Vertical Integration and Downstream Collusion∗
Sara Biancini†, David Ettinger‡, Andrea Amelio§.
March 2015
Very Preliminary Version
Abstract
We investigate the effect of a vertical merger on downstream firms’ ability to
collude in a repeated game framework. We show that a vertical merger has two
main effects. On the one hand, it increase the industry profits avoiding double
marginalization, increasing the stakes of collusion. On the other hand, it creates
an asymmetry between the integrated firm and the unintegrated competitors. The
integrated firm, accessing the input at marginal costs, faces higher profits in the
deviation phase and in the non cooperative equilibrium, which potentially harms
collusion. As we show, the optimal collusive profit-sharing agreement takes care of
the increased incentive to deviate of the integrated firm, while optimal punishment
erase the difficulty related to the asymmetries in the non cooperative state. As a
result, vertical integration generally increases collusion.
JEL Classification: D43, L13, L40, L42.
Keywords: Vertical Integration, Tacit Collusion.
∗
We would like to thank Régis Renault.
Université de Caen Basse-Normandie, CREM, [email protected].
‡
PSL, Université Paris Dauphine and Cirano, [email protected]
§
DG Competition
†
1
1
Introduction
The economics of vertical mergers have gained increasing attention in the last decades.
Whereas the classic results of the Chicago school critique, starting from Stigler (1964),
had created a prior of non harmfulness of vertical integration, the more recent contributions have raised attention on its anticompetitive effects (see Riordan, Riordan for
a review of the literature). The post-Chicago scholar have raised several objections to
the Chicago school view, showing first that vertical integration can produce foreclosure
raising-rival’s-costs (Ordover et al., 1990) and second that vertical integration can help
restoring monopoly power when an upstream monopoly initially lacks the necessary commitment to extract full monopoly rents (Rey and Tirole, 2007).
Starting from the raising-rival’s-costs result, Chen (2001) shows that vertical integration
can also induce induce independent downstream firms to be willing to contract with the
integrated supplier at a supra-competitive price, in order to soften downstream competition. As a result, vertical integration allows the realization of a collusive outcome. Chen
and Riordan (2007) develop this line of research, showing that vertical integration can
help an upstream firm to cartelize the downstream market via exclusive contracts with
the other downstream providers.
This first stream of literature took a static view of the interaction between firms. In
contrast, a potential anticompetitive effect of vertical integration is the possibility that a
vertical merger could facilitate the emerging of a collusive agreement when upstream and
downstream firms interact repeatedly. The main theoretical contribution in this sense is
Nocke and White (2007). They look at the possibility that vertical integration facilitate
upstream collusion in a repeated games framework. In their model, vertical integration
has both an ”outlet effect” (foreclosing part of the downstream market) and a punishment effect (integrated firms typically make more profit in the punishment phase than
unintegrated upstream firms). The main result of the paper is that the outlet effect always outweighs the punishment effect and vertical integration unambigously facilitates
collusion. The results of Nocke and White (2007) are obtained under two part tariffs.
Normann (2009) independently derived similar results in a model with linear tariffs.
When two-part tariffs are not available, in the absence of integration upstream collusion
does not guarantee maximal profits, because of double marginalization. Thus, the overall
welfare balance of vertical integration is not necessarily negative. The integrated firms
serves its downstream unit at marginal cost, and the elimination of the double markup
can imply a welfare gain. However, as in Nocke and White (2007) vertical integration
2
can expand the values of the discount factor for which collusion is feasible, thus creating
new opportunities of collusion and potentially reducing welfare.
