, θ = 0.75
Figure 1: Profit equilibria of the hub with different degrees of substitutability
an increase in bargaining power combined with fierce competition (θ → 1) clearly makes
the non-cooperating regime more attractive. This stems from the negative effect of fierce
competition on transfer prices and its subsequent positive effect on retailer bargaining
power. The results are incompatible with our basic assumption (that the hub will always
have an incentive to collude) as the hub may now find an interest in being in competition or
in a monopoly situation. Hence, an additional condition is proposed in the next paragraph.
Table 4: Equilibrium spoke profits under different market regimes
Vertical integration
Profits
S
π2M
∗ =
(a−g2M ∗ )2
4b
Competitive duopoly
S
πN
C∗ =
26
(a−gN C∗ )(1−θ))
b(1+θ)(2−θ)2
Triangular collusion
πCS ∗ =
(a−gC∗ )2
4b(1+θ)
a, θ = 0
b, θ = 0.25
c, θ = 0.5
d, θ = 0.75
Figure 2: Profit equilibria of the spokes with different substitutability measures
Inspired by Van Cayseele and Miegielsen (2014), the parameterization of factors a = 1,
b = 1 (unit elasticity), and c = 0 enables the provision of a function characterizing spoke
preferences. This new function depicts that profitability for retailers, included in collusion
or monopoly regimes, is decreasing with θ and increasing with γ. This is depicted as the
translation of the non-cooperative curb that transfers the intersections (of monopoly and
cooperative curbs with the non-cooperative one) towards higher levels of bargaining power.
As Figure 3 shows, a higher level of product substitutability must be balanced by a higher
level of a downstream bargaining power for collusion to remain sustainable. This is the
result of the retailer preferences for a low production cost. As the transfer price increases
with (meaning more bargaining power to the hub), the level of downstream bargaining
27
Figure 3: Preferences of the spoke
power must remain sufficiently high in order to maintain an interest in tacit cooperation.
Proposition 2 From a one stage game perspective, being part of a relatively competitive
duopoly market, a spoke will have a preference for the collusive profit only under the following conditions:




if



if





if
θ < θC ∗ (γ),
then
∗
θC ∗ (γ) ≤ θ < θM
(γ),
θ > θM ∗ (γ),
then
∗
∗
∗
S
S
πM
< πCS < πN
C
then
∗
∗
∗
S
πM
and
∗
∗
S
S
πN
C < πC
(39)
∗
S
S
S
πN
C < πC < πM
Condition: θC ∗ (γ) ≤ θ < θM ∗ (γ), with 0 < γ < 1.
4.4
4.4.1
Dynamic equilibria
Triangular Dynamic Model
Considering the above analysis as a warming up, the main contributions of this paper to the
economics literature will be developed as follows: In the first stage, the collusive relation
28
entailing both the downstream and the upstream market will be assessed in a repeated
game. This last concept has already been studied by the embargo Strategy. Our model
will additionaly endogenize the presence of antitrust authorities by means of a stochastic
variable of investigation. A second stage concerns the horizontal relationship in a tripartite
cartel, using the results obtained under the first stage (which will characterizes the hub’s
threat). The goal is to build a comprehensive leniency policy model for hub and spoke
cartels. The final stage will enable an evaluation of the impact of a leniency policy on
tripartite cartels, the conditions relative to their occurrences, and their potential of being
more damaging for the economy than classic horizontal cartels.
4.4.2
Repeated vertical relationships under AA investigation
We start this section by assuming that antitrust authorities do not make a distinction
between hub or spoke punishment after detection of a tripartite cartel(in the sense of the
amount of the fine probability of audit). This is a realistic assertion considering cases
such as the Replica Football Kit and Toys “R” Us. There is no doubt that the existence
of a transparent leniency policy will affect the strategy of the supplier. To examine how
the punishment probability affects the preferences of the supplier, we combine our previous
results with the Grim Trigger Strategy including leniency policy as well as with the embargo
strategy, as presented in the basic models. With regard to the vertical side of the dynamic
game we consider proposition 2 which stipulates that the hub will only opt for collusion if
θ > θM ∗ (γ). After integrating the elements fine and investigation, we obtain the following
relations:
H
π2M
∗ =
H
π2M
∗ =
1
(1 − γ)(a − c)[(a − c) + γ(a + 3c)]
(1 − γ)(a − c)[(a − c) + γ(a + 3c)] < πCH∗ =
8b
4b(1 + θ)
(40)
1
(1 − γ)(a − c)[(a − c) + γ(a + 3c)]
(1−γ)(a−c)[(a−c)+γ(a+3c)] < πCH∗ =
−ρF
8b
4b(1 + θ)
(41)
29
if and only iff:
ρF <
(θ − 1)(1 − γ)(a − c)[(a − c) + γ(a + 3c)]
8b(1 + θ)
(42)
Proposition 3 A stochastic factor of investigation has a deterrent effect on the hub’s
incentives to collude.
