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Merger Control with Merger Choice:
Market Consolidation in the Telecommunications Industry
Jean-Marc Zogheib∗
VERY PRELIMINARY AND INCOMPLETE
Please do not quote or circulate
May 20, 2016
Abstract
This paper studies how merger control affects the choice between merging in-market
or cross-border. A firm merging cross-border is uncertain on its post-merger cost, which
affects its expected payoff. A firm merging in-market considers antitrust authorities’ policy
towards mergers. We build a simple model where a firm has to choose whether to merge
cross-border or in-market. In our benchmark model, there is no possibility for a firm to
exit the foreign market via a merger after an inefficient cross-border merger. In this case,
antitrust authorities behaves by only evaluating in-market mergers’ choices whereas when
exit is possible, it must also consider cross-border mergers. We find that a lenient merger
policy can favour cross-border mergers in some cases. Thus, antitrust authorities can
orient market consolidation’s shape i.e. in-market or cross-border. This study is relevant
for the framing of a regional policy towards mergers in the telecommunications industry.
Keywords: merger control, in-market vs cross-border mergers, market consolidation,
telecommunications
∗Orange and Telecom ParisTech. Email: jean-marc.zogheib@telecom-paristech.fr
1
1 Introduction
Mergers in the telecommunications industry are today a hot topic. Indeed, while in the
European Union (EU), telecommunications companies regularly question the severity of
merger control1 by antitrust authorities (AA, henceforth), the European Commission has
expressed its desire for the emergence of “pan-European” telecommunication firms. Here
is an extract from the Financial Times (22/10/2015): “While regulators at the European
Commission are turning up their noses at in-country consolidation, they have signalled that
cross-border consolidation to create pan-European networks would be welcomed”. In an
industry under consolidation, a dominant trend is observed in favor of in-market merger
applications rather than cross-border ones in the EU2. But taking a global perspective, the
consolidation of this market appears to move quite slowly: for instance, EU counts for now
around a hundred mobile operators whereas the USA counts only four. Hence, an interesting
question to explore is in which way merger control shapes the way markets consolidates i.e.
through in-market mergers (IMM, henceforth) or cross-border mergers (CBM, henceforth).
These considerations raise new challenges for competition policy in the telecommunications
industry: indeed, we can wonder what should be the optimal policy towards mergers when
taking into account: (i) a dynamic view of merger policy: a currently proposed merger
may affect profitability and welfare effect of potential future mergers (Nocke and Whinston,
2010) and hence impact merger choice, (ii) the cross-border dimension: it raises questions
about economic integration and political economy’s stakes. In this context, Yves Gassot, the
president of IDATE3, highlighted that the constitution of huge paneuropean operators could
permit european companies to gain more bargaining power when negociating with giants as
Google, for instance.
When a firm wonders whether or not to merge cross-border, it first computes its expected
payoff upon this merger. Our idea is that the prospect of future mergers can influence this
payoff: if a firm is uncertain about its profitability ex-post (here, its cost), a future merger
may be a suitable way to exit the foreign market if after CBM were inefficient (high cost).
On the contrary, if the firm prospers in the market (low cost), a (potential) future merger will
allow it to be more beneficial. Thus, how strict is merger policy can impact merger decision.
1“Merger control” and “merger policy” will be used interchangeably throughout the paper.2In Austria, between Hutchinson 3G Austria and Orange Austria. In Germany, between Telefonica
Deutschland and E-Plus. There are also similar cases in Spain, Ireland.3IDATE is a think tank specialized in telecommunications, internet and media markets.
2
In our case, it impacts merger’s choice, that is IMM or CBM.
We explore this idea through a simple model where a firm faces two choices: merging in
its national market (IMM) or merging cross-border in the foreign market (CBM). National
and foreign markets are segmented which better fit with the shape of the telecommunications
markets. Upon choosing a merger, the firm takes into account the policy of a regional AA.
The AA has concerns on potential anti-competitive behaviors than can arise after IMMs. In
fact, a national merger reduces the number of actors in the market, which directly affect
the Herfindahl-Hirschman Index (market concentration) whereas, at short-term, it is not
the case for a CBM. This is the first distinction between a CBM and an IMM. The second
one is as follows: ex-ante, a CBM has an uncertain outcome (high or low cost) while the
IMM’s outcome is not subject to uncertainty. This modeling is justified by the fact that
domestic firms have usually little information about foreign demand, economic actors or
distribution networks (...). In a nutshell, an IMM can be rejected by an AA but involves no
uncertainty on its outcome while a CBM raises no immediate anti-competitive concerns but
has an uncertain outcome. In our settings, when the CBM is inefficient (high cost), it means
that the merged entity would be more efficient it were separated. On the contrary, when a
CBM is efficient (low cost), we claim that efficiency gains are greater than after an IMM.
