Mergers, Acquisitions and Firms’R&D Incentives

Christos Cabolis∗, Constantine Manasakis†, EmmanuelPetrakis‡§

Abstract

In this paper, we study the circumstances under which, processinnovations R&D investments induce profitable endogenous merg-ers and acquisitions in the subgame perfect equilibrium for a ho-mogenous goods Cournot triopoly. The driving factors behind theendogenous equilibria are found to be the efficiency of the R&Dtechnology and whether the integration takes place through amerger or an acquisition process. We also prove that the strate-gic behavior of the target firm in the acquisition process differen-tiates the incentives for acquisitions from the corresponding formergers. Our analysis offers a rational for the widely observedM&A in highly concentrated industries. Welfare analysis andpolicy implications are also discussed.

JEL classification: G34; L41; O31

Keywords: Endogenous Mergers and Acquisitions; Processes Innova-tions; Antitrust

∗Athens Laboratory of Business Administration, e-mail address: ccabo-lis@alba.edu.gr

†Department of Economics, University of Crete, e-mail address: man-asakis@stud.soc.uoc.gr

‡Department of Economics, University of Crete, e-mail address: pe-trakis@econ.soc.uoc.gr. Corresponding author. Tel.: +30-831-77409; fax: +30-831-77406.

§An early draft of this paper was written during a short time reserch visit of Cabo-lis at the Department of Economics, University of Crete. Manasakis acknowledgesthe Athens Laboratory of Business Administration for hospitality.

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1 Introduction

Horizontal mergers and acquisitions (M&A) along with technological in-novations have been extensively used by firms as vehicles for their growthand competitiveness strengthening in the global economy.1 Despite this,the theoretical literature on M&A typically does not investigate the con-sequences of R&D investments on the decisions for M&A transactions.The purpose of this paper is to study how investments in process

innovations R&D activities influence the profitability and the antitrusttreatment of horizontal integration through M&A.In their seminal paper, Salant et al. (1983), considering homoge-

neous goods, Cournot competition, linear demand and exogenously givenand equal marginal costs, find that only mergers that almost lead to afull-blown monopoly would be profitable. The supervening literature(e.g. Perry and Porter, 1985; Deneckere and Davidson, 1985; Farrel andShapiro, 1990) has challenged the robustness of this conclusion but in theabove series of papers, the role of R&D investments has not been exam-ined, and also, M&A are treated as identical types of firms’ integrationthat are formed exogenously in the subgame equilibrium.2

A recently arized line fo research deals with the effects of R&D in-vestments on the profitability of M&A. Stenbacka (1991), in a duopolywhere the cost-reducing R&D investments and the marginal cost real-ization are private information of the innovating firm, finds that theinnovating firm does not have ex ante incentives to reveal its cost real-ization prior to the takeover and that consumers ultimately benefit fromthis. Wong and Tse (1997), extending the analysis of Stenbacka (1991),

1Gugler et al. (2003), note that almost 42% of the completed 45,000 mergersaround the world during 1981-1998 were horizontal. Blonigen and Taylor (2000)present evidence according to which, average annual domestic acquisitions and theshare of domestic manufacturing acquisitions in the USA during 1989-1994 took placein R&D intensive industries (Chemicals and Drugs, Computer and Office Equipment,Electronic and Electrical Equipment, Measuring, Medical and Photographic Equip-ment).

2A more recent strand in the literature endogenizes the merger decision. Intheir seminal paper, Kamien and Zang (1990) analyze the conditions that limit thepossibility of monopolization of an industry by intra-industry acquisition of firms.Gowrisankaran (1999), using dynamic programming methods in a model where firmsmake merger, exit, investment and entry decisions before competing in the prod-uct market, argues that modeling the merger process as an endogenous one, can beused as a tool for policy analysis of the causes and consequences of mergers. Simi-larly, Rodrigues (2001), considering a process of endogenous mergers similar to the“sequential cartel formation process” concludes that the equilibrium market concen-tration decreases in the number of firms in the initial market structure and increasesin the expected competitive intensity and the fixed cost economies permitted by themerger.

