Efficiency gains and myopic antitrust authority in [614876]

Efficiency gains and myopic antitrust authority in
a dynamic merger gameB
Massimo Mottaa, Helder Vasconcelosb,*
aUniversitat Pompeu Fabra, Barcelona, European University Institute, Florence
bIGIER, Universita ` Bocconi, Milan
Available online 6 October 2005
Abstract
This paper models a sequential merger formation game with endogenous efficiency gains in which
every merger has to be submitted for approval to the Antitrust Authority (AA). Two different types of AAare studied: first, a myopic AA, which judges a given merger without considering that subsequent mergers
may occur; and, second, a forward looking AA, which anticipates the ultimate market structure a given
merger will lead to. By contrasting the decisions of these two types of AA, merger policy implications canbe drawn. In particular, the efficiency offence argument does not find any justification under a forward
looking AA.
D2005 Elsevier B.V . All rights reserved.
JEL classification: D43; L13; L41
Keywords: Endogenous mergers; Foresight; Efficiency offence
0167-7187/$ – see front matter D2005 Elsevier B.V . All rights reserved.
doi:10.1016/j.ijindorg.2005.08.001BWe are very grateful to Patrick Rey for comments, discussions, suggestions that substantially improved this paper.
Helpful comments from Jacques Cre ´mer, Vincenzo Denicolo `, Bruno Jullien, Liliane Karlinger, an anonymous referee and
seminar participants at the European University Institute, Universita ` Cattolica–Milano, WZB (Berlin), Faculdade de
Economia do Porto, Universidade Catolica Portuguesa (Porto), 2004 E.E.A. Conference (Madrid) and 2004 E.A.R.I.E.
Conference (Berlin) are also acknowledged. Vasconcelos thanks the Portuguese Ministry of Science and Technology andBocconi University for financial support. This paper was started when Vasconcelos was at IDEI, Universite ´ de Toulouse.
* Corresponding author.
E-mail addresses: [anonimizat] (M. Motta), [anonimizat] (H. Vasconcelos).International Journal of Industrial Organization
23 (2005) 777– 801
www.elsevier.com/locate/econbase

1. Introduction
Economic analysis suggests that efficiency gains play a crucial role in determining the effect
of mergers on consumer and total welfare.1Accordingly, Antitrust Authorities (AAs) should try
and estimate whether efficiency gains are likely or not to offset the higher market power enjoyedby the merging firms. This is precisely the approach indicated by the Merger Guidelines released
by the US Department of Justice, which
b…will not challenge a merger if cognizable efficiencies are of a character and magnitude
such that the merger is not likely to be anticompetitive in any relevant market. To make the
requisite determination, the Agency considers whether cognizable efficiencies likely
would be sufficient to reverse the merger’s potential to harm consumers in the relevantmarket, e.g. by preventing price increases in that market. Q(US Merger Guidelines, revised
April 8, 1997, Section 4).
The European Commission (EC) has so far had a more ambiguous approach towards
efficiency gains. It has been debated whether the wording of the European Merger RegulationNo.4064/89 allowed or not for an efficiency defence.
2However, in practice, the EC has so far
never used efficiency gains arguments to clear a merger. In the past, whenever cost reductionshave been claimed by the merging parties, the EC dismissed those claims on various grounds.
3
Further, the EC used possible cost reductions as an argument against a merger in at least one
of the early cases.4None the less, some of the recent EC decisions have raised doubts that the
EC is using again some version of efficiency offence arguments. The widely discussed General
Electric-Honeywell merger is a case in point.5General Electric is a leading producer of jet
engines for large commercial aircraft and Honeywell of avionics products. Among otherconcerns, the EC thought that the merged firms could have bundled engine and avionicsproducts, to the detriment of competitors. The EC argued that although the welfare effect wouldhave been beneficial in the short-run, in the long-run competitors would have left the industryand GE/Honeywell become a monopolist, thereby harming welfare.
6
The extent to which the EC might still use efficiency offence arguments has probably been
exaggerated, and we are convinced that European merger policy will soon explicitly accept
2See for instance Neven et al. (1993:62-63, and 116-117) , and Jacquemin (1990) . However, article 1.1 (b) of the
Merger Regulation says that in its appraisal of the merger, the Commission shall take into account, among other thingsb…the interests of the intermediate and ultimate consumers, and the development of technical and economic progress
provided that it is to consumers’ advantage and does not form an obstacle to competition. QThis would seem to allow for
efficiency considerations in mergers.
3For instance, in Ae´rospatiale-Alenia/DeHavilland (Case IV/M.053 (October 2, 1991), OJ L334/42, 1991, at 65) the
EC argued that cost savings would have been negligible, had not been properly quantified, were not merger-specific (theycould have been attained without the need of a concentration) and would have not gone in any case to consumers’
advantage. Other cases where defendants raised efficiency considerations were Accor/Wagon-Lits, MSG/Media Services,
Mercedes-Benz/Kassbohrer . See also Noe¨l (1997:512-514) .
4See AT and T/NCR, Case IV/M.050 (18 January 1991). Other cases are discussed by Noe¨l (1997:512) andNeven et
al. (1993:116-117) .
5General Electric/Honeywell, case COMP/M.2220.
6Similar concerns have also been expressed in other cases where the EC has proposed the so-called bportfolio theory Q
of merger effects. See e.g., Guinness/Grand Metropolitan (case IV/M.938); Coca-Cola/Amalgamated Beverages (case
IV/M.796); Coca-Cola/Carlsberg (case IV/M.833).1SeeFarrell and Shapiro (1990) and, for a general discussion of the effects of mergers, Motta (2004) .M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 778

efficiency defence arguments.7Nevertheless, a more general theoretical question remains open,
and this deals with whether efficiency gains might indeed be anti-competitive in some cases.In our opinion, there are two distinct, although possibly related, rationales for efficiencyoffence arguments. The first lies in the possibility that merged firms become so efficient that,even without engaging in strategic behaviour, their competitors will be unable to competeand will exit the market, causing an overall negative effect. The second resides in the
possibility that, after merging, two firms might engage in strategic anti-competitive practices
aimed at exploiting their increased (market or financial) power so as to force rivals to exit.
This paper focuses on the first possible motivation for an efficiency offence argument.
8We
analyse a simple model where a merger increases firms’ capacity, which in turn leads to scaleeconomies. When such efficiency gains are very small, there would be no merger (we use aCournot model). When they are of intermediate importance, outsider firms lose competitivenessbut continue to operate profitably, resulting in a more efficient market outcome, the case usuallyanalysed in the literature. However, a merger might give the two merging firms such important
cost savings that—without engaging in any predatory practice or any bstrategic Qaction—rivals
would be unable to survive in the industry.
The last case might seem to provide some rationale for the efficiency offence arguments. In
fact, there exist two objections that should be considered before drawing the conclusion thatefficiency gains might be detrimental. First, it is not enough to show that competitors would exitthe industry to conclude that the merger has negative effects: one should show that consumerswould be hurt as well (antitrust policy does not protect competitors, it protects competition!).Second, and perhaps more important, if the merger gives rise to such important cost savings,
should we not expect that competitors would react to attain similar savings, rather than waiting
to be forced out of the market?
Our simple formal setting allows to consider both points. First, we show that if efficiencies are
strong, prices might be lower after the merger—even if the competitive disadvantage obliges somefirms to exit. Second, we show that a static model where the effects of an exogenous merger are
analysed might be misleading. In a dynamic setting such as the one we propose here, if a mergerprovides important cost savings, then it will be followed by a merger of the rivals. In other words, ifthere exist efficiency gains to be reaped from a merger, outsiders will respond by merging as well.
Thisbdefensive Qmerger will allow the outsiders to the first merger to match the efficiency gains of
the first merger partners, leading to a final outcome which is positive for society. Indeed, we showthat if the AA is forward looking, that is if it takes into account that the first merger will be followedby another, no efficiency offence argument would be justified. Either cost savings are small, and themerger(s) should be blocked; or cost savings are large, and the merger(s) should be allowed.
While the possibility that AAs (and more particularly, the European Commission) might rely
on efficiency offence arguments has received some attention in the press and in law articles (seee.g.Noe¨l, 1997 ), economists have devoted scarce attention to this issue. Padilla (2002) offers an
informal discussion of efficiency offence arguments in recent EC practice. Motta (2004, chapter
8To our knowledge, the second motivation has never been the object of a formal analysis. The extent to which two
firms might behave anti-competitively after merging seems an interesting topic of research as well.7Since May 1, 2004, the new Merger Regulation No.139/2004 of 20 January 2004 has entered into force, amending
Regulation 4064/89. Introducing the changes to the Regulation, the Council clarifies at point (29) that efficiency arguments
are crucial in the assessment of mergers. The bGuidelines on the assessment of horizontal mergers Q(see Official Journal of
the EC C31 of 5 February 2004) further clarifies the approach of the EC towards efficiency gains, which—at least inprinciple, although there is no doubt it will be applied in practice—is now in line with economic thinking.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 779