The likelihood of investigation has been endogenized in the equation of equilibrium
profit under collusion. The hub’s preferences will not only depend on the product substitutability function (decreasing with the factor of bargaining power) but also on the
probability of being caught. The strategy for the manufacturer can then be depicted as
follows:
MtP S = D1 D2 (permanentsupplyf orbothretailers)
MtE =


D1 D2

D 1
if
or
D2
if
It = 0
H
H
andπM
∗ < πC ∗ − ρF,
It = 1
(embargo outcome).
(43)
(44)
A hub that is unsure about entering the collusive game (permanently supplying both
retailers, MtE ) faces a cartel on the downstream market (It = 0) or opts for the embargo
strategy. The supplier will then make a trade-off between the two strategies. On one
hand, as with the case before inclusion of the investigation mechanism, it could serve
the entire downstream market. On the other hand, it may play the embargo strategy,
creating an exclusive deal with one retailer if the other one cheats. But now, the hub will
face a risk of being detected and punished by antitrust authorities. As mentioned, the
supplier’s choice is limited to deciding whether to supply or not. Only if the bargaining
power is mainly situated downstream, with high substitutability of products and when
the probability of sanctions does not outweigh the hub’s preferences, it is reasonable to
assume that the supplier will favour collusion when it faces a cartel on the downstream
market. Imagine that a retailer decides to deviate from the agreement. As in the basic
30
model, the downstream output will be equal to the non cooperative equilibrium. In this
situation, the hub will make a trade-off between the embargo strategy with a monopoly
outcome and the permanent supply strategy resulting in the Nash equilibrium. Concerning
the determinants of the hub’s preferences we conclude that if θC ∗ (γ) ≤ θ ≤ θM ∗ (γ), and
H
H
0 < γ < 1, the manufacturer’s preferences will be πM
If θ > θM ∗ (γ), the
∗ < πN C ∗ .
H
H
supplier will chooset πM
∗ > πN C ∗ . In other words, the hub is constrained to deal with
non cooperating retailers. As a result, it will decide between the Nash equilibrium and
the monopoly outcome. Its choice will depend on the product substitutability function. If
the hub owns sufficient bargaining power, it will prefer to deal with two retailers. On the
contrary, if the bargaining power is situated at the retailer level, the manufacturer will have
low incentives to bargain with a downstream competitive market and thus opt for exclusive
dealing. The hub keeps little room to manoeuver as it can indeed only decide whether to
supply or not. Moreover, the manufacturer as well as as the retailers face the risk of being
investigated and fined when playing the embargo strategy. That fine only applies when
there is collusion in the downstream market. When a retailer free-rides on the downstream
agreement, the hub must merely balance between the monopolistic equilibrium profit and
∗
∗
H
the Nash equilibrium profit (πM
and πN C H ). In a leniency program context, the hub
should also have the possibility to report and hence its trade-off is summarized as:
H
πM
∗ =
[(a − c) − γ(a + c)]2 [c[(a − c) + γ(a + c)]]
−
(8b2 )
4b
[(a − c) − γ(a + c)]2
H
< πC ∗ =
− ρF
4b(1 + θ)
2gN C ∗ (a − gN C ∗ )(gN C ∗ − c))
H
< πN
+R
C∗ =
b(1 + θ)(2 − θ)
(45)
Furthermore, an exclusive deal between a retailer and its supplier can also be considered to constitute an infringement of competition law. In that case, the monopoly outcome
should also suffer from a probability of sanction. Finally, it becomes more complex to establish a reasonable set of supplier’s strategies when all the elements affecting its decisions
have to be endogenized. The downstream market follows the hypothesis of the hub and
31
spoke model developed in the static part. In addition, a sanction variable is inserted when
finding the set of manufacturer’s strategies. The reporting hub will not have the opportunity to apply for immunity as we see in the US treatment for ringleaders. For reasons of
simplicity, this model will not consider possible sanctions with respect to exclusive dealing.