We also investigate the impact of vertical mergers in a dynamic game of repeated
interaction between upstream and downstream firms, but, contrarily to Nocke and White
(2007) and Normann (2009), we concentrate on downstream collusion. This possibility
has been neglected by the existing literature, with the exception of Mendi (2009). The
latter considers a competitive upstream industry and a downstream duopoly. Downstream firms have asymmetric costs. The author shows that vertical integration can help
sustaining collusion under cost asymmetries, allowing for implicit side-transfers. The intermediate good can be priced by the vertically integrated firm above or below marginal
cost, helping to efficiently share monopoly profits. We consider a similar problem, but
we do not restrict the downstream market to be a duopoly. In addition, we assume that
the upstream market is also oligopolistic. We thus have two vertically related oligopolies.
Downstream firms are ex-ante symmetric but backward integration creates a cost asymmetry: the integrated firm can access the input at a lower cost. Moreover, we do not
restrict the attention to Nash reversion, but following Abreu, 1986, 1988 and MiklosThal (2011), we consider optimal punishment strategies: when a firm deviates from the
collusive agreement, all firms suffer maximal punishment, which means that their future
profits are driven to zero in the punishment phase.
Under our assumptions, we show that vertical integration generally favors collusion,
decreasing the critical discount factor above which collusion is feasible. Vertical integration generates a trade-off. On the one hand, it allows downstream firms to access the
input at a lower price, removing the upstream oligopolistic margin. On the other hand,
vertical integration creates an asymmetry which is potentially harmful to collusion. The
vertically integrated firm has a higher incentive to deviate from the collusive agreement
as well as in the punishment phase (because it has unlimited access to the intermediate
good at marginal cost). As we show, the optimal collusive agreement solve these two
asymmetries: the asymmetry in the punishment phase is balanced by allocating asymmetric shares of the collusive profit to the integrated and non integrated firms, and the
asymmetry in the punishment phase is solved by enforcing maximal punishment in case of
deviation from the collusive agreement. For this reason, ex-post cost asymmetries are not
an obstacle to collusion (see also Miklos-Thal, 2011 on the effect of asymmetries under
optimal punishment strategies).
3
The paper proceed as follows. Section 1.1 describes the current views about vertical
integration and collusion as expressed in the US and EU merger policy and law. Section
2 and 3 presents the model and the main results. Section ?? discusses some extensions
and the robustness of the results. Section 5 concludes.
1.1
Coordinated effects of vertical integration and merger policy
HERE DESCRIPTION OF Merger policy in US and EU, views about vertical merger,
etc. + RELEVANT CASES
2
The model
We consider an activity sector with vertically related firms. M ≥ 2 upstream firms
denoted U1 , ...,UM and N ≥ 2 downstream firms denoted D1 , ..., DN . The upstream firms
produce an intermediate good which is necessary for the production of the final goods by
downstream firms. The intermediate good is uniquely used by these downstream firms
(no alternative market).
There is no fixed cost. Any upstream firm Ui has a constant marginal cost for producing the intermediate good, ci . For the sake of simplicity, we order upstream firms so that
for any i < M , ci ≤ ci+1 , assume that 0 < c1 < c2 and denote C the vector of marginal
cost of size M .
In order to produce one unit of the final good, a downstream firm needs one unit of
the intermediate good. Besides, we assume that the only cost that downstream firms face
is the price they pay for the units of the intermediate good.
Neither upstream nor downstream firms have capacity constraints.
Units of the final good are sold to final consumers who consider them as homogenous.
Final consumers are characterized by a demand function D. There is a maximal price
p > c2 such that D(p) = 0 and for any p < p, D(p) > 0. D is strictly decreasing in
x on [0, p), twice differentiable and for all x ∈ [0, p], (p − x)D(p) is strictly concave on
[0, p). This ensures that the monopoly price on the downstream market depending on
the unit cost c, pm
c is well defined and that this monopoly price is increasing in c and the
monopoly profit πcm = qcm (pm
c − c) is decreasing in c.
We also assume that the differences between upstream firms are limited so that pm
c1 >
c2 and (x − c1 )D(pm
x ) is strictly increasing on [c1 , c2 ].
4
In the markets for the intermediate and for the final good, firms compete in price with
linear pricing. We denote wi the price offer of the upstream firm i and pj , the price offer
of downstream firm j.
