Better safe than sorry?
Ex ante vs ex post merger control
Andreea Cosnita-Langlais∗and Jean-Philippe Tropeano†
November 10th, 2014‡
Abstract
We study the optimal timing of merger control by comparing the pre- and
post-closing enforcement. Mergers have both pro- and anticompetitive effects,
and the verifiable information on them is endogenous: it depends on the timing
of the merger control, as well as on some investment in evidence production. The
ex post control is optimal whenever merger remedies are relatively costlier for
the pro-competitive merger projects and the cost of evidence production for the
agency is sufficiently low.
Keywords: merger control, merger remedies, hard evidence production,
JEL classification: L41, K21, D82
∗
†
EconomiX-CNRS and Université Paris Ouest Nanterre La Défense; [email protected].
Université de Paris 1 and Paris School of Economics; [email protected], coresponding au-
thor.
‡
We are indebted to Daniel Rubinfeld and Eirik K. Kristiansen for their helpful comments and
suggestions. We also thank various participants attending the EARIE 2012 conference in Rome,
the BECCLE 2012 conference in Bergen, the MaCCI-ZEW 2013 conference in Mannheim, and the
seminars at the universities of Paris 1 and Liege. All remaining errors are ours.
1
1
Introduction
The ability of the parties to provide evidence on the merger’s consequences for competition and consumers plays a critical role in current merger control. The following
examples illustrate this.
On February 1st, 2012, the European Commission (EC) prohibited the Deutsche
Börse/NYSE-Euronext merger (case M.6166). The EC banned ex ante this planned
merger to near monopoly on the European financial derivatives market, despite future
substantial efficiency gains argued by the parties (around 3 billion euros). By contrast,
in January 2004, the Federal Trade Commission (FTC) decided to close its investigation
of the consummated merger between Genzyme and Novazyme1 . The FTC’s decision
not to challenge this merger to monopoly was based on both evidence of a lack of
anticompetitive effects and of synergies made possible by the merger during the two
years that followed the merger2 . Had the merger been examined before consummation,
the mere fact that it led to monopoly would have recommended its prohibition3 . In
the UK, where merger notification is not mandatory and roughly half of the mergers
are not notified, the Competition Commission concluded ex post that the Tesco/Coop merger had led to a substantial lessening of competition after consummation, and
then ordered the full unscrambling4 . In most jurisdictions however, the pre-merger
notification is mandatory, and thus the likely competitive effects must be assessed ex
ante. Thus the very timing of merger assessment determines the quality of the evidence
available, and therefore the outcome of merger control. To a certain extent, this idea
underlies the appeal judgement by the European Court of First Instance in the General
1
See details at http://www.ftc.gov/opa/2004/01/genzyme.shtm.
See Chairman’s Muris statement, available at http://www.ftc.gov/os/2004/01/murisgenzymestmt.pdf.
3
See Commissioner’s Thompson dissenting statement, available at
2
http://www.ftc.gov/os/2004/01/thompsongenzymestmt.pdf.
4
See details at http://www.competition-commission.org.uk/assets/competitioncommission/docs/pdf/noninquiry/rep_pub/reports/2007/fulltext/534.pdf.
2
Electric/Honeywell merger. In dealing with the vertical and conglomerate aspects of
the case, the Court stressed that although the EC was entitled to base its merger
control decision on the evidence available ex ante on the future consequences of the
merger, the fact that the foreseen conduct of the parties could have been challenged
ex post as an abuse of dominant position (in case it actually materialized) called for
a high standard of proof and sufficiently convincing evidence within the prospective
analysis of the EC5 .
The above examples illustrate the very purpose of our paper, which is to study
the role of the timing of merger control enforcement for the evidence provision by the
parties, and thereby for the final outcome of merger policy. We aim to determine which
timing of merger control performs better, the pre- or the post-closing enforcement.