5)formally analyses an efficiency offence argument, but limits attention to the static framework
that corresponds to Section 3 of this paper.9,10
Apart from the discussion of the efficiency offence argument, we regard the dynamic feature
of our merger model as the main contribution of this paper. Most of the existing models ofmergers do not deal with the dynamics of the merger processes, as they simply compare a pre-merger situation with a post-merger situation, without taking into account that a merger might
trigger other mergers. Exceptions are Gowrisankaran (1999) ,Fauli-Oller (2000) , and Nilssen and
Sorgard (1998) .
Relative to these papers, we explicitly model the presence of an Antitrust Authority that is an
active player of our game, and is called to authorise or block a merger whenever one is proposed.
We contrast two games. In the first, the AA is myopic: when a merger is proposed, the AA
judges it without considering that further mergers might occur (i.e., it thinks that either theoutsiders stay bpassively Qin the industry or they leave it—it does not consider that outsiders
might take actions such as merging themselves). This myopic behaviour leads the AA to use an
efficiency offence argument and block the merger under some parameter constellations.
In the second game, the AA is forward looking and is able to correctly anticipate the future.
Along the equilibrium path, if efficiency gains are large enough the first merger between twofirms will be authorised, because the AA knows that it will be followed by another merger by theoutsiders—that will also be authorised, because otherwise there would be inefficient exit. (Theremaining two firms will also want to merge to monopoly, but this last merger will not beauthorised by the AA, unless efficiencies are extremely high). Therefore, in our model, theefficiency offence argument does not find any justification under a forward looking AA.
The paper continues as follows. Section 2 introduces the basic model, which is chosen as the
simplest possible setting where the elements we are interested in could emerge. Section 3analyses the game where the AA behaves myopically. Section 4 analyses the dynamic game,
where the AA is forward looking. Section 5 concludes the paper by discussing the results
obtained.
2. Basic model
We consider a model in which there are four firms which operate in a market with linear
demand
p¼1/C0Q; ð1Ț
where Qis the industry output.
What distinguishes firms is the amount of capital they own. The total supply of capital is
assumed to be fixed to the industry. For the sake of simplicity, the total quantity of capital
9The treatment in Motta (2004) is based on a differentiated products model with price competition, but the similarities
in the static analysis make us believe that the results we obtain in the dynamic setting would extend to his model.
10Of course, the economic literature on efficiency gains in general is much richer. The most authoritative formal treatment
is still given by the model of Farrell and Shapiro (1990) , which is also the basis of a more recent assessment of efficiency
gains by the same authors ( Farrell and Shapiro, 2001 ). A formalisation and a discussion of efficiency gains can also be found
inMotta (2004, chapter 5) . Recent papers on efficiency gains include empirical and theoretical works. Among the former,
Neven and Ro ¨ller (2002) use the Eckbo test to evaluate efficiency gains in EU mergers. Among the latter, Heidhues and
Lagerlof (2002) assume that the merger parties are privately informed about merger-specific efficiencies, and decide
whether to (costly) transmit such information to the AA to influence its decision on their proposed merger.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 780

available in the industry is normalized to one.11Letki;kia1
4;24;34;1/C8/C9
, denote the fraction of the
industry capital owned by firm i,ia{1,. . .,4}.
The cost structure is a key feature of this model. The cost function of a firm which owns a
fraction kiof the industry capital and produces qiunits of output is given by:
Cq i;kiðȚ ¼a
kiqiț4kif; ð2Ț
where az0,A4
i=1ki= 1 and fN0.
Hence, we assume that each firm operates with a constant marginal cost of production, but the
level of its marginal cost is a decreasing function of its share in the industry capital, ki.I n
addition, it is assumed that there exists a plant specific fixed cost f, which has to be paid for each
1/4 of the industry capital owned by the firm.
The previous function aims at capturing two distinct cost effects induced by a merger. First, a
merger brings the individual capital of merging firms into a single larger resulting firm and,
therefore, it gives rise to endogenous efficiency gains by decreasing marginal costs. The higher
the value of a, the stronger the efficiency gains induced by a merger.12Second, by creating a
larger firm, a merger also has the effect of increasing fixed costs proportionally. This effect iscaptured by the parameter fin the cost function.
13
In the analysis which follows, it will be assumed that firms compete a`l a Cournot and are
allowed to merge before competition in the product market occurs. However, when firms want tomerge, they will have to ask the Antitrust Authority (henceforth, AA) for authorisation.
Two different scenarios are dealt with. First, we assume that the AA has a completely myopic
behaviour (Section 3). When deciding whether to authorise or not a given merger, it does not
take into account that the merger under consideration can be followed by other mergers. We thenturn to a second scenario (Section 4 ) in which it is assumed that the AA is forward looking in the
12This essential feature of a merger was first proposed by Perry and Porter (1985) . In their framework firms’ marginal
cost is linear in output and mergers reduce variable costs. The same model is also used by Vasconcelos (2005) , who
analyses the possible pro-collusive effects of a merger.
13This specification is used to rule out further scale economies simply due to sharing of fixed costs. An effect of this
specification is that efficiency gains benefit both consumers and the merging firms, and allows unnecessary divergences
between a consumer welfare and a total welfare standard.11The assumption that capital is fixed, and that de novo entry into the industry is impossible, is made for simplicity.
Otherwise, the model should consider not only external growth (i.e., growth by mergers) but also internal growth (i.e.,growth by capital accumulation), which would greatly expand the set of strategies available to firms, considerably
complicating the analysis. Still, there are several industries that are characterised by fixed capacity and difficult (or
impossible) entry. Cases in point are the cement industry (availability of raw materials and environmental regulationsmake new production sites unlikely) and the mineral water industry (in most countries, mineral water must be bottledat the source, and existing sources are known and already exploited). These industries are probably characterised by a
low degree of efficiency gains (that is, by a low value of a, see below). Other industries which might fit the
assumption of fixed capital are those where entry is regulated by law and subject to licenses or authorisation. Think forinstance of radio, television, telecommunication services which make use of the spectrum of waves. In many countries,
the use of the spectrum for a particular purpose is given (or auctioned off) by the government. Firms can only expand
by buying existing licenses from competitors (i.e., merging). Very often, scale and scope economies arise when morelicenses are owned by the same operator, i.e. potential efficiency gains from a merger are large ( ais high). Yet another
example of fixed capacity is given by landing and take-off slots at any given airport. The number of slots is fixed, and
an airline can increase its slots if it merged with rivals. Since the frequency of flights is regarded by consumers as
crucial in the choice of the airline they want to fly with, efficiency gains (at least in this particular respect) might wellbe created by the merger.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 781