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demonstrate that the R&D investments under the two different informa-tion regimes depend on the spillover magnitude in the industry and tothe efficiency of the R&D technology employed by the innovating firm.Canoy Riyanto and Van Cayseele (2000) analyze the impact of potentialtakeovers on the investment decisions of managers. The synergy gainsthat the takeover generates will be distributed to the parties involvedin the takeover depending on the distribution of their bargaining power.Thus, the anticipation of the division of surplus affects the parties’ exante investment behavior and both over and underinvestment might pre-vail, depending on the relative bargaining powers of the parties. Socorro(2004) considers a homogenous triopoly, where firms have different mar-ginal costs and the most efficient firm bids in order to acquire one of theother two. Once the takeover has been achieved, the acquiring firm mustdecide whether to close one of the plants, or to transfer its technologyto the acquired firm and operate both plants in competition with eachother. This decision depends on the ability of the target firm to absorbnew technologies and Socorro (2004) argues that firms may strategicallyuse R&D investments to signal their ability to fit well.3

With this paper, we contribute to the literature as we outline underwhich circumstances cost-reducing R&D investments induce the endoge-nous emergence of horizontal M&A, in the subgame perfect equilibrium.We consider a three-firm Cournot oligopoly model with homogenous

products. Firms have equal marginal cost and each firm can invest inR&D for cost-reducing process innovations. The necessary amount tobe invested in R&D in order to obtain a given cost reduction indicatesthe efficiency of the R&D technology. Firms maximize their profits withrespect to the level of the R&D effort, whether to integrate or not,and the level of output. The integration of two firms leads to one firmdisappearing in the output stage.4 We distinguish between two different

3In this field, empirical findings are inconclusive. Blonigen and Taylor (2000),using a panel of 217 U.S. electronic and electrical equipment firms during 1985-1993,find a strong negative correlation between R&D intensity and acquisition activity. Incontrast, Lehto and Lehtoranta (2004), using data from Finland for the period 1994-1999, examine whether the likelihood that a firm acquires or is acquired by anotherfirm is influenced by the investments in R&D. Their central finding suggests that theprobability of becoming both the subject and the object of an acquisition increases inthe amounts invested in R&D. Incumbent firms in the product market, interested inbuying technology, use M&A as instruments to transmit knowledge from other firms.Thus, R&D investments increase a firm’s attraction as a target for an acquisition.Similarly, increase the compatibility between a bidder firm and an R&D intensivetarget firm.

4In the extentions of our analysis, we study the case of differentiated productswhere the post-integration firm produces two brands, making it ‘larger’ than eitherof the pre-merger firms, while the outsider continues to produce one brand.

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types of integration: the merger and the acquisition. In the case ofmerger, participants cooperate in both the R&D and output stages andthe collusion is perfect with no side payments. In case of acquisition,the acquirer firm (bidder firm) makes a bid in order to buy one of itscompetitors (target firm). In the R&D stage the target firm invests inR&D in order to maximize the acquisition price that the bidder firmwill pay in order the acquisition transaction to be held. Subsequently,the target firm makes it more expensive for the acquiring firm to bringabout a profitable acquisition. We prove that the strategic behavior ofthe target firm in the acquisition process differentiates the incentives foracquisitions from the corresponding for mergers.The literature on endogenous mergers has mainly focused on the

enogenous market structure through a M&A process and results havebeen reached through various approaches.5 We rather examine whether amerger (acquisition) endogenously emerges in the subgame perfect equi-librium, by using a common methodology in the game-theoretic litera-ture. We propose a candidate equilibrium outcome of firms’ strategiesand then we examine whether it survives all possible strategy deviations.If no firm has an incentive to deviate from the candidate equilibrium,then firms’ strategies will endogenously emerge in the subgame perfectequilibrium.Focusing on the central question of whether or not a profitable hori-

zontal integration endogenously emerges, the efficiency of the R&D tech-nology — as well as the type of integration — turn out to be of crucialimportance. Merger participants avoid the duplication of R&D effortsand deviating from the symmetric no-merger equilibrium, increase theirR&D investments and final-good production, compared with the out-sider firm. However, the profitability of the merger is affected negativelyby the reduction in the total output in the industry, that is caused bythe post-merger higher concentration. Although the reduction in totaloutput raises the industry price and the price-cost margin, the increasedpost-merger price-cost margin is insufficient to compensate for the fallin the merger participants’ post-merger output. Our analysis suggeststhat the positive effects of the cost efficiencies due to R&D investmentsdominate the negative effects of the higher concentration if and only if,the R&D technology is sufficiently efficient.