We base our analysis on a simple model where the merger has both pro- and anticompetitive effects, but this is the firms’ private information. The key assumption is
that the enforcement relies on the confrontation of hard evidence, and this confrontation takes place either before (ex ante) or after the closing (ex post). In order for the
merger to be cleared unconditionally, i.e. without remedies, the merging firms must
provide verifiable evidence on pro-competitive arguments in favor of their merger, such
as efficiency gains for instance, enough to counterbalance the hard evidence provided
by the competition agency (CA henceforth) on the anticompetitive effects it has identified during the assessment. We assume that the hard evidence is costly to provide,
and that the timing of the assessment has an impact on the availability of this evidence
and its production cost. We also assume that a set of feasible remedies always exists
and that they write off the full anticompetitive effect of the merger, although at the
cost of sacrificing part of the merger profit for the firms. Moreover, the remedies are
less costly for the merging firms if they are undertaken before rather than after the
merger.
5
See in particular recitals 74 to 76 of the Court judgement - case T-210/01, December 14, 2005.
3
Our model indicates that the optimality of the ex post merger control requires
two key conditions: that merger remedies be relatively costlier for the pro-competitive
projects and a low cost of information investment for the CA. The first condition allows
the CA to screen mergers ex post. Without it, the pooling of merger types ex post
may lead to an adverse selection problem where the pro-competitive mergers prefer to
undertake remedies, while the anticompetitive mergers are submitted without. The
second condition makes the merger screening optimal, by allowing the CA to correctly
assess the merger anticompetitive effects. In other words, we identify the conditions
under which the threat of an ex post control leads to the right incentives ex ante.
The literature dealing with the optimal timing of competition policy is quite small
and recent. Barros (2003) and Berges et al. (2008) study the opportunity of mandatory
notifications for the agreement exemptions under Art.101 TFEU. Choe and Shekhar,
(2009) consider the same question, of compulsory ex ante notifications, but in the case
of mergers. Our paper departs from these articles in two main aspects: we focus on
the role of evidence provision, both before and after consummation, while the existing
papers ignore this point, and moreover, we endogenize the evidence available. To our
knowledge, there is only one paper (Ottavianni and Wickelgren, 2011) dealing with
the impact of the information available on the timing of merger control. Their paper
shows that the ex post enforcement always performs better as long as the quality of the
information available to the CA after the merger is so poor that the merging firms face
a low enough risk of costly ex post remedies. We take one step further, by studying the
role of the endogenous asymmetric information between the firms and the competition
authority through the evidence production process. By so doing we also complement
in a dynamic framework Lagerlöf and Heidhues (2005), who also discussed the costly
evidence production, but in order to establish the desirability of an efficiency defense
in merger control.
The paper proceeds as follows: the model is presented next, and the main results
4
derived in Section 3. We then discuss possible policy implications before concluding.
2
The model
We consider a simple reduced-form merger control game between two risk-neutral
agents: the merging firms and the competition authority. The merger has both anticompetitive and pro-competitive effects. Depending on the magnitude of each, there
exist two types of mergers: a pro-competitive merger type, denoted H, and an anticompetitive merger type, denoted L. Both types occur with equal probabilities.
The payoffs
The profit earned from merger depends on both effects and is denoted π H for
type H and π L for type L. Typically, type H generates higher efficiency gains for
instance and thus makes a higher profit: π H > π L . The net impact of the merger on
consumers’ surplus also depends on the two opposite competitive effects. Denote W i
the consumers’ surplus variation due to merger for i ∈ {H, L}. Type H ensures an
increase in consumers’ surplus, while a type L merger leads to a decrease in consumer
welfare: W H > 0 > W L .
The CA applies a consumer surplus welfare standard. So as to avoid clearing
anticompetitive mergers, the CA may condition its approval on the adoption of some
corrective remedies. These remedies always exist and completely fix the anticompetitive
effect of the merger. Applying the remedies to type L ensures an increase in consumers’
surplus: W RL > 0. In turn, remedies applied to type H overfix the merger and thus
reduce consumers’ surplus with respect to the no remedies case: 0 < W HR < W H . We
put this down to a possible negative effect of remedies on merger synergies generated
by the pro-competitive projects. Nevertheless, remedies reduce merger profit whatever
the merger type i = H, L: 0 < π iR < π i . Finally, if the merging firms undertake the
remedies after the consummation of their merger, they incur an additional fixed cost
5
equal to k > 0.