sense that it anticipates the ultimate market structure a merger will lead to, and takes it into
account when deciding on a proposed merger.
Throughout the paper, we assume that the AA maximises consumer welfare . This is
consistent with the current standards used both in the US and in the EU to assess mergers. In theUS, the bsubstantial lessening of competition Q(SLC) test has been interpreted by both the
enforcement agencies (the DoJ and the FTC) and the Courts that a merger is unlawful if it is
likely that it will lead to an increase in price (that is, to a decrease in consumer surplus).
14Since
the recent changes in the Merger Regulation, the EU has moved from a dominance test to a SLCtest. It is less clear whether the EC follows a consumer welfare or a total welfare standard, butthe wording of the Merger Regulation (see Article 2.1(b)) states that an efficiency gain is inprinciple admitted to the extent that it benefits consumers, thus implying a consumer welfarestandard.
By assuming that the AA assesses mergers according to a consumer surplus standard we do
not want to imply that this should be the right standard.
15We adopt this assumption only
because it describes current practice in the major antitrust jurisdictions. An advantage of this
assumption is also that it allows us to keep the analysis extremely simple.
3.bStatic Qanalysis (myopic AA)
In this section, we analyse a simple game where from an initial symmetric market structure,
two of the four firms consider to merge. In the first stage, the two firms decide whether topropose a merger (they will do it, when the merger gives higher profits). In the second stage, the
AA decides whether to authorise the merger or not. This simple game is a restricted version of
the dynamic game we present in the next Section 4, where the first merger might be followed byother mergers. Since we assume in the present section that the AA is myopic, by definition it willnot take into account that other mergers might occur, and consequently there is no need toconsider the stages which follow the second stage of the game.
The reader should note that both in this section and in Section 4, we restrict attention to
symmetric equilibria, in the sense that we impose that firms which have the same share of theindustry capital will also have the same outputs and profits at equilibrium. The Appendix will
extend the analysis by discussing possible asymmetric equilibria.
3.1. Initial market structure
Let us assume that the status quo industry structure is a symmetric one. Hence, each firm has
a share 1/4 of the industry capital. Each firm i, therefore, chooses q
iby solving the following
maximisation problem
max
qi1/C0qi/C0X
jpiqj !
/C04aqi/C0f()
: ð3Ț
14Two oft-cited decisions are: FTC v. University Health, Inc., 938 F. 2d 1206, 1222–1223 (11th Circ. 1991); United
States v. United Tote, Inc., 768 F. Supp. 1064, 1084–1085 (D. Del. 1991). The quote from the revised US Merger
Guidelines at the beginning of this paper makes this approach explicit: efficiency gains arguments would be acceptedonly to the extent that they will prevent price increases in the market.
15SeeLyons (2002) for arguments in favour of the consumer surplus standard in merger control.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 782

From here we find that, due to symmetry, the equilibrium quantities at the initial market
structure are equal for all firms and are given by
q1
4;1
4;1
4;1
4/C18/C19
¼1/C04a
5: ð4Ț
It is easily checked that the associated equilibrium level of profit and the market price are
given by:
P1
4;1
4;1
4;1
4/C18/C19
¼1/C04a
5/C18/C192
/C0f; ð5Ț
p1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5: ð6Ț
Assumption 1. Let us assume that
ab1
4ua¯;fb1/C04a
5/C18/C192
uf¯: ð7Ț
These two conditions are imposed to exclude the trivial case in which production is not viable
at the status quo market structure.16
3.2. A merger between two firms
Suppose that there is a merger proposal between two of the four firms in the industry. If the
merger occurs, then a larger (and, hence, more efficient) firm is created, owning 2/4 of theindustry capital. In the post-merger Cournot equilibrium, the merged entity (say, firm l) and a
representative outsider (say, firm s
i) will choose their levels of output by solving the following
maximisation problems, respectively,
max
qi1/C0ql/C0X
jplqj !
ql/C02aql/C02f()
; ð8Ț
max
qsi¼ 1/C0qsi/C0X
hpsiqh !
qsi/C04aqsi/C0f()
: ð9Ț
Since we focus on symmetric equilibria, we have that qsi=qsj=qs. Very simple algebra shows
that the equilibrium level of output for the merged entity (firm l) and for each of the two
outsiders to this merger are respectively given by
ql2
4;1
4;1
4/C18/C19
¼1ț2a
4; ð10Ț
qs2
4;1
4;1
4/C18/C19
¼max 0 ;1/C06a
4/C26/C27
: ð11Ț
16Ifaz1/4, then d C(qi, 1/4)/d qi=4az1, which in turn implies that q1
4;14;14;14/C1
¼0/C0
. Likewise, four firms would
not co-exist if fNf.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 783

Remark 1. qs=0 if az1/6. Hence, if the merger gives rise to very high synergies, in a
symmetric equilibrium, the two (smaller) outsider firms are constrained to exit the market (in theAppendix we study the asymmetric equilibrium case where only one of the two outsiders leavesthe industry).
Suppose for the moment that ab1/6. From the equilibrium outputs above, one can obtain by
substitution the equilibrium levels of profits for the merged entity and for each of the merger
outsiders
P
l2
4;1
4;1
4/C18/C19
¼1ț2a
4/C18/C192
/C02f; ð12Ț
Ps2
4;1
4;1
4/C18/C19
¼1ț6a
4/C18/C192
/C0f: ð13Ț
In addition, the equilibrium price is given by
p2
4;1
4;1
4/C18/C19
¼1ț10a
4: ð14Ț
Now, notice that after a merger between two of the firms in the status quo market structure,
the induced post-merger market structure might be either2
4;14;14/C8/C9
or simply a monopoly market
structure of the type2
4/C8/C9
, depending on whether after the merger the two outsiders are able to
make positive profits or not. These two different cases will be dealt with in the analysis thatfollows, where we seek the symmetric subgame perfect Nash equilibrium (henceforth, SPNE) inpure strategies of the proposed two stage game.
3.3. Analysis of stage 2
At the second stage of the game, the AA has to decide whether or not to allow a merger
between two randomly selected firms, if the merger has been submitted for approval. Thebehaviour of the AA in each of the above mentioned possible scenarios is as follows.
!Ifab1/6 and fb((1/C06a)/4)
2uf˜, then from Eq. (13), one concludes that the two merger
outsiders are able to make positive profits after the merger has taken place. If this is the case,then the AA will decide to authorise the submitted merger only if:
p2
4;1
4;1
4/C18/C19
¼1ț10a
4Vp1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5; ð15Ț
which is equivalent to
1
14g0:071429 Vab1
6: ð16Ț
Hence, in order to authorise the merger, the AA will require that the efficiency gains obtained
through the merger are sufficiently high.
!If, instead,
(i)az1/6, or
(ii)az1/6 and1/C06a
4/C0/C12uf˜Vfbf¯,M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 784

then from Remark 1 and Eq. (13) , one concludes that in this case the merger induces the
outsiders to exit the industry. Notice that when after the merger the relevant market structure ischaracterised by a single monopolist operating with 2/4 of the industry capital, very simplealgebra shows that the merged entity equilibrium profit and the equilibrium price are given by:
P
2
4/C18/C19
¼1/C02a
2/C18/C192
/C02f; ð17Ț
p2
4/C18/C19
¼1ț2a
2: ð18Ț
Now, the AA faced with such a merger proposal inducing the exit by outsiders, will decide to
veto it if the following inequality holds:
p2
4/C18/C19
¼1ț2a
2Np1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5; ð19Ț
which in turn implies that a merger would not be authorised by the (myopic) AA if efficiency
gains induced by the merger are sufficiently low, i.e., if:
ab3
22g0:13636 : ð20Ț
Let us now turn to the analysis of the firms’ decisions at the first stage of the game.
3.4. Analysis of stage 1
As a preliminary remark, it should be stressed that we assume there are no administrative
costs that firms must incur for submitting the merger to the AA. Hence, when firms anticipate
that the merger will be blocked, they are indifferent between asking or not the AA forauthorisation. We assume throughout that in case of indifference, firms do propose a merger tothe AA.
17
In order to investigate the firms’ merger decision at the first stage on whether or not to submit
a merger, one has to distinguish again between the scenario in which a merger does not constrainoutsiders to leave the industry and the scenario in which it does push outsiders out of the market.
!Ifab1/6 and fb((1/C06a)/4)
2uf˜, then, as explained above, the two outsiders are able to
make positive profits after the merger has taken place. Therefore, from Eqs. (5) and (12), one has
that the insider firms will find this merger profitable if the following condition holds:
Pl2
4;1
4;1
4/C18/C19
¼1ț2a
4/C18/C192
/C02fN2P1
4;1
4;1
4;1
4/C18/C19
¼21/C04a
5/C18/C192
/C0f"#
; ð21Ț
which in turn implies that the merger is submitted to the AA if
1
289/C060ffiffiffi
2p
103/C18/C19
g0:020132 Vab1
6: ð22Ț
17As will become clear, the assumption that firms do not incur any administrative cost from filing a merger does not
matter much, as the equilibrium outcome would not change if we assumed positive filing costs (or that, when indifferent,
the firms do not propose the merger).M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 785

