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Please do not quote or circulate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

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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.

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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.

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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.

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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).

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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.

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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

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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

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∂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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