Our idea of greater efficiency gains is based on the idea that international firms are usually
assumed to have superior firm-specific assets (Markusen, 1995) or productivity (Helpman,
Melitz and Yeaple, 2004) compared to domestic firms. However, as pointed out by Qiu and
Zhou (2006), a domestic firm is more familiar with local consumers taste, rules and cultures
on the labor market, distributions networks or interactions with suppliers than a foreign one;
this information asymmetry is a source of uncertainty. In this respect, Lee, Kim and Park
(2015) work on “cultural clashes” by studying how employees from acquiring and acquired
firms experience cultural differences during post-acquisition integration by focusing at the
case of Sweden’s Volvo and South Korea’s Samusung. Thus, to resume, our modeling for
CBMs illustrates two possible polar situations that may arise after this merger.
We first solve this model in a benchmark case where there is no possiblity of exiting the
foreign market via a merger after an inefficient CBM; in this case, we find that AAs can exert
their merger policy by only taking into account in-market mergers’ choices. Indeed, because
there is no possibility of exit via a merger (with the foreign competitor) after an inefficient
CBM, merger policy does not directly affect CBM choice. Nevertheless, it affects CBM’s
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choice undirectly when the firm faces the tradeoff “IMM versus CBM”. Next, we extend the
benchmark case: when there is a possiblity of exit, merger policy by AAs directly affects
CBM’s expected payoff. Therefore, for some values of the parameters, a more lenient merger
policy can incentivize a firm to consolidate cross-border rather than in-market. To resume,
while in the benchmark, there is no direct link between merger policy and CBMs, we find the
contrary for the extended benchmark which helps us to draw conclusions on how AAs can
shape market consolidation. A next step is now to draw a welfare analysis.
2 Literature Review
This paper is related to the industrial organization literature on merger policy towards
horizontal mergers. A seminal paper of Williamson (1968) presents the tradeoff implied by a
merger: while it reduces competitive pressure and facilitate exertion of market power (price
increase), this effect can be offset if the merger generate sufficient efficiency gains. There
is also several major papers analyzing the private incentives to merge (Salant, Switzer and
Reynolds, 1983) and the impact of mergers (Farell and Shapiro, 1992; Perry and Porter, 1985;
McAfee and Williams, 1992)). These papers takes a static perspective.
Yet, a recent literature considers merger policy with a dynamic perspective: Nocke and
Whinston (2010) derived conditions under which a static, i.e. myopic, merger policy could be
optimal even in a dynamic framework. They analyse merger policy when merger proposals
are endogenous and subsequent mergers may also occur. A dynamic view of merger policy
is interesting because it allows us to analyse how it interacts with entry decisions. In this
context, Marino and Zabojnik (2006) study the impact of entry on merger policy. In a dynamic
framework of endogenous mergers, they analyze whether the ease and speed of entry can
mitigate anticompetitive effects of a merger. They show that low entry costs make entry less
appealing since it will be followed by other entries. The authors therefore conclude that in
this case AAs should be careful when allowing firms to merge.
Mason and Weeds (2013) investigate how competition policy may act as an entry barrier.
They show that merger control may have an impact on ex-ante decisions. Using the failing firm
defense standard, they show that if ex-post, a lenient merger policy may increase concentration
and decrease consumer surplus, future merger prospects increase the expected value of entry.
Jaunaux, Lefouili and Sand-Zantman (2016) provide an interesting generalization of Mason
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and Weeds’s framework. They are able to derive a simple statistic to characterize the design
of optimal merger policy upon entry.
The international economics’ literature has closely studied cross-border mergers. Close
to our idea, Horn and Persson (2001a) focus on international versus national mergers. In
their framework, the main advantage of an international merger (or CBM) is that it grant
access to a foreign market. The authors find that an increase in trade costs may increase the
profitability of domestic mergers relative to CBMs. The intuition is the following: with high
trade costs, domestic mergers limits international competition, which is a better situation
than a CBM resulting in fierce duopoly competition in both markets. Our work differs in
that market are segmented, implying no discussion on trade costs and that we study how
competition policy impacts merger choice.