Hence, in order for the insider firms to find the merger profitable, they will require efficiency
gains obtained through the merger to be sufficiently high.18It should be stressed, however, that
the set of parameter values given by the previous condition is larger than the one described byEq. (16) , which means that for low values of the efficiency parameter a, namely for
aa[0.020132, 1/14), the merger will be submitted by the firms but blocked by the myopic AA.
!If, instead,
(i)az1/6, or
(ii)ab1/6 and
1/C06a
4/C0/C12uf˜Vfbf¯,
then outsiders are constrained to exit the market after the merger. Hence, from Eqs. (5) and (17),
one concludes that the two potential merging parties will decide to merge if:
P2
4/C18/C19
¼1/C02a
2/C18/C192
/C02fN2P1
4;1
4;1
4;1
4/C18/C19
¼21/C04a
5/C18/C192
/C0f"#
; ð23Ț
which turns out to be satisfied for all aa[0,a¯), where a¯is given by Eq. (7). Hence, the selected
firms will always decide to submit the merger to the AA.
The behaviour of a myopic AA when deciding whether or not to authorise a merger which
triggers the exit of the outsiders to such a merger can be summarised as follows:19
1. If
(a)az1/6, or
(b) 3/22 Vab1/6 and fz1/C06a
4/C0/C12u˜ff, then the merger will always be authorised. Outsiders
would be pushed out of the market after the merger has taken place but efficiency gainsare so high that consumers would gain.
2. If, instead, 1/14 Vab3/22 and fz
1/C06a
4/C0/C12u˜ff, then the merger would notbe authorised by the
AA. After the merger, outsiders are not able to recover their fixed cost but consumers would
be worse off. This is the efficiency offence scenario and in what follows we argue that the AA
is behaving myopically when deciding to block such a merger.
Fig. 1 illustrates the full (that is, including the cases where the merger would not trigger exit
by outsiders) equilibrium outcome of this two stage game.
4. Dynamic analysis (forward looking AA)
In this section, starting from the same status quo industry structure1
4;14;14;14/C8/C9
, our aim is to
investigate the strategic interaction between firms (potential merging parties) and the AA, in asituation where the AA is endowed with foresight.
The AA, when making a decision on whether or not to allow a given merger, takes into
account that the merger may be followed by further mergers and, therefore, it speculates on the
19Remember that from Assumption 1, fbf¯.18Notice, in particular, that in the extreme case in which a=0 (no efficiency gains), no merger would occur. This is
related to Salant et al. (1983) . Their well known result in static Cournot games with constant marginal costs can be
summarised as follows. Two (coalitions of) firms will never be interested in merging if they only care about presentprofits and there are at least three existing (coalitions of) firms in the industry.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 786

(consumer) welfare (or, equivalently, on the market price) associated with the market structure
that the merger will lead to. This situation is modelled as a six-stage game involving thefollowing sequence of decisions.
!In the first stage , nature allows two of the four firms in the status quo industry structure to
merge if they wish so. If they decide to merge, they will have to ask the AA for authorisation.
!In the second stage , the AA decides whether to authorise the merger or not. If it does not
authorise it, then the game will have come to a final node (since even restarting at this node
would always lead us to a similar merger proposed and refused by the AA) and productmarket competition occurs between the four symmetric firms in the status quo industrystructure.
!In the third stage , if the AA has decided to authorise the merger at stage 2, it is the turn of the
next two firms (the outsiders to the previous merger) to decide if they want to merge or not. Ifthey do not want to, then the merger game stops and market realisation occurs. If, instead,they want to merge, they have to ask the AA for authorisation.
!In the fourth stage , the AA decides whether it wants to authorise the defensive merger
between the outsiders of the first merger. If the AA vetoes the merger, the merger gamestops here and the product market stage occurs, with associated payoff realisation. Else,we find ourselves at a structure
2
4;24/C8/C9
, but we allow for a further round of the merger
game.
!In the fifth stage , the firms are allowed to seek a merger to monopoly. If they decide not to do
it, the merger game stops and product market competition occurs. If, instead, they want tomerge, they will have to ask the AA for authorisation.
!In the sixth stage , the AA decides whether or not to allow the merger to monopoly and, after
its decision has been taken, product market competition occurs.
As in the previous section, we will look for the symmetric SPNE in pure strategies, so that we
proceed by solving the game by backward induction.1/16
1/25
3/22 1/14 1/6 1/4
αf
0.02f~
f42Allowed
42Blocked
41,41,42Allowed41,41,42BlockedMerger ProposalNo
{}
{}{}
{}
Fig. 1. Equilibria of the game with a myopic AA.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 787

4.1. Analysis of the SPNE of the game
4.1.1. Analysis of stage 6
If the game arrives at the sixth stage , then the AA will have to choose between the two
alternative market structures2
4;24/C8/C9
and {1}. If the AA decides to block the merger, then the
resulting market structure will be2
4;24/C8/C9
. This industry structure results from two previous
mergers (approved in stages two and four, respectively) and is composed of two equally efficient
firms (say, firms iandj), owning 2/4 of the industry capital each. When this is the industry
structure, firm ichooses its level of production qiby solving the following maximisation
programme:
max
qi1/C0qi/C0qj/C0/C1
qi/C02aqi/C02f/C8/C9
: ð24Ț
Now, due to symmetry, the equilibrium quantities are equal for both firms and they are given
by:
q2
4;2
4/C18/C19
¼1/C02a
3: ð25Ț
Hence, the Cournot profits per-firm in an industry structure2
4;24/C8/C9
are:
P2
4;2
4/C18/C19
¼1/C02a
3/C18/C192
/C02f: ð26Ț
In addition, the equilibrium market price is given by:
p2
4;2
4/C18/C19
¼1ț4a
3: ð27Ț
If, instead, the AA decides to approve the merger, then the resulting market structure will be a
monopoly operating with the whole industry capital, {1}. When this is the case, very simplealgebra shows that the equilibrium level of profit and the market price are, respectively, givenby:
P1ðȚ ¼
1/C0a
2/C18/C192
/C04f; ð28Ț
p1ðȚ ¼1ța
2: ð29Ț
Now, making use of Eqs. (27) and (29), one concludes that the AA will decide to block a
merger between two firms owning 2/4 of the industry capital towards complete monopolisation
of the industry if
p1ðȚ ¼1ța
2Np2
4;2
4/C18/C19
¼1ț4a
3; ð30Ț
which implies that the merger will be blocked if:
ab1
5: ð31Ț
Therefore, the AA will allow the merger to monopoly only if az1/5.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 788