The information available and the production of evidence
The CA provides hard evidence on arguments against the unconditional approval of
the merger, such as high market power and barriers to entry, slow pace of innovation and
outsiders’ capacity constraints (i.e. arguments justifying the merger’s anticompetitive
effect). Denote xA the amount of CA’s hard evidence, and cA (xA ) its corresponding
evidence production cost, with c′A (x) ≥ 0 and cA (0) = 0.
The merger type is the firms’ private information. In order to secure the merger
approval, the firms of type i (i = H, L) provide an amount xi of hard evidence on
the pro-competitive arguments in favor of their merger, such as substantial merger
efficiency gains, easy market access, fast pace of innovation, or incentives to increase or
maintain product quality. We assume the ex ante cost of production for xi to be infinite.
Ex post, we denote ci (xi ) the merging firms’ cost of evidence provision, where ci (xi )
is increasing and convex with ci (0) = 0. Ex post the firms may have the opportunity
and ability to provide convincing evidence in favor of the merger, such as actually
materializing efficiency gains or innovation. We also assume that c′H (xi ) < c′L (xi ).
This assumption captures the intuition that an additional piece of hard evidence is
relatively costlier to provide for the L type.
We thus aim to replicate the current evidence provision in merger control: the
CA uses various methods to assess the merger’s anticompetitive effect and provide
verifiable evidence on the probable price increase. In their turn, the firms must produce
convincing evidence in favor of the merger, such as enough efficiency gains for instance,
in order to avoid remedies.
The merger control game
The CA controls the merger and as a result decides whether to impose remedies. A
merger project will be unconditionally accepted only if the CA receives a signal that
the firms win the hard evidence confrontation. Let p be the probability of this signal,
6

 1 if xi ≥ xA
with p(xA , xi ) =
with i = H, L.
 0 if xi < xA
The timing of the game is the following:
Stage 1: The CA decides whether to control mergers ex ante. This decision is
observed by the firms. The firms also observe their merger type.
Stage 2: If no merger control takes place ex ante, the firms decide whether to
undertake remedies before the merger. This decision is not observed by the CA.
Stage 3: The merger control takes place: the CA sets the threshold xA and the
merging firms observe xA and invest xi . The merger is cleared without remedies if the
signal is observed and remedies are imposed otherwise.
We determine next the Perfect Bayesian Equilibrium of this game. The detailed
proofs are grouped in the final Appendix.
3
The optimal timing of merger control
We consider first the case of the ex ante merger control, and below we describe the
optimal CA decision in this case.
Proposition 1 If the ex ante merger control applies, the CA sets xA = ε > 0 iff
∆ = 12 (W HR − W H ) + 12 (W LR − W L ) > 0. Otherwise the CA sets xA = 0.
Proof. If the CA sets xA = 0, then the expected welfare is 12 W H + 12 W L . Instead
if the CA decides to impose remedies by setting xA = ε > 0, the expected welfare is
1
W HR
2
+ 12 W LR .
Let us explain this result. Ex ante, the merging firms cannot provide hard evidence
on the merger’s pro-competitive effect. Therefore, it is sufficient for the CA to provide
a very small amount of evidence on the anticompetitive effect (xA = ε > 0) in order
to clear the merger conditionally on remedies. However, whenever remedies are imposed, the CA avoids anticompetitive mergers, but it also runs the risk of overfixing
7
the pro-competitive ones. Thus, the CA needs to balance the social cost of clearing
anticompetitive projects and the social cost of overfixing the pro-competitive ones. The
CA’s decision will depend on the magnitude of both, as captured by the sign of ∆. In
short, since ex ante the firms cannot provide any information on their merger type, the
CA makes its decision based on its priors.
We turn now to the ex post merger control. The merger consummation will enable
the production of evidence on the pro-competitive effect. The main question is to
what extent the hard information available will relax the trade-off between both types
of merger control errors.
In order to hope for a better outcome of merger control ex post, the CA needs to
screen merger types so as to impose remedies only to the anticompetitive projects. For
that purpose, the CA must produce enough arguments on the anticompetitive effect
that may only be compensated by the pro-competitive arguments of type H. The
following lemma gives the conditions ensuring the screening of types:
Lemma 1 (i) If π H − π HR > π L − π LR (condition C), there always exists a level of
evidence threshold xA = x set by the CA that is only met by type H (screening of types),
where x is such that π L − π LR + k = cL (x).