In the industrial organization’s literature, Haufler and Nielsen (2005) compare national and
international mergers from a private and social perspective while allowing for synergies. In
their model firms from the two producing countries compete only on the third market, hence
the formation of national mergers leads to domestic monopoly. They are also able to compute
endogenous merger equilibria using the cooperative game of coalition formation of Horn and
Persson (2001b)4.
Finally, a recent literature deals with the determinants and welfare effects of endogenous
CBMs (Bjorvatn, 2004; Norback and Persson, 2008; Chaudhuri, 2014) while other papers
use labour market effects (Lommerud, Straume and Sorgard, 2006). In this context, the
recent trade theoretical models show that what motivates CBMs is that they are primarily
undertaken to gain access to complementary firm-specific assets in targets firms (Nocke and
Yeaple, 2008), capabilities that are non-mobile across countries (Nocke and Yeaple, 2007), or
country specific assets (Norback, Persson, 2007).
3 Model
3.1 General settings
Market characteristics. Consider two countries defined as a “home” (h) and a “foreign” (f)
market. The markets, which are segmented, have the same size and symmetric demands
(Q = Qh = Qf ). In each country, a duopoly is competing. Define firms 1 and 2, the firms
4Horn and Persson (2001b) study an model of endogenous merger formation in concentrated market. Theyshow that in this case, mergers are conducive to market structures with large industry profits.
5
competing in the home market and firm 3 and 4, in the foreign market. All firms are symmetric:
they have the same cost structure i.e. Ch(qi) = Cf (qi) = C(q) and realize the same profit
level: Π∗i (c) = Π∗(c) where i = 1, 2, 3, 4.
Agents. A regional antitrust authority (AA) exerts its merger control on both home and
foreign countries. The AA applies the same competition policy in both markets; therefore
the AA considers a regional market. It clears a merger with probability α ∈ [0, 1]. For the
moment we assume that α is exogenously given.
Among the four firms, some are active and the others are inactive. An active firm is a firm
that can choose betwenn a cross-border merger, an in-market merger, or no merger at all.
On the contrary, an inactive firm has no merger choice: it does not undertake any strategic
action in the game. Let firm 1 be the only active firm.
Figure 1: Markets Overview
Merger patterns. A merger may or may not be rejected depending on α ∈ [0, 1], the
merger control parameter. A merger is also subject to uncertainty upon its outcome (level of
efficiency); define β ∈ [0, 1] the exogenous probability that a merger is (cost-)efficient.
In our model, an IMM is subjected to the policy (α) of the AA towards mergers. Assume
an IMM has no uncertainty so that β = 1. The merged entity will achieve a profit with
marginal cost cin < c.5. A CBM raises no anticompetitive concerns for the AA since it does
not impact the number of competitors in the market6, which implies that α = 1. Nonetheless,
a CBM is perceived as risky: here, a good scenario occurs with probability β meaning that
5An important pattern of our model is that the IMM is a merger to monopoly. Yet, adding more that twofirms in each country would considerably complicate the analysis and would take as away from our idea ofCBM versus IMM. Since we then make use of a Cournot framework for numerical simulations, setting N > 2firms in each country would have created situations where a merger are unprofitable, absent a certain level ofsynergies; see Salant, Switzer, Reynolds (1983) for more explanations.
6These considerations may differ if we take a long-term perspective.
6
the merged entity achieves a profit with marginal cost c < c whereas a bad scenario happens
with probability 1− β meaning that the merged entity achieves a profit with marginal cost
c > c. We make the following assumption on costs:
Assumption 1. c > c ≥ cin > c
This assumption defines an inefficient CBM since its costs is higher than before the merger
(c > c). An IMM is always efficient since β = 1. It may or may not generate synergies7. But
an efficient CBM achieve higher synergies than an IMM. While discussable, this assumption is
based on evidence that international firms are usually assumed to have superior firm-specific
assets or productivity (Markusen, 1995; Helpman, Melitz and Yeaple, 2004) compared to
domestic firms. In other words, a firm merging cross-border becomes an “international firm”
and it achieves higher synergies - than if it merge in-market - in the case of an efficient
outcome after a CBM.