4.1.2. Analysis of stage 5
In the fifth stage , if a duopolistic structure has emerged from the previous stages of the game,
firms have to decide whether or not to seek a merger to monopoly. As in the previous section, weassume that there are no administrative costs that firms must incur for submitting the merger tothe AA and that in case of indifference between proposing or not, firms do propose the merger tothe AA. Now, from Eqs. (26) and (28), one has that firms will have an interest in merging to
monopoly if:
P1ðȚ ¼
1/C0a
2/C18/C192
/C04fN2P2
4;2
4/C18/C19
¼21/C02a
3/C18/C192
/C02f"#
; ð32Ț
which turns out to be satisfied for all aa(0,a¯), where a¯is given by Eq. (7). Hence, at the fifth
stage of the game the two coalitions in the market will always decide seek a merger leading tocomplete monopolisation of the industry.
This result is not surprising. Even in a Cournot setting with linear demand where firms have
the same (constant) marginal cost both before and after the merger, a merger from duopoly to
monopoly is always found to be profitable (see Salant, Switzer and Reynolds (1983)). In our
setting, firms have a double incentive to participate in the merger. Apart from reducingcompetition in the market, a merger allows the involved firms to realise a cost advantage throughendogenous efficiency gains. Hence, the incentive for merger is reinforced.
20
4.1.3. Analysis of stage 4
In the fourth stage, the AA has to decide whether to accept a merger between the outsiders to
the first merger. Two cases must be considered here.
1. Ifaz1/5, the AA anticipates that if the merger is approved, the final equilibrium market
structure will be a monopoly. It also anticipates that if it vetoes the merger, the outsiders ofthe first merger would be constrained to exit the industry.
21Therefore, it will authorise the
merger if:
p1ðȚ ¼1ța
2Vp2
4/C18/C19
¼1ț2a
2; ð33Ț
which always holds: since the merger allows to keep assets that otherwise would be forced
to disappear from the industry, it is always better to authorise it.22
2. Ifab1/5, the merger will lead to the creation of a perfectly symmetric duopolistic structure,
2
4;24/C8/C9
. Two sub-cases should be considered here:
!If1/C06a
4/C0/C12uf˜Vf, the AA correctly anticipates that if it said no to the merger the two
outsiders of the first merger would be constrained to exit the industry (they would not beable to cover fixed costs of production) and, therefore, the market structure at equilibrium
20Recall that fixed costs play no role in firms’ merger decision. Each firm’s share in the monopoly fixed cost equals the
fixed cost the firm would pay as an independent duopolist with 2/4 of the industry capital, 2 f.
22It is better in terms of welfare to have a (more efficient) monopolist owning the whole industry capital, than having a
monopolist with only half of the industry capital.21See Remark 1.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 789

would be2
4/C8/C9
. As a result, from Eqs. (18) and (27), one concludes that the merger will be
allowed only if:
p2
4/C18/C19
¼1ț2a
2Np2
4;2
4/C18/C19
¼1ț4a
3; ð34Ț
which is true for any ab1/5. Thus, the AA will always allow the defensive merger in this
interval.
!If instead fbf˜, the outsiders will not exit the industry if their merger were blocked.
Therefore, the merger will be allowed if:
p2
4;2
4/C18/C19
¼1ț4a
3Vp2
4;1
4;1
4/C18/C19
¼1ț10a
4; ð35Ț
which turns out to be satisfied for az1/14.
4.1.4. Analysis of stage 3
In the third stage , we have to check whether the outsiders of the first merger (if it has been
proposed in the first stage and approved in the second stage by the AA) will want to merge ornot. Again, we have to consider different cases according to the level of efficiency gains.
1. Ifaz1/5, it is easy to check that the merger is always profitable. By merging, firms will
eventually end up in a full monopoly, whereas by not merging, they will get zero profit, since
they would be unable to cover fixed cost and, therefore, would be constrained to exit the
market.
2. Ifab1/5, then three sub-cases arise:
(a) If 1/14 Vab1/5 and fzf˜, firms anticipate that by merging they will eventually be in a
duopolistic structure, whereas by not merging they would be obliged to exit. Hence, usingEq. (26), we have that the merger will be profitable if:
P
2
4;2
4/C18/C19
¼1/C02a
3/C18/C192
/C02fz0;
which is satisfied if:
fV1
21/C02a
3/C18/C192
ufV: ð36Ț
But it is easy to check that this condition is always satisfied in the relevant range of
parameter values as described by Assumption 1. Therefore, the two firms that have not beeninvolved in the first merger will always want to merge in this range of parameter values.
(b) If, 1/14 Vab1/5 and fbf˜, then outsiders correctly anticipate that by merging they will be
in a duopoly structure, but by not merging they will survive. Therefore, the merger isprofitable if:
P
2
4;2
4/C18/C19
¼1/C02a
3/C18/C192
/C02fz2Ps2
4;1
4;1
4/C18/C19
¼21/C06a
4/C18/C192
/C02f; ð37Ț
which holds for az19/C012ffiffiffi
2p/C0/C1
=146i:0139. Therefore, the merger will always be
proposed in this region of parameter values.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 790

(c) If instead ab1/14, then the outsiders anticipate that if this defensive merger does not
go through, they will survive. They also anticipate that, if submitted, this merger willbe blocked by the AA in the following stage (see Eq. (35)). However, since weassume no administrative costs for submitting a merger, firms do propose a mergereven when indifferent between proposing or not the merger. Hence, again, firmswill submit the merger to the AA when condition Eq. (37) holds, i.e., when
az19/C012ffiffiffi
2p/C0/C1
=146i:0139.
4.1.5. Analysis of stage 2
In the second stage , if the two randomly selected firms at the first stage decide to submit a
merger to the AA, the AA has to decide whether to allow it or not.
Three separate cases should be considered:
1. Ifaz1/5, the first merger will ultimately lead to a monopoly. Therefore, it will be allowed if:
p1ðȚ ¼
1ța
2Vp1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5; ð38Ț
that is always true in the interval 1/9 Vab1/4. Hence, it will always be authorised.
2. If 1/14 Vab1/5, the AA anticipates that this first merger will be followed by a second merger
that will give rise to a perfectly symmetric duopolistic structure. Therefore, the rightcomparison is not between p
2
4/C0/C1
andp1
4;14;14;14/C0/C1
, which is what a myopic authority would
do, but rather the first merger will be authorised if the following inequality holds:
p2
4;2
4/C18/C19
¼1ț4a
3Vp1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5; ð39Ț
which, as can be easily checked, holds if az1/14, or ak.0714286. Therefore, in the interval
we consider here, the first merger will be allowed.
3. Ifab1/14, the AA anticipates that the first merger will not be followed by another,23
implying that the first merger will be authorised if:
p2
4;1
4;1
4/C18/C19
¼1ț10a
4Vp1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5: ð40Ț
But we know from Section 3 (in particular, from Eqs. (15) and (16)) that this inequality is
always false in the interval considered. Therefore, the merger will not be authorised.
Case 2 is the most interesting among those analysed here. As can be seen from Fig. 2 , our
result implies that the merger will be authorised even in the area where 1/14Vab3/22 and
f˜Vfbf¯, that corresponds to mergers blocked by a myopic AA under an efficiency offence.
The comparison with Section 3 shows that when aa[1/14, 3/22) and fzf˜, a myopic AA
would want to block a merger by using an efficiency offence argument, but a forward looking
AA would authorise the same merger because it expects that the outsiders would react bymerging in their turn, thus leading to a market structure that is associated with a higher consumer
23From Eq. (35), one has that a defensive merger would be blocked by the AA at stage 4 when ab1/14.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 791