In any period of the game, the market works as follows.
• Stage 1: Upstream firms simultaneously make a public offer: a unit price wi from
upstream firm i to any downstream firm for units which can only be bought and
used during this period of the game (no possible storage).
• Stage 2: Each downstream firm chooses one or several proposals of the upstream
firms without specifying the quantity of units that she will buy from her supplier.
• Stage 3: Downstream firms simultaneously make price offers to consumers for the
final goods.
• Stage 4: A quantity D(p) of final goods is sold to consumers with a price equal to
p = minj pj , the final good price. If only one firms proposes price p, she sells the
whole quantity D(p). In case of tie, if there is no specific agreement among firms
having proposed the lowest price, the demand is split between the firms having
proposed price p in any way consistent with the equilibrium (no firm has an incentive
to deviate to a different price). The firms having proposed a price equal to p may
also jointly decide of a specific allocation of the total quantity among themselves.
Any agreement can be sustained as long as the total quantity is equal to D(p) and
no firm sells a strictly negative quantity.
• Stage 5: Downstream firms who sold units to consumers pay the intermediate good
units to their suppliers, choosing freely how to share the total quantity among her
suppliers.
All the firms intend to maximize their discounted sum of payoff with a common
discount factor δ ∈ (0, 1). The game consists in an infinite repetition of the period stage
game. At the end of a period of the game, all the decisions of the players are perfectly
observed by all the players (perfect monitoring). If a firm is vertically integrated, we
assume that it maximizes the joint profit of her upstream and her downstream branch.
This means that in stage 1, the upstream branch of the integrated firm makes an offer to
the downstream branch at a price equal to its marginal cost.
5
Since, we focus on the effect on downstream collusion of a vertical integration, we
assume that a vertical merger does not affect the cost functions of the firms.1
In order to study the effect of vertical integration on collusion, we will mainly focus
on δ, the critical collusive discount factor defined as follows. There exists a collusive
equilibrium in which downstream firms sell at a monopoly price2 if and only if δ > δ.
If δ is lower (resp: higher) with vertical integration than without it, we will say that
vertical integration raises (resp: reduces) collusion opportunities. We will denote, δ N OIN T
and δ IN T , respectively the critical collusive discount factor without integration and with
integration.
3
The Analysis
3.1
The case without vertical integration
The game also has an infinity of collusive equilibria but we focus on collusive equilibria
in which downstream firms obtain the highest total profit.
We can show that the vertical dimension of the situation does not affect much the
conditions for the existence of collusion in the downstream market. The critical collusive
discount factor coincides with what we observe in a market where firms have an identical
constant marginal cost.
Result 1 δ N OIN T =
N −1
.
N
The intuition of this result works as follows. When downstream firms collude, they all
buy the intermediate good at the lowest proposed price w and propose a price equal to
m
pm
w . They equally share a profit equal to πw so that each downstream firm obtains
m
πw
N (1−δ)
if they cooperate. If a downstream firm deviates, she can propose a price arbitrarily close
m
to pm
w and obtain a revenue arbitrarily close to πw . However, in all the following periods,
at least two downstream firms will choose a price equal to w so that no downstream firm
will make any profit. Hence δ N OIN T must be such that the cooperation profit:
equal to the deviation profit: πwm . Hence, δ N OIN T =
m
πw
N (1−δ)
N −1
.
N
Let us also notice that even if we consider collusion on a different price, lower than
pm
w , the lowest δ allowing collusion remains equal to
1
N −1
N
since we can apply exactly the
However, assuming that vertical integration reduces the marginal cost for producing the intermediate
good would not affect the result as long as the upstream branch of the integrated firm has the lowest
marginal cost for producing the intermediate good. We may even explain the lower marginal cost of the
integrated firm by the advantages of the merger.
2
Considering the best offers of upstream firms as their joint cost function.