The next paragraph will present the downstream consequences of implementing a leniency
program on triangular cartels.
4.4.3
Horizontal relationship in a triangular conspiracy under leniency policy
The deviation profit To introduce the horizontal dynamic part, and to later develop
the Grim Trigger Strategy with leniency policy, we will first examine the deviation profit of
a spoke. Undertakings in the downstream market are able to maintain collusion when the
weight they give to their future payoff, being affected by the discount factor, is above the
minimum discount factor threshold, δ ≥
π d −π c
.
π d −π n
This variable reflects the relevant market
setting for sustainability of collusion. The determination of this minimum discount level
provides a way to assess the scope of the tacit agreement (Ivaldi & al., 2003), wwhich we
study later. We now compute the benefit from a deviating in a tripartite perspective. A
free-rider will aim to undercut the collusive price and maximize its profit in a one stage
game as follows:
πiD (pi , pjC ) = [pi − gC ]qin=2 (pi , pjC )
(46)
knowing that,
pC ∗ =
(3a + c) − γ(a + c)
4
(47)
qC ∗ =
(a − c) + γ(a + c)
4b(1 + θ)
(48)
(a + c)(1 − γ)
2
(49)
gC ∗ =
32
qin=2 (pi , pj ) =
pj − pi
a − pj
+
2
b(1 − θ ) b(1 + θ)
(a + c)(1 − γ)
πiD (pi , pjC ) = pi −
2
pSDEV ∗ =
S
qDEV
∗ =
(3a+c)−γ(a+c)
4
1 − θ2
− pi
(50)
+
1−
(3a+c)−γ(a+c)
4
1+θ
(51)
1
(3a + c) − γ(a + c)
[6a + 2c + θ(2a + c) − γ(a + c)(2 + θ)] < pC ∗ =
8
4
(52)
2(a + c) − θ(4a − 3c) + γ(a + c)(3θ − 2)
(a − c) + γ(a + c)
> qC ∗ =
2
8b(1 − θ )
4b(1 + θ)
(53)
Lemma 9 The direct outcome of a free-rider will be higher than its collusive profit and
S
S
S
correspond to the Grim Trigger Strategy basics such that πN
C ∗ ≤ π C ∗ ≤ πD .
These computations clarify prices and quantity outputs for a deviating firm in a one
period game perspective (without punishment phase). Logically, they are assumed to be
higher than the collusive profit. Keeping these results in mind, we now have all the elements
to understand our blend of the static outcome with a leniency mechanism.
The spokes and leniency - Assumptions From the perspective of horizontal cartel
prosecution, our model should make three assumptions. First, succesful cartel investigation
by the authorities renders the self-reporting option redundant. Second, exchanged information disappears after each period. Third, evidence provided by the leniency applicant
must be sufficient to prove the existence of the entire cartel. The probability ρ of audit, the
level of fine F and a level of reward R are important parameters to take into account. For a
collusion to exist and remain sustainable, there must be an efficient information exchange.
In addition, the reward must be large enough to outweigh the punishment from retaliation
such that R ≥ −ρF . The super-game is played in three stages. At the beginning of the
game, undertakings decide to communicate or not. Next, at least one competitor decides
to communicate. As mentioned earlier, at this stage, the retailers decide to free-ride or
not. In this second phase of the game, the retailers basically choose to comply or deviate
33
under the cosideration that the punishment phase is repeated indefinitely. T = ∞, for the
sanction to be credible. The third and last stage introduces the possibility of reporting
together with the audit phase. If we study the hub and spoke model, one supplier and two
retailers participate in the game. Also here, three stages make up the repeated game. In a
first stage, a retailer reveals sensitive information to the hub with the intention to distort
market conditions by passing this information to its competitor. In the second stage, the
hub manages effectively to pass the information to the other spoke, this one being aware of
the circumstances. The transfer price is then negotiated. In the last stage, both retailers
must use the disclosed information and fix future prices simultaneously. The retailers behave in accordance with the Grim Trigger Strategy. The supplier has to make a strategic
choice between supplying all the spokes or to enter into exclusive dealing. The supplier
has the opportunity to sanction a deviant firm by means of an embargo punishment. The
chosen strategies of both the hub and the spokes depend on three variables:
1. The number of retailers being supplied, here Nt ∈ 1, 2.
2. The deviation indicator, It , which takes the value It = 1 when at least one retailer
deviates from the agreement in the previous periods.