5Kamien and Zang (1990) examine the possibility of monopolization of an industryby intra-industry acquisition of firms, where firms post bids for other firms and askprices for their own. Gowrisankaran (1999) and Gowrisankaran and Holmes (2004),apply dynamic programming methods and find Markov-Perfect Nash Equilibria. Fi-nally, Horn and Persson (2001) and Rodrigues (2001), employing ideas on coalitionformation from cooperative game theory, study the endogenously determined patternof mergers in oligopolistic industries.

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In case of acquisition, the effects of R&D investments are differen-tiated. The profitability of the acquisition is affected positively by thebidder firm’s R&D investments. The target firm invests in R&D in orderto maximize the acquisition price that the bidder firm will pay in orderthe acquisition transaction to be held. Thus, it is the strategic behaviorof the target firm that reduces the profitability of the acquisition anddemands the efficiency of the R&D technology has to be higher, thanthe corresponding in case of merger, for an acquisition transaction to beprofitable.Our analysis reveals that a horizontal integration has positive effects

on social welfare, given that a minimum efficiency of the R&D technologyis ensured and our policy implications contain the subsidization of R&Dinvestments for firms that are about to integrate and the encouragementof M&A in R&D intensive industries.The paper is organised as follows. In the next section, we present the

model. In Section 3, we investigate the horizontal integration througha merger, while in Section 4, we analyze how our results change if weconsider the integration through an acquisition process. In Section 5,we discuss some extensions of our model and in Section 6 we carry outa social welfare analysis. We offer some concluding remarks in Section7.

2 The model

We consider an industry that consists of three identical firms producing ahomogeneous good. The firms are denoted by i = 1, 2, 3 and the outputthey produce by qi. We further assume that the inverse demand functionis linear, given by p = α−Q, where p is price, α is a positive constant, and

Q =3X

i=1

qi, is the total output. There is no entry or threat of entry and

firms compete in Cournot fashion. We also consider that competitorshave the equal marginal cost c (c ≤ α) and identical R&D technologies.Firm i can invest in R&D for cost-reducing process innovations. Thus,the overall marginal cost for firm i is given by c−xi, where xi is the costreduction due to firm i’s R&D investment. Following d’Aspremont andJacquemin (1988), the cost of R&D is assumed to be quadratic, havingthe form γx2i /2, reflecting the existence of diminishing returns to R&Dexpenditures. When γ increases, the expenditure to obtain a given costreduction also increases. Thus, we argue that the parameter γ relates tothe efficiency of the R&D technology: higher γ means lower efficiency ofa given amount invested in R&D. The total cost function Ci for firm i

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is given by Ci = (c− xi)qi + γx2i /2.6

Firms are assumed to maximize their profits with respect to threedecision variables: The level of the R&D effort, whether to integrateor not, and the level of output. The integration can take place eitherthrough a merger or through an acquisition process.7 We restrict ourattention on how process innovations R&D investments, prior to thedecision whether to integrate or not, induce profitable horizontal M&A.However, when a firm invests in R&D there is there is unobservabilityfor the competitors’ investments. Thus, as a simplifying assumption, weconsider that both decisions, R&D investments and whether to integrateor not, are taken as if they were simultaneous. Practically, this can bethe case where both decisions are part of a long-run strategic plan of thefirms. Thus, we consider a two-stage game with the following timing:Stage 1: The three market participants decide simultaneously on

both, the level of R&D effort, xi, and whether to integrate or not, Ii. Iiis an indicator function that can take the values 0 or 1 as follows:

Ii =

½1 if firm i integrates0 if firm i does not integrate

Formally, the first stage of the game is characterized by the strategyvector {{x1, I1} , {x2, I2} , {x3, I3}}.Stage 2: Firms set quantities.We solve the above model by employing the Subgame Perfect Nash

Equilibrium (SPNE) solution concept. To investigate the conditionsunder which a strategy (to merge or not to merge and to acquire ornot to acquire) emerges as an equilibrium in the first stage of the game,we use a methodology common in the game-theoretic literature. Webegin by proposing a candidate equilibrium outcome of firms’ strategiesand then, we examine whether this candidate equilibrium survives allpossible strategy deviations. Thus, if no firm has an incentive to deviatefrom the no-merger (merger) or the no-acquisition (acquisition) strategy,the corresponding strategy is stable. Equivalently, this strategy willendogenously emerge in the subgame perfect equilibrium.

3 The case of merger

In this section, we investigate the conditions under which the no-merger(merger) strategies emerge as equilibria. We begin with the case of theno-merger (NM) strategy. Under this configuration, in the second stageof the game, firms compete a la Cournot in a triopoly. Thus, given R&D

6Although in our basic analysis we abstain from taking into account the spilloversof R&D activities, we do so in the extensions of our analysis.

7We assume that integration to monopoly is not allowed by antitrust laws.

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investments and the no-merger decision, each firm i sets output level inorder to maximize profits:

ΠNMi = (a−Q− c− xi)qi, i = 1, 2, 3 (1)

The first-order-condition (foc) of eq. (1) provides firm i’s reactionfunction RNM

i (q−i) ≡ qi =12(α − c − q−i + xi), where q−i =

P∀j 6=i qj is

the aggregate output of all the firms except i.8 Solving the system ofthe foc, we get the equilibrium firm-level output:

qNMi =

1

4(α− c+ 3xi − x−i) (2)

where x−i =P∀j 6=i xj is the sum of competitors’ R&D investments.

The first stage of the game is characterized by the strategy space{©xNM1 , 0

ª,©xNM2 , 0

ª,©xNM3 , 0

ª} and firms invest in R&D simultane-

ously so as to maximize their profits:

ΠNMi =

∙1

4(α− c+ 3xi − x−i)

¸2− γ

x2i2

(3)

From the foc of the above equation, we obtain the reaction function offirm i, RNM

i (x−i) ≡ xi = 3 (a− c− x−i) /(8γ−9). Note that dxi/dx−i <0, i.e., R&D investments are strategic substitutes for the firms. Then,the equilibrium firm-level R&D investments are:

xNMi =

3 (a− c)

8γ − 3 (4)

Substituting (4) into (3) yields firm-level output and profits:

qNMi =

2γ (a− c)

8γ − 3 ΠNMi =

(8γ2 − 9γ) (a− c)2

2(3− 8γ)2 (5)

The non-negativity constraint for R&D and output in equilibriumimplies that γ > 3

8. Furthermore, to avoid corner solutions, equation

ΠNMi > 0 requires that γ > 9

8. The latter stronger restriction will be

imposed to parameter γ.Let us now examine the merger (M) strategy. We suppose that firms

1 and 3 decide to merge into firm m. The merger changes the industryfrom a triopoly to a duopoly. In the second stage of the game, givenR&D investments and the decision to merge, each duopolist sets output

8The reaction function outlines the standard properties of a Cournot reactionfunction where the own output is inversely related to the rivals’ output. Note alsothat a higher level of R&D effort during stage-1 results in higher total output instage-2, ceteris paribus.

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in order to maximize profits. The foc of the profit function provides firmi’s reaction function RM

i (q−i) which is identical to RNMi (q−i). In the

present case, the first stage of the game is characterized by the strategyvector {

©xM1 , 1

ª,©xM2 , 0

ª,©xM3 , 1

ª}.