(ii) If π H − π HR < π L − π LR , (condition S), there always exists a level of evidence
threshold xA = x set by the CA that is only met by type H (screening of types) iff
x > x where x is such that (π H − π HR ) − (π L − π LR ) = cH (x) − cL (x) and x is such
that π L − π LR + k = cL (x).
When the merging firms decide whether they invest in evidence provision to obtain the merger clearing, they make a simple cost-benefit analysis between the cost of
evidence provision ci (xA ) and the cost of remedies (π iR − π R ) + k. The screening of
types requires a level of evidence that can be profitably met only by type H. Lemma
8
1 indicates that the cross-impact of remedies and merger type on the merger profit
plays a key role on the CA’s ability to screen types ex post. Two cases are possible.
In the first case, remedies are relatively costlier for the pro-competitive merging firms:
π H − πHR > πL − π LR . We call this situation complementarity. In the second case, the
pro-competitive merger type suffers a relatively lower profit loss when merging with
remedies: π H − π HR < π L − π LR . We call this substitutability 6 .
In case of complementarity, the CA can always screen types ex post. Because the
complementarity implies that undertaking remedies is relatively costlier for type H
than for type L, the former is more eager to invest in evidence provision to avoid
remedies than the latter. This enables the screening of types by having the CA set an
evidence threshold high enough to deter the investment in evidence provision by the L
type without chilling the evidence investment of type H. Screening may not eventually
be the optimal strategy of the CA, but it is always feasible.
On the contrary, in case of substitutability (for instance when the efficiency gains
well compensate the profit loss from merger remedies), the CA cannot always screen
types, because the ultimate incentive to invest in evidence provision is the outcome of
two opposite effects: while remedies are relatively costlier for the L type, the evidence
provision is cheaper for the H type. In fact, the higher the substitutability, the cheaper
the choice of ex ante remedy for the H type, and therefore the larger the incentive gap
6
One way to understand the complementarity/substitutability is to assume that the extent to which
merging firms benefit from their synergies depends on the amount of assets they are left with in case
remedies/divestitures are required. In the case of complementarity, this relationship is positive: the
more assets the firms own, the higher the profit gain from synergies. In the case of substitutability,
the efficiency gains compensate for the profit loss from the imposition of remedies, so the higher the
cost savings, the cheaper the remedies for the firms. Note that in a continous-type framework, the two
conditions would come down to the sign of the remedy/synergy cross-derivative of the merger profit.
For a toy-model example with Cournot competition displaying such properties, see Cosnita-Langlais
and Tropeano 2012.
9
between both merger types. This gap is captured by the amount of evidence x above
which the H type has relatively more incentives to invest in evidence provision than
the L type. The screening of types requires the CA to set a threshold of evidence x,
but this amount of evidence may be so high that it could be no longer profitable for
the H type to invest in evidence production (that is the case iff x < x). Therefore, for
screening to be possible, the before-mentioned substitutability needs to be low enough.
Clearly, the ability to screen merger types as well as the cost incurred by the CA
to do so determine the optimal merger control outcome. For instance, the inability to
screen types will constrain the CA either to impose remedies to both types, or to clear
them both without remedies. Eventually, this may deter the H type from merging
without remedies, and thus lead to a suboptimal outcome. The following proposition
summarizes the possible outcomes of the ex post merger control:
Proposition 2 The Perfect Bayesian Equilibrium of the ex post merger control game
is characterized by the following strategies:
Under condition (C) or under condition (S) and x < x:
(i) If cA (x) < (W LR − W L ), the CA sets xA = x with probability a∗ =
π L −π LR
k+π L −π LR
and sets xA = 0 otherwise, type H invests xH = x and always merges without remedies
(mH = 1), while type L invests xL = 0 and merges without remedies with probability
mL =
cA (x)+W H
.
(W LR −W L )
(ii) If cA (x) > (W LR − W L ) − W H , then the CA sets xA = 0 and both types merge
without remedies (mH = mL = 1).