3. And finally, a variable indicating the identity of the deviating firm, spoke one or
spoke two, IDt ∈ [S1 , S2 ].
The set of company strategies can be summarized as follows:




pC ∗



p(i, t)(Nt , It ) = pN C ∗





p M ∗
if
Nt = 2
and
It = 0,
if
Nt = 2
and
It = 1,
if
Nt = 1.
MtP S = D1 D2 permanent supply for both retailers
34
(54)
(55)
MtE
=


D1 D2

D1
4.5
if
or
D2
if
∗
∗
M
C
πH
< πH
− ρF,
It = 0
and
It = 1
embargo outcome.
(56)
Leniency policy for hub and spoke model
To observe the impact of a reward policy on a tripartite collusion, the hub’s embargo
strategy and the classic Grim Trigger Strategy under leniency policy are combined. This
leads to a punishment equal to zero for the free-rider in the next periods of the game.
Under the above developed conditions the cartel will be sustainable if:
1
S
(π S ∗ − ρF ) ≥ πDEV
∗ + R
1−δ C
min
δ ≥ δH,S
=
min
R ≥ RH,S
=
S
S
(πDEV
∗ + R) − (πC ∗ − ρF )
S
(πDEV
∗ + R)
δ
S
S
(π S ∗ − ρF ) − (πDEV
∗ − πC ∗ − ρF )
1−δ C
(57)
(58)
(59)
This interesting result clearly indicates that the minimum discount factor is lower when
a supplier decides to cooperate with the downstream market. This fosters the punishment
of the deviating company. This subsequently impacts the level of reward needed to distort
cartel stability. The prosecution of tripartite cartels seems to be harder for antitrust
authorities to implement. The Polish DIY case constitutes an interesting example for
which Bolecki (2011, p.45) has explicitly indicated that: “Hub-and-spoke conspiracies were
not recognized by the UOKIK President as an independent restrictive practice. Instead,
the transmission of information on prices applied by other retailers was recognized as an
element of vertical retail-price fixing. The existence of the hub-and-spoke practice was
the very reason why the Polish Competition Authority decided that the vertical practice
caused a horizontal effect. As a result, the UOKIK President substantially increased the
level of the fines imposed.” This quote clearly documents that combining leniency with
a hub and spoke set-up is very difficult in terms of prosecution and possibly necessitates
35
a higher punishment (directly linked with a higher reward for the case of a full immunity
application). Finally, it seems reasonable to consider that a leniency policy will have a
deterrent effect on hub and spoke collusion. . Our model contributes to the extension
of this type of model by implementing the effect of a leniency program on the dynamic
tripartite game. Summarizing, a supplier being aware of a leniency program will prefer to
help downstream cartel formation and sustainability under four conditions:
min
Condition1 δ ≥ δH,S
=
S
S
(πDEV
∗ +R)−(πC ∗ −ρF )
S
(πDEV ∗ +R)
Condition2 0 < γ < 1
Condition3 θ > θM ∗ (γ)
H
H
Condition4 πM
∗ < πC ∗ − ρF
5
Discussion
Our aim was to develop a theory of leniency policy with regard to hub and spoke cartels and
their singular system of indirect information exchange. Using static equilibria, the model
shows that spoke incentives to form a tripartite collusion are constrained by two conditions:
a relatively competing downstream market blended together with a sufficiently high level
of upstream bargaining power. In a dynamic setting, a hub and spoke leniency program
exacerbates the occurrence of such conspiracy. A cartel leader under investigatory pressure
will find it less interesting to orchestrate collusion. In comparison to a classical leniency
policy, leniency for triangular cartels introduces harsher sanctions for the ringleader (hub)
and higher rewards for the spokes. Subsequently, the preferences of colluders are restricted
additional conditions which are in turn characterized by discount factor variations. The
theoretical results can explain the recommendations described by Odudu (2011) pointing
to possible under enforcement.