In the first stage, duopolists invest in R&D in order to maximizeprofits

ΠMi =

∙1

3(α− c+ 2xi − x−i)

¸2− γ

x2i2, i = m, 2 (6)

The reaction function of firm i, RMi (x−i) ≡ xi = 4 (a− c− x−i) /(9γ−

8) indicates that the R&D investments are strategic substitutes for thefirms.Solving the system of the foc, we find that firm-level R&D invest-

ments are given by:

xMi =4 (a− c)

9γ − 4 (7)

Then, from eq. (6) and eq. (7), firm-level output and profits are:

qMi =3γ (a− c)

9γ − 4 ΠMi =

(9γ2 − 8γ) (a− c)2

(4− 9γ)2 (8)

The non-negativity constraint for R&D and output in equilibriumimplies that γ > 4

9. To avoid corner solutions, ΠM

i > 0 requires thatγ > 8

9, a restriction that will be imposed to parameter γ.

Let us now examine whether the no-merger (merger) strategies emergeas an equilibrium outcome. The no-merger outcome will endogenouslyemerge in the subgame perfect equilibrium, if and only if no firm hasan incentive to deviate from it. The only deviation available is that twofirms (1 and 3) decide to merge. In this case, the stage-1 strategy spacebecomes {

©xnmdm , 1

ª,©xNM2 , 0

ª,©xnmdm , 1

ª}. In order for the merger to

be formed, it has to be profitable. Therefore, the criterion to be usedis that the profits of the merged firm m, under the deviation from theno-merger, has to be greater than the sum of the profits of the two firms,that would participate in the merger, under the no-merger strategy.Suppose that in the first stage of the game, firms 1 and 3 deviate

from the no-merger equilibrium and decide to merge into firmm, takingfirm’s 2 R&D level

¡xNM2

¢as given. Thus, firmm, following the reaction

function RMi (x−i) with x−i = xNM

2 , invests in R&D:

xnmdm =

8(4γ − 3)(α− c)

72γ2 − 91γ + 24 (9)

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with xnmdm > xNM

2 . Then, given RMi (q−i), firm m and firm 2 set

quantities

qnmdm =

(24γ2 − 18γ)(α− c)

72γ2 − 91γ + 24 qnmd2 =

(24γ2 − 23γ)(α− c)

72γ2 − 91γ + 24 (10)

with qnmdm > qnmd

2 . Observe that firms 1 and 3, deciding to merge,increase their R&D investments and expand their output, compared withthe outsider firm and subsequently, they escape from the symmetric no-merger equilibrium.Then, firm m’ s profits, when firms 1 and 3 deviate from the no-

merger equilibrium and merge, are:

Πnmdm =

4γ(4γ − 3)2(α− c)2

(8γ − 3)2(9γ − 8) (11)

Comparing Πnmdm with 2×ΠNM

i , we find that the no-merger strategyemerges as an equilibrium outcome for values of the γ higher than 5.27.Recall that, the parameter γ relates to the efficiency of the R&D tech-nology with higher values of γ indicating lower efficiency of the R&Dinvestments. Thus, the no-merger is an equilibrium outcome for lowlevels of the R&D efficiency.In the same lines, the merger outcome is an equilibrium outcome

only if there is no firm that has an incentive to deviate from it and theonly deviation available is that in the first stage of the game, firms 1 and3 decide not to merge. In this case, the stage—1 strategy space becomes{©xmdnm, 0

ª,©xM2 , 1

ª,©xmdnm, 0

ª}. Firms will decide not to merge if they

find it more profitable and subsequently, the criterion to be used is thatthe profit of each firm, that would participate in the merger, has to behigher than the share of the profits of the firm m that each participantwould receive, under the merger strategy.Thus, suppose that in the first stage of the game, firms 1 and 3 devi-

ate from the merger equilibrium. Acting as Cournot players, each firmfollows the the reaction functionRM

i (x−i), while the outsider firm investsxM2 . Subsequently, the R&D investment for each firm that deviates fromthe merger equilibrium, is given by:

xmdinm =

3(9γ − 8)(α− c)

72γ2 − 86γ + 24 i = 1, 3 (12)

with xmdinm > 1

2xMm . Then, given RNM

i (q−i), each firm sets its optimaloutput level

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qmdinm =

(9γ2 − 8γ)(α− c)