welfare. In other words, having an AA that, in making a decision about a given merger, takes
fully into account the reactions of firms in response to this merger, avoids the mistake ofblocking some mergers in which the outsiders are expected to react by merging too, thusavoiding exiting the industry and giving rise to a final market structure where consumer welfareis enhanced.
4.1.6. Analysis of stage 1
In the first stage of the game, two randomly selected firms in the status quo industry structure
are given the opportunity to decide whether or not to merge. As explained above, there are no
administrative costs of submitting a merger to the AA for approval. Thus, when firms anticipatethat a merger will be blocked, they are indifferent between submitting or not the merger to the AA.
Three cases are relevant here:
1. Ifaz1/5, firms anticipate that the first merger will be followed by a merger by outsiders, and
eventually by a merger grouping the whole industry. Therefore, the first merger will beproposed if:
P1ðȚ
2¼1
21/C0a
5/C18/C192
/C04f"#
z2P1
4;1
4;1
4;1
4/C18/C19
¼21/C04a
5/C18/C192
/C0f"#
: ð41Ț
It is possible to check that this inequality is true in the interval considered: the merger will be
proposed.
2. If 1/14 Vab1/5, firms anticipate that if the first merger is approved, then the outsiders will react
by merging in their turn, thus leading to a symmetric duopoly market structure,2
4;24/C8/C9
.24As a16/1
25/1
αf
4/1 6/122/3 14}{}{
/1f~
f42,42Predicted Market Structure:allowed.mergers:4and2Stages
5/1Predicted
Market Structure:
41,41,41,41{}1Stages2, 4, 6:
mergersallowed
Predicted Market
Structure
Fig. 2. Equilibrium outcomes with a forward looking AA.
24From Eq. (34), one knows that a defensive merger will always be allowed by the AA at the fourth stage. On the other
hand, Eq. (31) implies that a merger from a symmetric duopoly towards complete monopolisation will not be allowed by
the AA (at the sixth stage) for the considered range of values for the efficiency parameter a.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 792

result, and making use of Eqs. (5) and (26), one concludes that the selected firms will decide to
submit the merger to the AA if
P¼2
4;2
4/C18/C19
¼1/C02a
3/C18/C192
/C02fz2P1
4;1
4;1
4;1
4/C18/C19
¼21/C04a
5/C18/C192
/C0f"#
: ð42Ț
The previous condition turns out to be satisfied for all aa[0,a¯), where a¯is given by Eq. (7),
which implies that selected firms will always decide to merge and submit the proposal to theAA.
3. Ifab1/14, the first merger will not be followed by others. The merger is profitable if
P
l2
4;14;14/C0/C1
V2P1
4;14;14;14/C0/C1
, a case we have already analysed in Section 3, where we found
this inequality holds for az.020132.25
This completes the analysis of the whole game, which is summarised by Fig. 2 .
Notice that in the area where ab1/6 and f˜Vfbf˜(that is, where an efficiency offence
argument would push the AA to block the merger), the AA will authorise the merger submittedfor its approval at stage 2. The reason for this is that the AA knows that along the equilibriumpath, this merger will be followed by a defensive merger by the first merger outsiders. Thedefensive merger (but not a further merger which would lead to complete monopolisation of theindustry) will also be authorised at stage 4, and consumer welfare will increase.
Furthermore, note that our dynamic mergers game where the AA plays an active role in
authorising mergers predicts (in the case where the AA is forward-looking) a market structure
which depends on the efficiency gains. The higher the scope for efficiency gains, the moreconcentrated the market structure that will arise from this dynamic merger game.
5. Conclusion
This paper has taken seriously the efficiency offence argument that has (rightly or
wrongly) sometimes been attributed to the EC. We have showed that efficiency gains
attained by merging parties are never detrimental in our model, even when they might lead
to exit of competitors. This is for two reasons.
26First, in some cases there might be such
25See Eqs. (21) and (22).
26There is also a third reason that for brevity we have not formally analysed in the paper. Even if after the first merger
further mergers would not be possible, it might well happen that if a firm were to exit the industry, its capital would be
reallocated in some way amongst the remaining active firm(s). Take an extended version of the basic static gamedescribed in Section 3 where we include a third-additional stage in which (after the merger decision by the AA and beforeproduct market competition) the assets belonging to the firms which would be constrained to exit the industry after a
merger can be bought over by the remaining active firm. In particular, suppose that, in stage 3, if the merger was proposed
and approved by the AA and the outsiders to this merger would be pushed out of the industry, then the merged entitymakes a take-it-or-leave-it offer to buy the capital assets of the exiting firms. (For simplicity, assume that the exiting firmsdo not have the possibility to sell its capital outside this industry). Analysis of the SPNE of this game discloses that: first,
the assets of the exiting firms will always be absorbed by the unique active firm (at no cost); and, second, if fixed costs
are below a certain threshold (so that a merger is proposed at the first stage), and if fzf˜and 1/9 Vab3/22—a subregion
of the efficiency offence area in Fig. 1 —then at stage 2 the AA will decide to approve the merger, whereas a myopic AA
would not. This is because the AA playing the present game anticipates that since the assets belonging to the outsiders to
the merger will be absorbed by the merged entity at a later stage, then if the merger is approved, it will induce a final
equilibrium market structure where there is a monopolist owning the whole industry capital, and consumer welfare willincrease. This extended version of our basic static game, therefore, provides a further illustration of the weak rationale
behind the use of efficiency offence arguments in merger control.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 793

important efficiency gains that they would lead to lower prices despite the lower number of firms
in the industry (but even a myopic Antitrust Authority would recognise this argument). Second,and more important, we have showed that when there exist efficiency gains, a merger betweentwo firms will be followed by a merger between its rivals, that also want to take the opportunityof saving costs. The final structure after the two mergers would be more concentrated but moreefficient (if a further merger to monopoly is proposed, it will not be authorised unless efficiency
gains are extremely high—and in this case complete monopolisation would be benefficial too).
A forward looking AA would anticipate this outcome, and rightly allow the first merger,knowing that it will be followed by a second one. A myopic AA would instead block the firstmerger whenever it puts (un-merged) rivals in such a competitive disadvantage that they wouldbe forced to exit the industry.
Apart from hopefully clarifying the weak rationale behind efficiency offence
arguments, our main contribution here probably lies in the attempt of going beyond astatic setting when analysing the effects of mergers, and in explicitly considering the role
of the Antitrust Authority in a dynamic merger game. Nevertheless, we are fully aware
that the game we analyse here is an extremely simple one, and we plan to fullyendogenise the merger process, by allowing any coalition among the firms in the industryto be possibly formed.
27,28Currently, we are also working to endogenise the game in another
respect, which is to allow firms to attain efficiency gains through internal, rather than externalgrowth, that is to let them choose between merging or investing in accumulating additionalcapacity.
29,30
To conclude the paper, let us make some comments on the policy issue of whether AAs
should be forward-looking in the sense described by our paper. Merger control is already a
predictive exercise, and therefore it is by its nature a forward-looking one. Our papersuggests that when predicting the possible impact of the merger, possible reactions by theoutsiders should be properly taken into account. More particularly, before hastilyconcluding that a merger will create such a more efficient merged entity that rivalswould not be able to compete with it, AAs should consider whether in the industry at handthere exists room for further mergers allowing outsiders to attain similar efficiency levels,and/or whether the outsiders might be able to enhance efficiency through internal growth
(although our model considers only the former mechanism, not the latter).
Of course, anyone is aware of the fact that AAs might make mistakes in the real world,
and that further mergers are hard to predict. But AAs might make mistakes also in predictingthat following a merger outsiders might leave. Indeed, this efficiency offence argument isbased itself on a prediction which might be wrong. Consider efficiency offence in our model.
27For instance, after the first merger between two firms, there might be either a merger between the two outsiders, or a
merger that involves an outsider and the two first merger insiders. This leads to a richer, but also more complex, game.
Given our focus on the effects of efficiency gains, we have chosen here the simpler game within which our results couldbe showed.
28For endogenous mergers, see for instance Kamien and Zang (1990) ,Horn and Persson (2001a,b) andGowrisankaran
(1999) .
29Gowrisankaran (1999) considers a dynamic model where firms take merger, entry, exit, investment and production
decisions. The price to pay is that the analysis becomes extremely complex, though: analytical results are not obtained in
his model.
30Obviously, in the real world there might well be situations where the outsiders of a merger—for whatever reasons—
are unlikely to merge. This case was not considered here, but could be addressed properly in a model where the outsiders
could respond by increasing their capacity by investing, rather than by merging.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 794