36
Comparison with classical horizontal and vertical structures Studying tripartite
cartels, it seems interesting to compare our equilibrium outcome to that of a classical
industrial organization model with regard to (i) its potential damaging effect as well (ii)
consumer welfare.
Damaging effects are reflected by the discount factor, that is, the sustainability of a
cartel. As already demonstrated by the embargo strategy, intervention of a hub requires a
lower minimum discount factor in comparison with a horizontal collusion. The supplier’s
embargo strategy decreases the discount factor (increases cartel stability) and excludes
thereby the non-cooperative profit for the next periods. Similar effects may be found in
the classic Grim Trigger Strategy when the downstream market is considered to compete
in prices, where the non-cooperative profit equilibrium with substitutable products is equal
to zero. The damaging effect can be thus derived by a simple comparision of deviation
and collusion profit equilibria. For reasons of comparison we opt for a=1, b=1 and c=0.
The transfer price does not seem to have an impact on the hub and spoke discount factor
(it has an equal impact on both collusive and deviation equilibria). When the product
substitutability factor is higher than 0.5, a hub and spoke cartel is clearly more stable as
presented in Table 5 and Figure 4. The damaging effect of a tripartite cartel increases
in function of the downstream competition, and overtakes the one of a classical Cournot
duopoly cartel when θ ≥ 0.5. Furthermore, when considering Bertrand-Nash competition
in a duopoly cartel with substitutable goods, the minimum discount factor equates 0.5.
Here again, when θ ≥ 0.83, tripartite collusion embeds more potential to divert from the
competitive outcome.
37
Table 5: Comparison with classical structures
Classical cournot duopoly profit equilibra Hub and spoke cartel profit equilibria
R
πD
∗ =
(9(a−c)2 )
64
πCR∗ =
(a−c)2
8
=
=
9
64
S
πD
∗ =
1
8
1
(1
64
πCS ∗ =
δ min =
2
+ γ)2 (2−θ)
1−θ2
(1+γ)2
16(1+θ)
πD∗ −πC ∗
πD ∗
Figure 4: Comparison of damaging effects.
Consumer well-being may be evaluated through two inextricably linked variables, i.e.,
prices and quantities. Comparing collusion equilibria between the classic duopoly Cournot
model and the hub and spoke model suggests that all depends on the level of the transfer
price. Consumer welfare decreases with increasing prices which vary with production costs
(or in other words: with transfer prices). In a nutshell, our model assesses that whenever
bargaining power does not fully rest in the downstream market (meaning a transfer price
equating zero), a hub and spoke collusion is more harmful for consumers than classical
38
horizontal cartels. Such insight worsens the above analysis on damaging effects. Undeniably, this last assertion must be tempered by the conditions presented at the end of the
dynamic model.
Implementing shocks in demand The nature of the demand function varies in the
literature on hub and spoke cartels as well as in studies on leniency policy. Endogenizing
substitutability of products and bargaining power in the inverse demand function is a key
point in shaping the static equilibria. As a result, the equilibria differ mainly based on the
level of product substitutability. Sahuguet Walckiers (2013) assume a demand function
endogenizing possible shocks. In their model the oligopolistic downstream market competes
la Rotemberg Saloner (1986). It permits to study retailers (here also considered as spokes)
pricing behavior under stochastic demand. Considering separated vertical relationships,
the choice of wholesale price (transfer price) is a set of strategies for the spokes, playing
independently. When the equilibria are implemented in a dynamic game, the collusive
outcome is computed and compared to the competitive one. As mentioned in the economics
literature, both retailers and the manufacturer consequently collude in the case of low
demand. With this endogenous formulation, strategic behavior only depends on demand
variation. In this case, leniency policy for hub and spoke cartels would have been closer to
the model of Harrington Zhao (2013), i.e., with risk of being caught fluctuating in function
of stochastic periods. Although researching this mechanism is important, it falls outside
the scope of our theoretical model for hub and spoke cartels.