Payoffs. We denote by Π∗ij the optimal profit achieved after the merger of firm i and j,
where i 6= j. If firm 1 (the only active firm) chooses an IMM and the merger is accepted, the
merged entity earns Π∗12(cin) and this profit is shared between the two merging firms (1 & 2)
with respect to an exogenous bargaining parameter b12 ∈ [0, 1] (respectively b21) for firm 1
(for firm 2). If firm 1 chooses a CBM, say with firm 3, the merged entity earns Π∗13(c) with
probability β and Π∗13(c) with probability 1− β. As before, the profit is shared with respect
to an exogenous bargaining parameter b13 ∈ [0, 1] (respectively b31) for firm 1 (for firm 3).
Let Mk designs all possible market structures where k = 0, in, cb, cb′ with in meaning
in-market and cb meaning cross-border. Therefore, at the beginning we have M0 = {1, 2, 3, 4}.
After an IMM, we obtain M in = {12, 3, 4} whereas after a CBM, we get M cb = {13, 2, 4} or
M cb′ = {14, 2, 3} (which are symmetric situations). In the following frameworks, we use M cb.
Define V ja (Mk) the expected payoff from choosing its merger type for an active firm where
j = E,NE, a = 1, ..., 4 with a ∈ A is the set of active firms and . Since for now firm 1 is the
only active firm, a = 1; E stands for “exit” (possibility of exit via a merger) and NE (no
possibility of exit via a merger) for “no exit”.
7A question is if the synergies are sufficiently high so that they do not decrease welfare or consumer surplus.It depends if an AA takes a consumer surplus criterion or not. In fact, there are more involved analysis wherethe AA requires merger remedies and synergies to accept it. But it is beyond the extent of that paper. Formore information, see Chone and Linnemer (2008) or Dertwinkel-Kalt and Wey (2016).
7
Remark 1. “Exit the foreign market via a merger” means that firm 1 separates from firm 3
by “selling” firm 3 to firm 4, the foreign firm. Therefore, it translates into a merger between
firm 3 and 4. The fee f is the cost of exit via a merger, set exogenously.
Timing. We consider the following sequence of events:
• Stage 1a: the AA or Nature draws the probability α of merger acceptance.
• Stage 1b: firm 1, the active firm, observes α and decides whether to merge cross-border
or in-market. If it merges cross-border, uncertainty on its efficiency (β) is realized.
Payoffs are realized.
• Stage 2 : If firm 1 has previously merged in-market, its second-period payoff is realized.
If firm 1 has previously merged cross-border:
– (i) In the case of a low-cost realization (c), its second-period payoff is realized.
– (ii) In the case of a high-cost realization (c), it assesses, the possibility to exit the
foreign market by merger at a fee f .
Remark 2. Upon stage 2-(i), it can be discussed that if firm 1 would like to merge (exit
via a merger) if the CBM were inefficient (c), it would also like to merge with firm 2 (the
domestic firm) or with firm 4 (the foreign firm) if the CBM were efficient (c). Indeed, if firm 1
prospers in the foreign market, another merger would make its CBM choice more beneficial.
Though, initially, we would like to highlight the uncertainty upon a CBM by focusing on the
possibility or not to exit the foreign market after an inefficient CBM. In addition, would an
AA allow an IMM if the cross-border merged firms have no profitability issue? There could
be anti-competitive concerns that may not justify an IMM in this case. Therefore, we assume
here that α = 0 (that is a merger is never accepted) if an efficient CBM has occured8.
Participation Constraints. Importantly, no merger at all is the firm’s outside option.
It is a status quo situation. Therefore, to participate to the merger game, the following
participation constraints have to be respected:
V ji (M in)− V j
i (M0) > 0 (3.1)
V ji (M cb)− V j
i (M0) > 0 (3.2)
8We will add the possibility of merger after an efficient merger in the extension section.
8
These participation constraints translates into the following lemma:
Lemma 1. Firm i chooses to merge (cross-border or in-market) if and only if:
• (i) α > 0 or β ≥ β if there is no possibiity of exit.
• (ii) α > 0 or β ≷ ¯β - depending on the value of δ1+δ - if there is a possibility of exit.
A proof is given on the appendix.
Following lemma 1, we make the following tie-breaking assumption:
Assumption 2. When the firm is indifferent between merging or not merging, it prefers not
merging at all.
3.2 A benchmark: no possibility of exit
In this section, we assume that the fee f , that is the exit cost, is so high that the firm that
chooses a CBM can never exit the foreign market via a merger i.e. f =∞.