Under condition (S) and x > x:
(i) If x > x and cA (x) > (W LR − W L ) − (W H − W HR ), the CA sets xA = 0 and
both types merge without remedies (mL = mH = 1);
(ii) If x > x and cA (x) < W LR − W L , the CA sets xA = x with probability a∗ =
π L −π LR
k+π L −π LR
and xA = 0 otherwise, type H always merges with remedies (mH = 0) whereas
type L merges without remedies with probability mL =
10
cA (x)+W H
.
(W LR −W L )
Proposition 2 indicates that the ability of the ex post merger control to give the
right incentives to merge with or without remedies depends on the CA’s decision to
screen types ex post or not, and thereby relies on both the cross-impact of remedies and
merger type (substitutability or complementarity) and the cost of evidence production
for the CA.
In case of complementarity, the outcome of the ex post merger control only depends
on the CA’s cost of evidence production: complementarity ensures screening if the CA
provides enough evidence. If its evidence provision cost is high, the screening of types
is too costly and then the CA prefers to clear both merger types without imposing
remedies. This obviously induce both types to merge without remedies. For a lower
cost of evidence provision, the CA will afford to screen types ex post, which then induces
the L type to undertake remedies ex ante with a positive probability. Note that the
L type will merge without remedies with a positive probability because the evidence
provision makes it costly for the CA to always control mergers ex post. It is easy to
check that a decrease in the evidence cost for the CA makes more likely the control,
and thus reduces the probability for type L to choose to merge without remedies. In
turn, the ex post screening of types leads the H type to always choose to merge without
remedies - this is a direct implication of Lemma 1. To sum up, whereas Lemma 1 made
clear that screening is always feasible in case of complementarity, Proposition 2 shows
that it is also optimal as long as the cost of evidence for the CA is low enough.
In case of substitutability, for the screening of types to be optimal it takes both a
low cost of evidence for the CA and a low level of the before-mentioned substitutability. Much as in the previous case, a low level of substitutability makes the screening
of types possible, whereas the low cost of enforcement for the CA makes it optimal.
This yields the same merger control outcome as before. In turn, a high level of substitutability makes impossible the screening of type, and then the CA can only either
impose remedies to both types or clear them both. The optimal decision depends on
11
its cost of evidence provision and the expected welfare with and without remedies. In
particular, Proposition 2 shows that if the expected welfare is higher with rather than
without remedies, and if the evidence cost for the CA is relatively low, then an adverse
selection outcome obtains. Let us explain this. Since the ex post screening is not
feasible, and since the CA can increase welfare by imposing remedies to both types, it
will do so whenever its evidence cost is low enough. But this incentivizes the H type
to undertake the remedies ex ante, whereas the L type will prefer to run the risk of ex
post remedies and thereby choose the merger without remedies ex ante. This adverse
selection outcome is made possible by the cross-impact of merger remedies and merger
type on the firms’ profit, because in this case it is relatively cheaper for the H type
to undertake remedies rather than invest in the costly provision of evidence ex post,
whereas the opposite holds for the L type. Moreover, the adverse selection outcome
turns out to be an equilibrium because it is too costly for the CA to always control
mergers ex post. Note also that the threshold level of substitutability above which the
CA is unable to screen types depends on the cost of evidence provision for the merging
firms: basically, the lower this cost, the higher the incentives for the H type to merge
without remedies and then provide ex post hard evidence on pro-competitive effects to
match the evidence threshold set by the CA.
Finally, it is worth stressing that the adverse selection outcome identified in Proposition 2 comes down to a situation where the imperfect ex post merger control prevents
efficient merger decisions ex ante despite the fact that the merging firms know with
certainty their true merger type ex post. In other words, we show that the ex post
merger control may be suboptimal without resorting to uncertainty as a possible source
of inefficiency, as opposed to Ottaviani and Wickelgren’s (2011) analysis.
After having identified the outcome of the ex post merger control, the remaining
step of the analysis is to determine the optimal timing of merger control. The following
12
proposition displays the result of the expected welfare comparison between the ex ante
and the ex post merger control:
Proposition 3 Under condition C, the ex post control is strictly preferred if cA (x) is
low enough. Under condition S, the ex post control is strictly preferred if cA (x) is low
enough and x < x.