U.S. vs EU legal framework The creation of an optimal leniency policy seems to be
food for debate in several jurisdictions and is discussed extensively in both the economics
and legal literature. The Federal Trade Commission (U.S.) operates a system of full immunity and exclusion of the ringleader. The European Commission however implemented
digressive immunity without exclusion the ringleader. It is generally accepted that, for an
optimally functioning leniency policy, the highest reward should go to the first disclosing
firm. Recent research shows that exclusion of the ringleader always relaxes the incentive
39
constraint of undertakings (Bos & Wandschneider, 2013). Such insights are confirmed by
an experiment of Clemens and Rau (2014). In a dynamic game, the authors compare
discriminatory and non-discriminatory situations. The results show that the U.S. system
would induce more firms to facilitate coordination in the cartel. Our model is rooted in
the U.S. framework where the highest reward is attributed to the first discloser and the
hub is excluded from rewards. Our tripartite relation contains a monopolistic supplier
taking the lead of a collusion where previous and related theory and experiments on the
ringleader focus on pure horizontal negotiation links. Considering the limitations of hub
intervention, an investigation threat is assumed to suffice for deterring orchestration of the
cartel. The assertions of Bos and Wandschneider (2013) and Clemens and Rau (2014) still
need to be empirically examined. The question hence remains whether, compared to the
U.S. corporate leniency program, the EU faces less cartel ringleaders under a digressive
leniency system?
6
Conclusion
When one level of the value chain is dominated by one firm and the other side is duopolistic, the market players may find an interest to tacitly collude. The incentives guiding such
strategic behavior depend on both final demand and transfer prices. These variables vary
in function of product substitutability and bargaining power. Inextricably linked, a downstream competitive market, i.e. dealing with relatively substitutable products, drives up
the dominant supplier’s bargaining power and its preferences toward a collusive outcome.
In comparison with classical duopoly cartels, a tripartite collusion is potentially more detrimental to competition. Acting as a ring leader, the hub stabilizes the conspiracy through
an embargo threat. As a result, a classical leniency policy looses optimality following the
indirect system of communication, causing a decrease in profitability from deviation.
This challenging problem for competition authorities is characterized by three intrinsic conditions: (i) a competitive downstream market with limited bargaining power, (ii)
substitutable products creating an upward pressure on final demand and (iii) a discount
40
factor high enough to maintain collusion for the spokes. These particularities are mutually reinforcing. For example, more substitutability soars competition which substantially
decreases the downstream bargaining power. Combining both effects, the discount factor
as well as the profitability for undertakings to form a tripartite cartel augment.
Implementing a leniency program for hub and spoke cartels, considering the hub as a
ring-leader, will have two potential consequences with regard to cartel deterrence. First, it
reduces the hub’s incentives to form a cartel by introducing stochastic investigations. As
a result, such policy subsequently impacts the minimum discount factor downward. New
conditions restrict thus the likelihood of occurrence of hub and spoke cartels: a discount
factor lower than the one under classic leniency policy and an upstream collusion profit
compensating the effect of the new investigation factor. These results exacerbate assertions
on the high range of conditions needed to sustain such triangular conspiracy. In addition,
this study proposes a new type of leniency mechanism proving its efficiency with respect
to hub and spoke cartels.
The hub and spoke literature suggests that the available legislative guidelines about
indirect information exchange are too tight regarding standard of proof and may lead to
under enforcement by competition authorities. Hence, it would not be without value for
antitrust authorities to rethink the level of sanctions for triangular cartels. It has been
shown, taking into account the complexity of indirect information exchanges, that a higher
and more transparent pressure for hubs and spokes will result in better deterrence resulting
form the instabilization of the cartel.
As this field of study is quite recent, the future topics to be explored are numerous.
Testing the predictions of our general model, experiments on leniency policy for hub and
spoke cartels would constitute substantial added value. Base lines of the experimental
game come from the developed sub-equilibria. Under an investigation probability ρ ∈
[0, 1] and a stochastic repetitive game δ ∈ [0, 1], two paradigms could be investigated: a
tripartite cartel under leniency or without leniency. As an extension of the work of Sahuguet
and Walckiers (2013), endogenizing demand shocks in our model would be an interesting
research avenue. The isolation of a stochastic demand factor which does not depend on the
41
product substitutability would permit to establish new assumptions. Such research will
undoubtedly reinforce the robustness of our analysis. There are several other specifications
of the theoretical model that could be considered for an extension. By far, it is possible to
introduce a multi-player market with, for instance, an oligopoly structure downstream and
a duopoly structure upstream. Last, it would be interesting to also analyze the impact of
new variables at the downstream level, such as innovative markets or capacity asymmetries.
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