We can now just study the payoffs from both types of mergers for a discount factor
δ ∈ (0, 1), evaluated at their optimal level:
V NE1 (M in) = (1 + δ)[α∆Πin
1 + Π∗1(c)] (3.3)
V NE1 (M cb) = (1 + δ)b13[β∆G+ Π∗13(c)] (3.4)
Where
• ∆Πin1 = b12Π∗12(cin)−Π∗1(c) is the gain from the IMM for firm 1.
• ∆G = Π∗13(c)−Π∗13(c) designates the “gap” between an efficient and inefficient CBM.
Let us derive the effect of merger policy according to the merger choice:
∂V NE1 (M in)
∂α= (1 + δ)∆Πin
1 ≥ 0
∂V NE1 (M cb)
∂α= 0
We observe from the above expressions that a less severe merger control (↗ α) increases the
expected value of an IMM whereas no effect is observed on the CBM payoff. To emphasize the
9
possible tradeoff of a firm 1 between choosing IMM or CBM, we can compute the minimum β
for which a CBM is preferred to an IMM. It is such that V s1 (M cb)− V s
1 (M in) ≥ 0 or:
β ≥ α∆Πin1 + Π∗1(c)−Π∗13(c)
b13∆G≡ βNEmin (3.5)
The more βNEmin is high (β being the probability of efficient merger), the more it is difficult to
choose a CBM for a firm. Interestingly, the sign of the derivative of βNEmin with respect to α
is strictly positive (∂βNE
min∂α =
∆Πin1
b13∆G). It means that when facing the choice between the two
types of mergers, firm 1 realizes that a lenient merger policy (↗ α) increases the minimum β
for which it would opt for a CBM.
Figure 2: CBM vs IMM: Benchmark caseCournot framework: a = 10, b = 1, c = 3, cin = 2.5, c = 4, c = 1.9,b12 = b13 = 0.5
Figure 2 fixes ideas on the tradeoff between choosing a CBM or an IMM and the impact of
merger control. On the x-axis, the probability of efficient merger (β) is represented while the
choice between a CBM and an IMM (V s1 (M cb)− V s
1 (M in)) is on the y-axis. We observe that
the less merger control is severe (α↗) , the less there is scope for CBM choice (shaded area).
We also notice that firm 1 chooses a CBM for β ≥ 0.45 when merger policy is strict (α = 0.2)
whereas if merge policy is lenient (α = 0.8), it does the same choice for β ≥ 0.6. Another way
to interpret figure 2 is to see that as the scope for CBM decreases (CBM > IMM ’s area),
the one for IMM increases (IMM > CBM ’s area) as α goes up. We can resume our intuition
into the following proposition:
Proposition 1. Under lemma 1(i), if there is no possibility of exit via a merger after an
inefficient cross-border merger (c = c, f = ∞), a lenient merger policy (higher α) favors
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in-market mergers at the expense of cross-borders mergers (∂βNE
min∂α ≥ 0).
It means that in the context of a regional market consolidation, an AA can shape
this consolidation by implementing a stricter merger policy, thereby incentivizing firms to
consolidate cross-border rather than in-market. It is crucial to keep in mind that here, merger
control by the AA indirectly affects CBM’s choice.
3.3 Merger Strategies with Possibility of Exit
In this section, firm 1 has the possibility to exit the foreign market via a merger after an
inefficient CBM (high cost c). In other words, firm 1 would be able to “sell” firm 3 to the
foreign competitor, firm 4, and thus exit the foreign market. Importantly, it brings us to
study two issues. First, after an inefficient CBM, firm 1 will want to exit the foreign market
via a merger; therefore it has now to consider merger control by the AA. Indeed, exit via a
merger means selling firm 3 to firm 4 and that translates in an IMM between firms 3 and
4. We would end up with the following market structure: ME = {1, 2, 34}. Thus, when
computing its expected CBM payoff, firm 1 will now consider merger control. The second
issue is the way firm 1 and the new merged entity, composed of firm 3 and 4, will share the
foreign monopoly profit. Indeed, our idea is that the gain of firm 1 from separating from firm
3 is represented by a share of this monopoly profit, thanks to a bargaining parameter. In our
numerical application, we assume it is shared equally between firms 1, 3 and 4.
Since there is now a possibility of exit, we, for simplicity, normalize the exit cost f to zero.