6
same reasoning. The collusion profit for any downstream firm is
π col
,
N (1−δ)
the deviation
profit is arbitrarily close to π col and there is no profit in the periods following a deviation.
3.2
The case with vertical integration
We assume that U1 and D1 merge to create I1 3 . Before analyzing the situation, we need
to specify the way we will represent it.
First, the integrated firm, I1 . Its profit is equal to the sum of the profits of U1 and
D1 . Besides, we assume that D1 always has the possibility to buy an unlimited quantity
of intermediate goods to U1 at a price equal to c1 .
Second, the other competitors. As long as there is no collusion, their situation is
not modified. In case of collusion between downstream firms, we assume that in period
1 of the stage game, in addition to the public offers, the integrated firm can make a
private offer to downstream firm j at a price wjcol per unit for a maximum quantity qj
of intermediate goods. In period 2, in addition to public offers, downstream firms may
accept or refuse the private offer made by the integrated firm (if such an offer has been
made in period 1).
Now, we see that the vertical merger has two effects. First, it creates an asymmetry
among downstream firms. D1 has a direct access to intermediate goods for a lower price
than other firms. As any asymmetry, this does not favor cooperation among downstream
firms. Second, if downstream firms cooperate, D1 can share its access to cheaper intermediate goods with the other members of the cartel so that the total cartel profit can
be higher (equal to the monopoly profit with a marginal cost c1 ). We will show that the
second effect is always stronger than the first.
Proposition 1 The critical collusive discount factor is strictly lower with vertical integration than without integration, δ IN T < δ N OIN T .
Corollary 1 Vertical integration facilitates downstream collusion.
In order to understand this result, let us first present the best collusive outcome for
downstream firms. In order to maximize the joint profit of I1 , D2 , ... and DN , all the units
of the intermediate goods must be sold by I1 (with the lowest marginal cost). Then, the
m
joint profit is maximized with a p equal to pm
c1 so that the total profit is equal to πc1 . Now,
contrary to the case without vertical integration, there is, a priori, no reason to assume
that all the firms obtain the same fraction of πcm1 in a collusive equilibrium since they are
3
If another upstream firm rather than U1 merges with a downstream firm, this will not affect the
competition outcome.
7
not identical. However, all the downstream firms except I1 are symmetric. Therefore, we
will introduce α ∈ (0, 1) and denote the collusive equilibrium profit of firm I1 , απcm1 and
1−α m
π
N −1 c1
the collusive equilibrium profit of all the other downstream firms.
Even if we exclude collusive transfers between downstream firms, there are several
ways to obtain this division of the collusive profit since downstream firms buy units of
the intermediate goods to I1 . As a matter of fact, its is possible to maintain the same
distribution of profits among firms by giving a higher (resp: lower) market share to D1
and lowering (resp: raising) the price of the intermediate good. In order to simplify the
exposition, we will consider the simplest way to distribute profits among downstream
and show that with this distribution, there exists a collusive equilibrium for downstream
firms with values of δ strictly lower than δ N OIN T . We will consider a collusive equilibrium
in which the secret offer of U1 to downstream firms except D1 is a quantity
1−α m
q
N −1 c1
at a
price equal to c1 for all the other downstream firms. The firms’ market shares are equal
to their respective shares of the total profit. U1 sells a total quantity qcm1 at a unit price
c1 and no upstream firm derives any profit.
Let us consider continuation payoffs after a possible deviation. We can easily build
equilibrium strategies such that if Dj with j 6= 1 deviates from the collusive behavior
in a period, its profit in all the posterior periods is equal to zero. For instance, this is
the case if, after such a deviation, U1 and U2 and all the downstream firms propose a
price equal to c2 in all the posterior periods (assuming, for instance, that U1 sells all the
units). We can also propose equilibrium strategies such that I1 ’s continuation payoff is
equal to zero after a deviation. Suppose that, after a deviation by I1 , in all the posterior
periods, p1 = p2 = c1 and ∀j > 2, pj > c1 for any value of the vector (w1 , ..., wM ) and the
equilibrium allocation rule is such that D1 sells a quantity D(c1 ) of the final good and
D2 sells zero unit of the final good. Without specifying the value of (w1 , ..., wM ), this is
an equilibrium in which all the players obtain a payoff equal to zero (for a discussion of
this type of continuation in a collusive environment, see Miklos-Thal, 2011).