Clearly, for the ex post assessment to be optimal, the screening of types is absolutely
necessary, otherwise the ex post control is at best equivalent to the ex ante control.
It is then straightforward to see that in case of complementarity (condition C), the
ex post control strictly dominates the ex ante control if the cost of evidence provision
for the CA is low enough. As before argued, the complementarity ensures the screening
of types, and such screening is optimal as long as the CA can provide evidence and
thus control mergers at a reasonable cost. Then ex post the CA will impose remedies
only to the L type and will clear the H type unconditionally, which explains why the
ex post merger control is preferred. Otherwise, for a high evidence cost for the CA, the
ex post control is weakly dominated. It is even strictly dominated whenever its high
evidence cost makes the CA inefficiently clear ex post both merger types.
To sum up, if merger remedies are relatively costlier for the H type, the crucial
parameter explaining the optimality of the ex post merger assessment is the cost of
merger assessment and hard evidence provision for the CA: if this is low enough, the
complementarity enables the CA to correctly incentivize the two types of merging firms
and leads to an efficient outcome of merger control.
Nevertheless, in case of substitutability, a low cost of evidence for the CA is no longer
sufficient for the ex post merger control to be optimal: a low level of substitutability
is also required. Otherwise, the ex post control is strictly dominated by the ex ante
control because of the adverse selection effect, according to which the H type prefers
avoiding a costly ex post control and instead undertakes remedies ex ante, while the L
13
type prefers to merge without remedies. In other words, the H type exploits its relative
remedy-cost advantage beforehand. Instead, the L type lacks such an opportunity and
can only go ahead and merge without remedies, even if they may be imposed ex post
by the CA. Thus, in order for the ex post control to remain optimal, it takes not only
a low cost of evidence for the CA, but also that the remedies impact on the H type
should be weak enough, i.e. a low degree of substitutability.
At the end of the day, two main factors play against the ex post control: the crosseffect between the merger remedies and merger type, and the cost of information for
the CA.
4
Conclusion
This paper studied the optimal timing of merger control by comparing the pre- and
post-closing enforcement. Mergers have both pro- and anticompetitive effects, and
in order to avoid costly remedies, the merging firms need to provide enough hard
evidence on the merger’s pro-competitive effect to counterbalance the anticompetitive
effect argued by the agency. Investing in hard evidence provision is costly, both for
the firms and for the agency, and the timing of merger assessment impacts on this
cost, as well on that of remedies for the merging firms. We show that the post-closure
merger control is optimal whenever merger remedies are relatively costlier for the procompetitive merger projects and the cost of evidence production for the agency is
sufficiently low. Our results may help explain why the ex ante merger control is the
preferred choice of most agencies.
14
References
[1] Barros, P., 2003, "Looking behind the curtain - effects of the modernization of the
European competition policy", European Economic Review 47(4), p. 613-624.
[2] Berges, F., F. Loss, E. Malavolti and T. Vergé, 2008, "European Competition
Policy Modernization: From Notification to Legal Exception", European Economic
Review 52(1), p. 77-98
[3] Choe, C. et C. Shekhar, 2009, "Compulsory or voluntary pre-merger notification?
Theory and some evidence", International Journal of Industrial Organization 28(1),
p. 10-20.
[4] Cosnita-Langlais, A. and J.-P. Tropeano, 2012, "Do Remedies Affect the Efficiency
Defense? An Optimal Merger-Control Analysis", International Journal of Industrial
Organization, 30(1), p. 58-66.
[5] Lagerlöf, J. and P. Heidhues, 2005, "On the desirability of an efficiency defense
in merger control", International Journal of Industrial Organization 23(9-10), p.
803-27
[6] Ottavianni, M. et A. Wickelgren, 2011, "Ex ante or ex post competition policy, A
progress report", International Journal of Industrial Organization 29(3), p. 356-35.
5
Appendix
Proof of Lemma 1.
If condition C holds then for all x one has that π H − π HR −
cH (x) > π L − π LR − cL (x). Then to induce only type H to invest in evidence provision
the CA sets xA = x, where x is such that (π L − π LR + k) = cL (x).