36γ2 − 43γ + 12 i = 1, 3 qmd2 =

(18γ2 − 11γ)(α− c)

72γ2 − 86γ + 24 (13)

with qmdinm > 1

2qMm . When firms 1 and 3 decide not to merge, they

invest more and increase output, compared with the firm-level share ofinvestments and output in case of merger and as a result, they escapefrom the symmetric merger equilibrium.Finally, the profits for firm 1 and 3 in case of deviation from the

merger equilibrium are:

Πmdnm =

γ(8γ − 9)2(9γ − 8)2(α− c)2

8(4γ − 3)2(9γ − 4) (14)

Comparing Πmdnm with

12ΠMi , we find that themerger strategy emerges

as an equilibrium outcome for values of the γ lower than 5.27. Themerger is an equilibrium outcome if the efficiency of R&D investmentsexceeds a minimum level.The following proposition summarizes.

Proposition 1 Merger (No-Merger) is the subgame perfect equilibriumif and only if γ < 5.27 (γ > 5.27).

The intuition behind our result goes as follows. In our setting, theprofitability of the merger depends on two effects. The first one is theR&D investments that affect the profitability positively, through twoways. According to the first one, merger participants invest in processR&D that reduces the marginal cost. According to the second one,merger participants undertake their R&D projects in one single lab andthus, they avoid the duplication of R&D activities. On the other hand,the profitability of the merger is affected negatively by the reduction inthe total output in the industry, that is caused by the merger of the twocompetitors. Although the reduction in total output raises the indus-try price and the price-cost margin, the increased post-merger price-costmargin is insufficient to compensate for the fall in the merger partici-pants’ post-merger output. This effect has been well cited by Salant etal. (1983). Our analysis suggests that the positive effects of the costefficiencies due to R&D investments dominate the negative effects of thehigher concentration if and only if, the R&D technology is sufficientlyefficient (γ < 5.27). Although a merger is more profitable for the out-sider than for a participant, our attention is restricted to the endogenousemergence of the merger strategies in the subgame perfect equilibrium.We proved that cost efficiencies, by process innovations R&D invest-

ments, induce endogenous profitable mergers if the efficiency of the R&D

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technology exceeds a minimum level. Thus, our analysis offers a ratio-nale for why we do observe horizontal mergers in highly concentratedindustries.

4 The case of acquisition

In this section, we maintain our assumptions about the initial industrystructure and we study the second type of horizontal integration, thecase of acquisition. Thus, we assume an acquisition process where theacquirer firm (bidder firm) makes a bid to buy one of its competitors(target firm) given that the formation of a monopoly is not allowed by theantitrust authorities. Although the merger can be considered as a typeof a joint venture where participants cooperate in both the R&D andoutput stages and the collusion is perfect with no side payments, in caseof acquisition, the target firm acts strategically in the acquisition processin order to maximize the acquisition price that the bidder firm will pay inorder the acquisition transaction to be held. Thus, the target’s strategicbehavior makes it more expensive for the acquiring firm to bring aboutacquisition and reduces the profitability of the acquisition.9

We begin the analysis with the case of the no-acquisition (NA) strat-egy. In the second stage of the game, firms compete a la Cournot in atriopoly. The first stage of the game is characterized by the strategyspace {

©xNA1 , 0

ª,©xNA2 , 0

ª,©xNA3 , 0

ª} with firms investing in R&D si-

multaneously so as to maximize their profits. Results for R&D invest-ments, output and profits under the no-acquisition equilibrium (xNA

i ,qNAi , ΠNA

i ) are identical with those obtained under the no-merger (NM)equilibrium.Let us now examine the acquisition (A) strategy. We suppose that

firm 1 bids in order to acquire the firm 3. The acquisition changes theindustry from a triopoly to a duopoly. Thus, in the post-acquisitionmarket, in the second stage of the game, given R&D investments andfirm 1’s decision to acquire the firm 3, the new firm a will competewith firm 2 in quantities. The foc of the profit function provides firmi’s (i = a, 2) reaction function RA

i (q−i) that is identical with RMi (q−i).