Now, what are the deviation profits? Downstream firms have the possibility to deviate
from the collusive behavior and propose a price strictly lower than pm
c1 but arbitrarily
close to it. D1 , since it has an unlimited access to the intermediate good at a price c1 ,
its deviation profit is arbitrarily close to πcm1 . For Dj with j 6= 1, if it proposes a price
m
arbitrarily close to pm
c1 , it will also sells a quantity arbitrarily close to qc1 but since this
quantity is higher than
1−α m
q ,
N −1 c1
it will have to buy the extra units at a price at least equal
to c2 (no upstream firm has any motive for proposing a public price strictly lower than
c2 ). Hence, its maximum deviation payoff is arbitrarily close to
8
1−α m
1−α m m
πc1 + (1 −
)q (p − c2 )
(1)
N −1
N − 1 c1 c1
This is strictly lower than πcm1 as long as α is strictly positive (N > 2 is also a sufficient
π̂(α) =
condition).
If we choose α =
1
,
N
except that the size of the pie is bigger, the situation is exactly
the same for D1 as in the case without vertical integration. It obtains a fraction
1
N
of the
profit in all the periods in cooperation, the whole profit in deviation and nothing after
the first period of deviation. Therefore, the critical collusive discount factor is exactly
the same as without vertical integration for D1 . For Dj with j 6= 1, it is slightly different.
If it cooperates, its expected profit is
πcm1
N (1−δ)
and π̂( N1 ) < πcm1 if he deviates so that it
cooperates if and only if:
πm
N − π̂(c11 )
N π̂( N1 ) − πcm1
N
δ>
=
1
N
N π̂( N )
(2)
This is strictly lower than δ N OIN T since π̂( N1 ) is strictly lower than πcm1 . Therefore,
we can always find an ε > 0 and sufficiently small such that if α =
collusive equilibrium with a price of the final good equal to
pm
c1
1
N
+ ε, there exists a
for a δ strictly lower than
δ N OIN T . This condition is satisfied for any ε > 0 for D1 since by raising α, we raise the
collusive profit without affecting the deviation payoff and the continuation payoff. For
other downstream firms, ε decreases both the collusive payoff and the deviation payoff
but if ε is sufficiently small, the critical collusive discount factor will remain higher than
δ N OIN T .
Imperfects collusion. We may also consider the creation of a collusive cartel among
col
downstream firms choosing a price lower than pm
c1 . Let us denote a collusive price p
with c2 < pcol ≤ pm
c1 and assume again that market shares are equal to the shares of the
profit of each downstream firms (the intermediate good is sold at price c1 to the other
downstream firms by firm I1 . Again, after a deviation by any firm, its continuation profit
in the posterior periods is equal to zero.
I1 ’s collusive profit is
col
D(p )(p
col
αD(pcol )(pcol −c1 )
1−δ
and its deviation profit is arbitrarily close to
− c1 ) so that a deviation is not profitable for I1 as long as δ > 1 − α.
The collusive profit of firm j with j 6= 1 is
(1 − α)D(pcol )(pcol − c1 )
N (1 − δ)
And its deviation profit is arbitrarily close to:
9
(3)
(1 − α)D(pcol )(pcol − c1 )
1−α
+ (1 −
)D(pcol )(pcol − c2 )
N
N
So that a deviation is not profitable for Di as long as
δ>(
(4)
N − 1 + α p − c2
N − 1 + α p − c2
)/(1 +
)
1 − α p − c1
1 − α p − c1
(5)
This value tends towards zero when pcol tends towards c2 , for any strictly positive
value of α. Then as pcol becomes closer to c2 , it is possible to raise α closer to 1 so that
both U1 and the other downstream firms prefer cooperating than deviating in a collusive
equilibrium with a collusive price pcol for any strictly positive value of δ.