We simply compare two equilibria: before the merger, when all firms sell, and after the
merger, when two (or one, in the asymmetric case) firms leave the market. Clearly, in realitythe latter case refers to a medium/long-run equilibrium. In the short-run (that is, before firmsadjust outputs and divest their assets), there will be a disequilibrium situation (not illustratedin the paper, which just compares equilibrium outcomes) where the two outsiders willcontinue to sell at a loss. One of two possible medium/long-run equilibria might then follow.
Either the one where outsiders will not be able to adjust by merging in their turn (or by
investing, in a more general model) and will exit the industry. Or, in alternative to the first,an equilibrium where the outsiders will react by merging (or investing, or by pursuing otherbusiness strategies) and will be able to survive. We regard the second equilibrium (that wewould call ddynamic T) as the more likely because it takes into account that firms are not
passive players, and will take actions that counter the merging strategies of the insiders. Ofcourse, in reality there might well be industries where, for several reasons (going fromimperfect capital markets to non-rational or non-profit maximising behaviour of players),
merging or investing are not feasible strategies for the outsiders. But in any event, AAs
should not spouse an efficiency offence argument without considering the capability ofreaction by the outsiders.
There is another possible reading of our results. In the short-run (that is, in a
disequilibrium situation not illustrated in the model), a merger which entails efficiency gainshas a positive impact on welfare. Indeed, before outsiders might take any exit decision (orany counter-strategies), the immediate impact of the merger is to increase welfare (the moreefficient firms produce more and prices will fall). An AA speculating that the efficiency
gains (which, incidentally, often do not materialise immediately in the real world) obtained
by the merging firms will make rival firms exit the industry is trading off a (relatively)certain welfare gain with a future (and more uncertain) welfare loss (i.e., when firms leave).What the paper points out is that: first, if efficiency gains are strong enough, the finaloutcome would be positive even if it leads to exit of rivals (see Figs. 1 and 2 , for high
values of a); second, that the future welfare losses, if any (intermediate values of a), are
rendered even more uncertain by the presence of possible counter-strategies by theoutsiders.
Appendix A. The asymmetric case
So far, we have considered only symmetric equilibria, in the sense that we have imposed that
firms endowed with the same capital also have the same output and profits at equilibrium.Focusing on symmetric equilibria is standard when dealing with Cournot models. Even thestandard Cournot duopoly model admits asymmetric equilibria where one firm produces such alarge output that the rival’s best response is simply to produce zero output, but it is customary to
focus on the symmetric equilibrium where both firms share the market, probably the most
reasonable outcome of the game.
In the merger game we have analysed, asymmetric equilibria arise—for certain parameter
values—under many of the configurations analysed. For instance, under the initial marketstructure,
1
4;14;14;14/C8/C9
, apart from the benchmark symmetric equilibrium we have found, where
four firms equally share the market, there might also be at least another equilibrium31where
31To be more precise, there are four asymmetric equilibria of the same nature, and differing only in which firm (1, 2, 3,
or 4) produces zero.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 795

three firms sell a larger quantity and the fourth firm’s best response is to sell zero;32and in a
market configuration after two mergers have been realised,2
4;24/C8/C9
, there is also an asymmetric
equilibrium where one firm sells a larger quantity than at the symmetric duopoly equilibrium andthe other produces zero.
33
In our paper, a complete treatment would require dealing with all possible asymmetric
equilibria, but the reader can easily see that this would lead to a very complicated setting (just
think that there are different possible initial market equilibria, and that for each one would have
to analyse the merger game, with a multiplication of cases as one proceeds to a further stage ofthe game) without gaining any further insight.
Nevertheless, there is one asymmetric case which is probably worth considering, and to
which this appendix is devoted. We have seen that when efficiency gains are large enough, thefirst merger will lead to the exit of both outsiders, unless they react by merging in their turn. The
case where both outsiders leave after a merger corresponds to our restricting attention to asymmetric equilibrium: the outsiders have the same share of the industry’s capital, and we focus
on the equilibrium where they have the same output, which turns out to be zero for some
parameter values. The reader might wonder whether the results of the paper hold good when,after the first merger, only one of the outsiders might be forced to leave the industry (unless amerger between them occurs). This appendix deals with this asymmetric case, and shows thatindeed the qualitative results of the paper are fully confirmed. In particular, a forward-lookingAA would not block a merger that under a static approach would not be authorised due to anefficiency offence argument.
A.1. A merger leading to exit of one outsider only
Let us consider the case where a merger has taken place, so that the distribution of the
industry’s capital is such that one firm holds one-half of it and the two outsiders hold one-quartereach of it. We look for an asymmetric equilibrium where one outsider sells positive output andthe other sells zero output.
Suppose that an outsider sells zero output. The large firm will choose q
lso as to maximise
Pl¼1/C0ql/C0qs/C02a ðȚ ql/C02f, and the active outsider will choose qsso as to maximise
Ps¼1/C0ql/C0qs/C04a ðȚ qs/C0f.
Solving the FOCs gives the equilibrium quantities and price
ql¼2
4;1
4/C18/C19
¼1
3;qs2
4;1
4/C18/C19
¼1/C06a
3;p2
4;1
4/C18/C19
¼1ț6a
3ð43Ț
32Suppose that the fourth firm sells zero output. Each of the remaining firms will choose qiso as to maximise
Pi¼1/C0qi/C0Rjpiqj/C04a/C0/C1
qi/C0f. Taking FOCs and imposing symmetry among the three active firms, one obtains
q1
4;14;14/C1
¼1ț4a
4/C0
,p1
4;14;14/C1
¼1ț12a
4/C0
, and P1
4;14;14/C1
¼1/C04aðȚ2
16/C0f/C16
. This solution is feasible if ab1/4 (which
corresponds to our Assumption 1) and fb1/C04aðȚ2
16. Now we have to check that when the three firms sell the output1/C04a
4,i t
is indeed optimal for the fourth firm to sell zero. If it decides to produce, given the output of the rivals, its profit is
P*
4q4ðȚ ¼ 1/C0q4/C031/C04a
4/C04a/C0/C1
q4/C0f, from which one can check that the profit maximising output is q*
4¼1/C04a
8, and
associated profit is P*
4¼1/C04aðȚ2
64/C0f. Therefore, this asymmetric equilibrium exists if1/C04aðȚ2
64bfb1/C04aðȚ2
16.
33Suppose that the rival firm sells zero output. Firm 1 will choose q1so as to maximise. P1q1ðȚ¼1/C0q1/C02a ðȚ q1/C02f
from which one obtains q2
4/C1
¼1/C02a
2/C0
andP2
4/C0/C1
¼1/C02aðȚ2
4/C02f. This solution is feasible if fb1/C02aðȚ2
8. Now we
have to check that when q1¼1/C02a
2, it is optimal for the rival to sell zero. From P2q2ðȚ ¼ 1/C0q2/C01/C02a
2/C02a/C1
q2/C02f/C0
,
one can find the profit maximising output as q2¼1/C02a
4, and associated profit as P2¼1/C02aðȚ2
16/C02f. Therefore, this
asymmetric equilibrium exists if1/C02aðȚ2
32bfb1/C02aðȚ2
8.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 796