Let us know derive the expected payoffs of when exit via a merger is possible:
V E1 (M in) = (1 + δ)[α∆Πin
1 + Π∗1(c)] (3.6)
V E1 (M cb) = β[(1 + δ)b13∆G− δα∆E] + δα∆E + (1 + δ)b13Π∗13(c) (3.7)
Where ∆E = Π∗1(c) + bEΠ∗34(cin)− b13Π∗13(c). It is the gain from exit via a merger where the
first term is the duopoly profit in the home market, the second term is the “gain” from selling
firm 3 to firm 4 thanks to a bargaining parameter (bE) and the last term is the profit if the
merger is rejected after an inefficient CBM. Notably, f , the exit cost, does not appear since it
has been normalized to zero.
The possibility of exit now makes the expected payoff of merging cross-border direclty
impacted by merger control (α). Let us derive the effect of merger control according the
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merger choice:
∂V E1 (M in)
∂α= (1 + δ)∆Πin
1 ≥ 0 (3.8)
∂V E1 (M cb)
∂α= δ∆E(1− β) ≥ 0 (3.9)
Thanks to expression (3.9), we observe that the effect of a less severe merger policy (↗ α)
increases the expected value of choosing a CBM; this effect is all the more important that the
uncertainty on the efficiency of the CBM increases (↘ β). In a way, a lenient merger control
“decreases” the level of uncertainty for CBM. However, it also increases the expected value of
an IMM. Therefore, we resume our intuitions in the following proposition:
Proposition 2. Under lemma 1(ii), if there is a possibility of exit via a merger after an
inefficient cross-border merger (c = c, f = 0), a lenient merger policy (higher α) balances
between two effects:
(i) it raises the expected value of a cross-border merger (∂V E
1 (Mcb)∂α ≥ 0) as it get more uncertain
(∂2V E
1 (Mcb)∂α∂β ≤ 0);
(ii) It increases the expected value of merging in-market (∂V E
1 (M in)∂α ≥ 0) since a higher α
increase the probability that an in-market merger will be accepted.
We observe now that merger policy directly affects CBM’s payoff, which was not the case
in the benchmark section. To illustrate the tradeoff between the two types of merger, we
can know compute the minimum β for which a CBM is preferred to an IMM. It is such that:
V E1 (M cb)− V E
1 (M in) ≥ 0 or:
β ≥ α[(1 + δ)∆Πin1 − δ∆E]
(1 + δ)b13∆G− δα∆E+
(1 + δ)[Π∗1(c)− b13Π∗13(c)]
(1 + δ)b13∆G− δα∆E≡ βEmin (3.10)
δ1+δ 0 b13
∆G∆Πin1
∆E∆Πcb1
12
∂βEmin∂α + -
Table 1: Sign of βEmin with respect to α
Here, contrary to the static framework the sign of the derivative of βEmin with respect
to α varies depending on some values of the parameters as shown in table 1. In this table,
∆Πcb1 = b13Π∗13(c)−Π∗1(c) is the gain from merging cross-border for firm 1. From this table,
we notice that a stricter merger control could discourage a CBM for some values of the
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parameters. We resume this result into the following proposition:
Proposition 3. If lemma 1 holds:
(i) For δ1+δ ∈ (0, b13
∆G∆Πin1
∆E∆Πcb1
), a more lenient merger policy (↗ α) lowers the incentive to
merge cross-border since it increases minimum β for which this merger would be chosen
(∂βE
min∂α > 0).
(ii) For δ1+δ ∈ (b13
∆G∆Πin1
∆E∆Πcb1, 1
2), a more lenient merger policy (↗ α) raise the incentive to
choose a cross-border merger since it decreases the minimum β for which this merger would be
chosen (∂βE
min∂α < 0).
Figure 3: Incentive for CBM with respect to βEminCournot framework: a = 10, b = 1, c = 3, cin = 2.5, c = 4, cm, c = 1.9,b12 = b13 = 0.5, bE = 1
3
Figure 3 provides us with more insights. It gives the evolution of βEmin as a function of α.
For a low level of the discount factor δ (δ = 0.2), as in the static framework, a lenient merger
policy decrease the incentive to do a CBM since it increases βEmin. For slightly higher values
(δ = 0.53), merger policy becomes almost independent from CBM’s choice. When δ = 0.97,
meaning that firm 1 gives a higher weight to its second-period expected payoff, clearly, the
more merger control is lenient, the more βdmin decreases thereby encouraging the choice of a
CBM. It means that an AA should take into account CBMs’ uncertainty when implementing
its merger policy. Here, the expected value of a CBM is increased when firm 1 gives more
value to the future (high δ). Nevertheless, a less severe merger control also makes an IMM
more attractive as seen in proposition 2.