In the present case, the first stage of the game is characterized by the

9In our case, the “acquisition process” is similar to the “endogenous merger”, inthe spirit that has been used by Gonzalez-Maestre and Lopez-Cunat (2001) and Ziss(2001) who examine the profitability of horizontal mergers under the delegation ofoutput decisions. In their models, “a merger is endogenous if the target firms actstrategically in the acquisition process by holding out for a buy-out price equal tothe profits they would obtain if they were the only hold-out in a multi-firm merger(Kamien and Zang, 1990).” In the above papers, the acquisition price of the targetfirm is equal with its profits in case of no-merger, while in our model, the target firminvests strategically in R&D, in order to maximize its acquisition price.

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strategy vector {©xAab, 1

ª,©xA2 , 0

ª,©xAat, 1

ª}. xAab and xAat indicate R&D

investments by the bidder firm and the target firm respectively and xA2is the R&D investment of the outsider firm.Thus, in the first stage, the three firms invest in R&D in order to

maximize profits given by:

ΠAab =

∙1

3(α− c+ 2x1 − x3)

¸2− γ

x212−∙1

4(α− c− x1 + 3x2 − x3)

¸2(15)

ΠA2 =

∙1

3(α− c+ 2x2 − x3)

¸2− γ

x222

(16)

ΠAat =

∙1

4(α− c− x1 + 3x2 − x3)

¸2− γ

x232

(17)

Observe that, the profits of the bidder firm¡ΠAab

¢are the profits in

a duopoly reduced by the acquisition price of the target firm (firm 3),that the acquiring firm has to pay for the acquisition transaction tobe held. The acquisition price of the target firm is equal with the grossprofits that the firm would earn in case of no-acquisition

¡ΠNA3 = ΠNM

3

¢.

Note also that when the target firm invests in R&D, its objective is tomaximize its net acquisition price.Then, asymmetric firm-level R&D investments, output and profits

are:

xAab =(41γ − 36) (α− c)

4 (18γ2 − 26γ + 9) xAat =9 (3γ − 4) (α− c)

4 (18γ2 − 26γ + 9) (18.1)

xA2 =(8γ − 9) (α− c)

18γ2 − 26γ + 9 (18.2)

qAa =3γ (4γ − 3) (α− c)

36γ2 − 52γ + 18 qA2 =3γ (8γ − 9) (α− c)

4 (18γ2 − 26γ + 9) (19)

ΠA∗ab =

(504γ4 − 1681γ3 + 2448γ2 − 1296γ) (α− c)2

32 (18γ2 − 26γ + 9) (20.1)

ΠA∗at =

(72γ2 − 81γ) (4− 3γ)2 (α− c)2

32 (18γ2 − 26γ + 9) (20.2)

ΠA∗2 =

(9γ2 − 8γ) (9− 8γ)2 (α− c)2

16 (18γ2 − 26γ + 9) (20.3)

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The non-negativity constraint for R&D output and profits in equi-librium implies that γ > 4

3.

Let us now examine whether the no-acquisition strategies emerge asan equilibrium outcome. The no-acquisition outcome will endogenouslyemerge in the subgame perfect equilibrium, if and only if no firm hasan incentive to deviate from it. The only deviation available is that thefirm 1 makes a bid in order to acquire firm 3. In this case, the stage-1strategy space becomes {

©xnadab , 1

ª,©xNA, 0

ª,©xnadat , 1

ª}. In order for

the firm 1 to deviate and make a bid, it has to find it profitable andthus, the criterion to be used is that the profits of the firm 1 in case ofdeviation, from the no-acquisition strategy, have to be greater than itsprofits under the no-acquisition one.Thus, suppose that in the first stage of the game, given firm’s 2

R&D level xNA2 , firm 1 deviates from the no-acquisition equilibrium and

makes a bid in order to acquire firm 3. Firm 3 optimally responsesby readjusting its R&D investments. Given xNA

2 , firm 1 and firm 3invest simultaneously in R&D. Firm 1’s objective is to maximize profitsunder the deviation from the no-acquisition and firm 3’s objective isto maximize the net acquisition price that the bidder firm will pay. Bysubstituting xNA