Contrary to what we observed without vertical integration, the possibility to sustain a
collusive equilibrium depends on the collusive equilibrium price. If we consider a collusive
equilibrium price p ∈ (0, 1), the smaller p, the smaller the lowest δ which allows to sustain
this collusive equilibrium. With vertical integration, for any value of δ > 0, there exists
a collusive equilibrium but when δ becomes smaller, the collusive price must get closer
to c2 (the non collusive price).
Welfare analysis. If δ >
N −1
,
N
with or without vertical integration, a collusive
equilibrium exists and the price is lower with vertical integration since it is equal to the
monopoly price with a marginal cost of c1 rather than the monopoly price with a marginal
of cost c2 . The integration allows to avoid double marginalization.
If 0 < δ <
N −1
,
N
without vertical integration, there is no collusive equilibrium and the
price is equal to c2 . With vertical integration, there always exists a collusive equilibrium
in which the final price is strictly higher than c2 and without collusion, the price is equal
to c2 .
Hence, it is interesting to accept the integration only if the regulator that δ >
N −1
.
N
In
that case, collusion occurs anyway and the integration allows to avoid double marginalization.
4
Nash reversion
In the base model presented in Section 2, we have assumed that firms inflict maximal
punishment in case of deviation. This strategy is optimal and maximizes the scope of
collusion, but one can argue that maximal punishment might be difficult to enforce in
practice. Moreover, the optimal punishment illustrated above requires that in every
period, at least one firm plays a weakly dominated strategy in the one-shot game. In this
section, we study the alternative possibility than, in the punishment phase, they revert
10
instead to the equilibrium of the stage game, which corresponds here to an asymmetric
Bertrand game. In this case, the merger creates an asymmetry also in the punishment
phase, in which the integrated firm can produce the intermediate good at lower marginal
cost, while the competitors have to buy it from the oligopolistic upstream market. It
is easy to see that in our framework the integrated firm I1 has not interest in serving
the downstream competitors, but it would rather directly serve the downstream market
at the asymmetric Bertrand equilibrium price c2 . Contrarily to the case of maximal
punishment, illustrated in Section 2, now firm I1 is able to get a positive profit in the
punishment case, thus lowering its incentive to stick to the collusive agreement.
With respect to the case of maximal punishment, the effect of asymmetry is now enhanced,
because it affects also the continuation payoff in the punishment phase. While the nonintegrated firms still get zero in the punishment case, firm I1 now gets at each period
the asymmetric Bertrand profit π1pun = c2 D(c2 ). All other payoffs are unaffected. In
particular, under collusion, firms share the monopoly profit such that π1col = απcm1 and
firm I1 would get the
πjcol = (1 − α)πcm1 . When deviating from the collusive equilibrium,
(1−α)
full monopoly profit, while firm j 6= 1 gets πjdev = πcm1 − c2 D(Pcm1 ) − N −1 D(Pcm1 ) .
Following the intuition, increasing the deviation payoff of firm I1 complicates collusion,
increasing the critical discount factor δ with respect to the case of optimal punishment.
In addition, we show that this negative effect is sufficient to offset the benefits created by
the merger. As a result, the critical discount factor is now higher than the one prevailing
in the absence of vertical integration (notice that without vertical integration, there is no
distinction between optimal punishment and Nash reversion. In both cases, downstream
firms profits after a deviation are equal to zero.).
Proposition 2 With Nash reversion punishments, vertical integration increases the critical collusive discount factor δ IN T,N rev > δ N OIN T .
Corollary 2 Vertical integration under Nash reversion punishments makes downstream
collusion more difficult since it increases δ.