If condition S holds, then to induce type L not to invest in evidence provision, the
CA is constrained to invest xA = x. For that level of evidence, firm H invests in evidence
15
provision iff x < x, where x is such that (π H − π HR ) − (π L − π LR ) = cH (x) − cL (x). x
is unique because c′H (x) < c′L (x).
Proof of Proposition 2. We determine the Perfect Bayesian Equilibrium of the
game with ex post merger control.
Condition C holds.
• The CA can successfully screen types by investing xA = x. We determine first an
equilibrium with screening of types ex post.
Equilibrium:
The CA invests xA = x with probability a =
πL −π LR
k+π L −π LR
and does not control other-
wise.
Type H invests xH = x.
Type L invests xL = 0.
Type H always merges without remedies (mH = 1) and type L merges without
remedies as well with probability mL .
Let us check that there are no incentives to deviate from theses strategies:
- for type L: following Lemma 1, there are no incentive to invest in evidence
provision. In addition, type L is indifferent between merging with and without remedies
for π LR = a(π LR − k) + (1 − a)π L , i.e. iff a =
π L −π LR
.
k+π L −π LR
- for type H: according to Lemma 1, it has incentives to invest in evidence provision
xH = x. Ex ante the H firms have no incentives to merge without remedies.
- the CA is indifferent between controlling or not mergers iff mL =
cA (x)+W H
.
(W LR −W L )
We have mL < 1 iff (W LR − W L ) > cA (x) + W H
We thus conclude that the previous set of strategies are an equilibrium iff (W LR −
W L ) > cA (x) + W H .
16
• If the above cost condition (W LR − W L ) > cA (x) + W H is not satisfied, the CA
is induced to deviate and will not control mergers.
Equilibrium:
The CA does not control mergers xA = 0
Both types merge without remedies: mH = mL = 1.
Let us check that there are no incentive to deviate:
- the firms face no risk of ex post remedies and thus merge without remedies.
- the CA does not control merger and gives up screening types iff (W LR − W L ) >
cA (x) + W H .
Condition S holds.
Case x < x
Here the screening of types is possible: the same reasoning applies as when condition
C holds.
Case x > x
• No screening is possible. Then the CA decides whether to impose remedies to
both types or not.
Let us consider first the equilibrium where the CA invests in evidence provision and
requires remedies:
The CA invests xA = x with probability a =
π L −π LR
k+π L −π LR
Type H merges with remedies (mH = 0).
Type L merges without remedies with probability mL =
cA (x)+W H
(W LR −W L )
and does not
invest in evidence provision (xL = 0).
Let us check that agents have no incentive to deviate.
- type L is indifferent between merging without remedies and merging with remedies
iff a =
πL −π LR
k+π L −π LR
(see above).
17
- type H prefers merging with remedies because x > x.
- the CA is indifferent between controlling or not mergers iff mL =
cA (x)+W H
.
(W LR −W L )
This
probability is below 1 iff (W LR − W L ) > cA (x) + W H .
We thus conclude that the set of strategies is an equilibrium iff (W LR − W L ) >
cA (x) + W H .
• If the above cost condition is not satisfied, then the CA will deviate and will not
control mergers.
Equilibrium:
The CA does not control mergers xA = 0
Both types merge without remedies: mH = mL = 1.
If the CA deviates and impose remedies to both types, the welfare gain is equal to
(W LR − W L ) − (W H − W HR ). This a profitable strategy iff cA (x) > (W LR − W L ) −
(W H − W HR ).
Proof of Proposition 3. Condition C holds.
If the CA screens types, the expected consumer surplus equals W H + mL W LR +
(1 − mLR )W L . Since the probability mL decreases as the cost cA (x) decreases, there
exists a cost level cA (x) such that W H + mL W LR + (1 − mLR )W L > Max(W HR +
W LR , W H + W L ).
Condition S holds.
Case x < x is similar to condition C.
Case x > x: screening is not possible. Then, the expected welfare is either W H +W L
if ∆ < 0, or W HR + mL W LR + (1 − mL )W L if ∆ > 0 and the CA is induced to impose
remedies. In both cases the ex ante control ensures higher expected welfare.
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