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3.4 Comparison
In this section, we establish a comparison between both frameworks.
Figure 4: βmins comparisonCournot framework: a = 10, b = 1, c = 3, cin = 2.5, c = 4, cm, c = 1.9,b12 = b130.5, = bm = 1
3
From Figure 4, we can notice that the static case is almost similar to the extended one for
a small δ. Otherwise, we see it is the contrary. So how should the regulator behaves towards
mergers appears to be the result of a tradeoff: favor CBMs with a less severe merger policy
without making it too attractive so that firms would prefer to choose IMMs.
An Example in a Cournot Framework
To compare the benchmark (no exit) and the extended benchmark (possibility of exit), we
specify the model in a Cournot framework and determine the equilibrium market structure
depending on α, the merger control parameter. We are able to do this work by assigning
numerical values to the parameters.
Figure 5 and Figure 6 shows what is the equilbrium merger choice (hence the equilibrium
market structure) with respect to merger control. The vertical-dotted line delimit the
equilibrium merger zones. If there is no possibility of exit after an inefficient CBM, for
αNE ∈ [0, 0.23], firm 1 chooses, at equilibrium, to merge cross-border; we end up with the
following market structure: M cb = {13, 2, 4}. On the contrary, for αNE ∈ [0.23, 1], the
equilbrium choice of firm 1 is to merger in-market so that we get the following market
structure: M in = {12, 3, 4}. When an exit via merger is possible, firm choose a CBM for
αE ≤ 0.61 and the equilibirum market structures are: M cb = {13, 2, 4} if firm 1 stays in the
foreign market and ME = {1, 2, 34} if it finally separate from firm 3 via a merger. Firm 1
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Figure 5: Equilibrium merger choice if noexitCournot framework: a = 10, b = 1, c = 3,cin = 2.5, c = 4, c = 2.3, b12 = b13 = 0.5,bE = 1
3 , δ = 0.5, β = 0.6
Figure 6: Equilibrium merger choice if exitpossible
opts for an IMM if αE ≥ 0.61 and the market structure is M in = {12, 3, 4}. Therefore, one
conclusion based on our numerical simulations shows that if a firm is able to exit a foreign
market via a merger after an inefficient CBM (f = 0, c = c), an AA should take this into
account and have a more flexible merger policy (αNE ≤ αE).
When Participation Constraints are not binding
The above proposition and intuitions have been presented when lemma 1 holds, that is when
participation constraints are respected. Here, we explore the equilibrium outcome when it is
not the case. We study the results when there the firm can exit via merger the foreign market
after an inefficient CBM9.
Figure 7 presents a particular specification. When IMMs are not authorized (α0 = 0), at
equilibrium, firm 1 prefers not merging at all. For α ∈]0, 0.56], it opts for IMM where as for
α ∈ [0.56, 1], firm 1 merges cross-border. This result is due to our parameters: an IMM is
weakly cost efficient (cin = 2.9) and the probability of efficient CBM is small (β = 0.3) but
when it is efficient, the CBM achieves high synergies (c = 1.9). Here, because of the high level
of uncertainty upon merging cross-border, firm 1 will choose this merger for a sufficienty high
9In our simulations, for the benchmark case (no possibility of exit), we found that for α = 0, no merger atall is preferred whereas for α ∈]0, 1], IMM is chosen at equilibrium.
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Figure 7: Equilbrium merger choice (unbinding carticipation constraints, exit possible)Cournot framework: a = 10, b = 1, c = 3, cin = 2.9, c = 3.8, c = 1.9,b12 = b13 = 0.5, bE = 1
3 , δ = 0.5, β = 0.3
α that is αE ≥ 0.56.
The insight from this example is that when a cross-border merger is subject to a high
level of uncertainty and merger control is very severe (low α), firms may prefer not merging
at all. Even for IMMs: in reality, they are accepted for sufficient merger-specific efficiencies in
addition to merger remedies (divestitures). We did not take them into account here but it
were the case, the status quo equilibrium may exist for higher values of α than α0.
4 Welfare Analysis
5 Extensions
6 Conclusion
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