Because of cost asymmetry, for firm I1 , the deviation profit now writes:
π1pun = c2 D(c2 )
(6)
col
m
col
m
All other profits have the
same form as in Section
3, i.e. π1 = απc1 , π2 = (1 − α)πc1 ,
π1dev = πcm1 , πjdev = πcm1 − c2 D(Pcm1 ) −
(1−α)
D(Pcm1 )
N −1
for the integrated firm can thus be written:
11
and πjpun = 0. The critical threshold
δ1 =
(1 − α)πcm1
πcm1 − c2 D(c2 )
(7)
and for the non-integrated competitors i = {2, 3, ..., N }:
(N − 2 + α)(πcm1 − c2 D(c2 ))
δj =
(N − 1)πcm1 − (N − 2 + α)D(Pcm1 )c2
Now set α such that δ j =
N −1
N
(8)
so that for the non-integrated firm the crucial threshold
of the discount factor is the same as in the case with no vertical merger. This happens
when:
α=
πcm1 + (N − 2)D(c2 )c2
nπcm1 − D(c2 )c2 )c2
(9)
Replacing in equation (7) we obtain:
(n − 1)πcm1 (πcm1 − D(Pcm1 )c2 )
δ1 = m
(πc1 − D(c2 )c2 )(nπcm1 − D(c2 )c2 )
N −1
.
N
N −1
.
N
We can easily verify that δ 1 is strictly larger than
δ1 →
(n−1)πcm1
m
nπc1 −D(Pcm
)c
1 2
, which is always greater than
(10)
In fact, when D(c2 ) → D(Pcm1 ),
For larger values of D(c2 ) the
threshold further increases. Because the Bertrand quantity D(c2 ) is strictly larger than
the monopoly quantity D(Pcm1 ) under our assumptions, the threshold δ 1 is always strictly
larger than
N −1
.
N
Because by construction δ j =
N −1
,
N
there is no way to rearrange the
market shares under collusion in order to obtain a threshold delta which is lower than
N −1
.
N
As a consequence, we can conclude that, under Nash reversion punishment, vertical
integration never favors collusion.
This result sheds a new light on the result of Proposition 1. Vertical integration can
reduce the critical discount factor (and thus favor collusion) only in the presence of
punishments that are harsher than Nash reversion. Under Nash reversion, the collusive
strategy (market share allocation) cannot solve the problem of double asymmetry (in the
deviation and in the punishment stage) raised by the vertical merger.
5
Conclusion
Work In Progress
12
References
Abreu, D. (1986). Extremal equilibria of oligopolistic supergames. Journal of Economic
Theory 39 (1), 191–225.
Abreu, D. (1988). On the theory of infinitely repeated games with discounting. Econometrica: Journal of the Econometric Society, 383–396.
Chen, Y. (2001). On vertical mergers and their competitive effects. RAND Journal of
Economics, 667–685.
Chen, Y. and M. H. Riordan (2007). Vertical integration, exclusive dealing, and expost
cartelization. The Rand Journal of Economics 38 (1), 1–21.
Mendi, P. (2009). Backward integration and collusion in a duopoly model with asymmetric costs. Journal of Economics 96 (2), 95–112.
Miklos-Thal, J. (2011). Optimal collusion under cost asymmetry. Economic Theory 46 (1),
99–125.
Nocke, V. and L. White (2007). Do vertical mergers facilitate upstream collusion? American Economic Review 97 (4), 1321–1339.
Normann, H.-T. (2009). Vertical integration, raising rivals’ costs and upstream collusion.
European Economic Review 53 (4), 461–480.
Ordover, J. A., G. Saloner, and S. C. Salop (1990). Equilibrium vertical foreclosure. The
American Economic Review , 127–142.
Rey, P. and J. Tirole (2007). A primer on foreclosure. Handbook of industrial organization 3, 2145–2220.
Riordan, M. H. Competitive effects of vertical integration.
Stigler, G. J. (1964). A theory of oligopoly. The Journal of Political Economy, 44–61.
13