and profits are
Pl¼2
4;1
4/C18/C19
¼1
9/C02f;Ps2
4;1
4/C18/C19
¼1/C06a ðȚ2
9/C0f: ð44Ț
This solution is feasible if ab1/6 and fb1/C06aðȚ2
9(in the area considered in the paper, Pl2
4;14/C0/C1
is always positive, since Assumption 1, which restricts attention to fbf¯, ensures that fb1/18).
Next, we have to check that given ql¼1
3andqs¼1/C06a
3, it is optimal for the other small firm (say,
firm 4) to leave the market. Its profit is P4q4ðȚ ¼ 1/C01
3/C01/C06a
3/C0q4/C04a/C0/C1
q4/C0f, from which
one can check that the profit maximising output is q4¼1/C06a
6, resulting in profit P4¼1/C06aðȚ2
36/C0f.
Therefore, this asymmetric equilibrium exists if:
ab1=6 and1/C06a ðȚ2
36bfb1/C06a ðȚ2
9: ð45Ț
It is on this region of the parameters’ space that we focus here. Like in the rest of the paper,
we now deal with the two cases of myopic and forward-looking AA in turn.
A.2.bStatic analysis Q(myopic AA)
If the AA is myopic, it decides whether to authorise a merger between two firms by
comparing the consumer surplus arising under the initial market structure (we focus for
simplicity on the symmetric equilibrium identified by expressions (4)–(6)) with that arising afterthe merger, where for the latter we focus on parameters such that the merger will lead to exit byone firm only (the remaining cases are already dealt with in the previous sections of the paper).
Consumer surplus is (weakly) higher under the merger if:
p
2
4;1
4/C18/C19
¼1ț6a
3Vp1
4;1
4;1
4;1
4/C18/C19
¼1ț16a
5;oraz1
9: ð46Ț
Therefore, the merger will be authorised if az1/9. For lower values of a, the merger will be
blocked.
Fig. 3 summarises the predicted market structure under a myopic AA.
A.3. Dynamic analysis (forward-looking AA)
The dynamic game is fully described in Section 4. We solve it by backward induction,
restricting attention to the region of parameter values described above, where an asymmetric
equilibrium might arise after the first merger takes place.
A.3.1. Analysis of Stage 6
If the game arrives at the sixth stage, the AA has to choose between the two alternative
market structures2
4;24/C8/C9
and {1}. The analysis is the same as in Section 4, where we found that
the AA would allow the merger to monopoly only if az1/5. In the area considered here,
therefore, the merger to monopoly will never be authorised .
A.3.2. Analysis of Stage 5
In the fifth stage, if a duopolistic structure has emerged from the previous stages of the game,
firms have to decide whether or not to seek a merger to monopoly. Again, the analysis here is asin Section 4, where we found that the two duopolists will always have an incentive to proposethe merger to monopoly.M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 797

A.3.3. Analysis of Stage 4
In the fourth stage, the AA decides whether to accept a merger between the outsiders
to the first merger. In the area considered here, the AA anticipates that if it said no to themerger one of the two outsiders of the first merger would exit the industry, thus leadingto the equilibrium market structure
2
4;14/C8/C9
. It also anticipates that even if the merger
between outsiders were allowed, a further merger to monopoly will not be authorised.
Therefore, the AA compares the consumer surplus under the two market structures2
4;14/C8/C9
and2
4;24/C8/C9
.
Since p2
4;14/C0/C1
¼1ț6a
3zp2
4;24/C0/C1
¼1ț4a
3,the AA will always authorise the defensive merger .
Note that this was not always the case under the symmetric case dealt with in Section
4. In particular, there was an area ( fbf˜) where no outsider would leave the market after the
merger, while here we restrict attention to the case where one outsider leaves the marketafter the merger. Of course, the former counterfactual calls for a tougher stance against thedefensive merger (if the AA does not allow it, both outsiders will still operate in the
market).
A.3.4. Analysis of Stage 3
In the third stage, we have to check whether the outsiders of the first merger (if it has been
proposed in the first stage and approved in the second stage by the AA) will want to merge or not.
In the region considered, the outsiders know that if they do not merge, only one of them will
survive. They also correctly anticipate that a further merger to monopoly will not be authorised,so that the final market outcome after the defensive merger will be a symmetric duopoly.
Therefore, they will have an incentive to merge if:
P
2
4;2
4/C18/C19
¼1/C02a ðȚ2
9/C02fzPs2
4;1
4/C18/C19
¼1/C06a ðȚ2
9/C0f;f251
361f 9
( )
36612α–( )612α–
91Blocked
41,42
41}{ }{ ,42Allowed
141
α61
Fig. 3. Equilibrium outcomes with a myopic AA (asymmetric case).M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 798

which is satisfied if fV8a1/C04aðȚ
9. Therefore:
!IffV8a1/C04aðȚ
9, in the continuation game the equilibrium2
4;24/C8/C9
will prevail (a defensive
merger is proposed and allowed, a further merger is not allowed).
!IffN8a1/C04aðȚ
9, in the continuation game the equilibrium2
4;14/C8/C9
will prevail (a defensive
merger will not be sought by the outsiders).
A.3.5. Analysis of Stage 2
In the second stage, if the two randomly selected firms at the first stage decide to submit a
merger to the AA, the AA has to decide whether to allow it or not.
Two separate cases should be considered:
1. If fV8a1/C04aðȚ
9, the AA anticipates that this first merger will be followed by a second merger
that will give rise to a perfectly symmetric duopolistic structure. Therefore, a forward-lookingAA will compare p
1
4;14;14;14/C0/C1
not with p2
4;14/C0/C1
, but rather with p2
4;24/C0/C1
. This has already
been analysed in Section 4 (see Eq. (39)), where we found that the first merger will beallowed if az1/14.
2. If fN
8a1/C04aðȚ
9, the AA anticipates that the first merger will not be followed by another,
implying that the first merger will be authorised if CS2
4;14/C0/C1
zCS1
4;14;14;14/C0/C1
. This inequality
amounts to p2
4;14/C0/C1
¼1ț6a
3Vp1
4;14;14;14/C0/C1
¼1ț6a
5, which (see Eq. (46)) holds for az1/9.
However, in the parameters’ region such that fN8a1/C04aðȚ
9and fbf¯(the latter being our
Assumption 1), amust take lower values than 1/9. Therefore, in this region the first merger will
not be authorised.
251
361
f
α141
91
619
( )
36612α–( )612α–f( )
9418αα–
Predicted
Market Structure:
41,41,41,41
PredictedMarket
Structure:
41{{
}}
{},41,41,41
42,42PredictedMarket
Structure:
Fig. 4. Equilibrium outcomes with a forward looking AA (asymmetric case).M. Motta, H. Vasconcelos / Int. J. Ind. Organ. 23 (2005) 777–801 799

A.3.6. Analysis of Stage 1
In the first stage of the game, two randomly selected firms in the status quo industry structure
are given the opportunity to decide whether or not to merge. (Recall that there are noadministrative costs of submitting a merger to the AA. Therefore, when firms anticipate that amerger will be blocked, they are indifferent between proposing or not the merger).
Two cases are relevant here:
1. If fV
8a1/C04aðȚ
9, a symmetric duopolistic structure will prevail in the continuation game, and
firms will submit the merger P2
4;24/C0/C1
z2P1
4;14;14;14/C0/C1
. This has already been analysed in
Section 4, where we found that firms will always want to make the first merger proposal.
2. If fN8a1/C04aðȚ
9, the first merger will not be followed by another, implying that it will be
proposed if Pl2
4;24/C0/C1
z2P1
4;14;14;14/C0/C1
. This amounts to the inequality1
9/C02fz21/C04aðȚ2
25/C02f,
which is satisfied for all values of ab1/4ua¯ (Assumption 1). Again, the first merger will be
proposed (but in this area it will be rejected by the AA).
This completes the analysis of the whole game, which is summarised by Fig. 4 .
Notice that in the area where 1/14 bab1/9, at stage 2 the forward-looking AA would
authorise the first merger submitted for its approval, whereas a myopic AA would not (since itconsiders that the merger will force one outsider to leave the market—a version of the efficiencyoffence argument—and does not take into account a defensive merger). This is because the
forward-looking AA knows that along the equilibrium path, this merger will be followed by a
defensive merger by the first merger outsiders. The defensive merger (but not a further mergerwhich would lead to complete monopolisation of the industry) will also be authorised at stage 4,and consumer welfare will increase.
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