2 in the profit functions ΠAab and Π

Aat, we find firm 1’s and

firm 3’s R&D investments, in case of deviation from the no-acquisitionequilibrium:

xnadab =(164γ2 − 267γ + 108) (α− c)

288γ3 − 652γ2 + 492γ − 108 (21.1)

xnadat =(108γ2 − 225γ + 108) (α− c)

288γ3 − 652γ2 + 492γ − 108 (21.2)

with xnadab > xNA2 . Then, given RA

i (q−i), firm a and firm 2 set quan-tities

qnada =3γ (3− 4γ)2 (α− c)

144γ3 − 326γ2 + 246γ − 54 (22.1)

qnad2 =(96γ3 − 200γ2 + 117γ) (α− c)

288γ3 − 652γ2 + 492γ − 108 (22.2)

with qnada > qnad2 . When firm 1 acquires the firm 3, deviating from theno-acquisition equilibrium, increases its R&D investments and expandsits output and its profits are:

Πnadab =

(504γ4 − 1681γ3 + 2448γ2 − 1296γ) (3− 4γ)2 (α− c)2

32 (−72γ3 + 163γ2 − 123γ + 27)2(23)

13

Comparing Πnadab with ΠNA

i = ΠNMi , we find that the no-acquisition

strategy emerges as an equilibrium outcome for γ > 3.02. Thus, the no-acquisition is an equilibrium outcome for low levels of the R&D efficiency.In the same lines, the acquisition outcome is an equilibrium one only

if there is no firm that has an incentive to deviate from it and the onlydeviation available is that in the first stage of the game, firm 1 doesnot bid in order to acquire the firm 3. In this case, the stage-1 strategyspace becomes {

©xadna, 0

ª,©xA2 , 1

ª,©xadna, 0

ª}. The firm 1 will not bid in

order to acquire the firm 3 if it finds it more profitable and subsequently,the criterion to be used is that the profit of firm 1 in case of deviation,from the acquisition strategy, has to be higher than its profits under theacquisition strategy.Suppose that in the first stage of the game, given firm’s 2 R&D level

xA2 , firm 1 deviates from the acquisition equilibrium (that is, firm 1 doesnot bid in order to acquire firm 3) and firm 3 optimally responses inthis deviation by readjusting its R&D investments. Firm 1 and firm 3invest simultaneously in R&D in order to mazimize their profits given byeq.(3). By substituting xA2 in the profit functions Π

Aab and ΠA

at, we findfirm 1’s and firm 3’s symmetric R&D investments, in case of deviationfrom the acquisition equilibrium:

xadai =(27γ2 − 51γ + 27) (α− c)

72γ3 − 158γ2 + 114γ − 27 i = b, t (24)

with xadab > xA2 . Then, given RNAi (q−i), each firm i (i = 1, 2, 3) sets

its optimal output level

qadnai =(18γ3 − 34γ2 + 9γ) (α− c)

72γ3 − 158γ2 + 114γ − 27 i = b, t (25.1)

qad2 =(18γ3 − 29γ2 + 9γ) (α− c)

72γ3 − 158γ2 + 114γ − 27 (25.2)

with qadnab > qad2 . Finally, firm 1’s profit if it deviates from the acqui-sition equilibrium is:

Πadab =

(8γ2 − 9γ) (9γ2 − 17γ + 9)2 (α− c)2

23− 4γ)2 (18γ2 − 26γ + 9)2(26)

ComparingΠadab withΠ

A∗ab , we find that the acquisition strategy emerges

as an equilibrium outcome for values of the γ lower than 3.02. The ac-quisition is an equilibrium outcome if the efficiency of R&D technologyexceeds a minimum level.The following proposition summarizes.

14

Proposition 2 Acquisition (No-Acquisition) is the subgame perfect equi-librium if and only if γ < 3.02 (γ > 3.02).

Intuitively, the profitability of the acquisition is affected by the cost-reducing R&D investments and the reduction in the total output in theindustry. R&D investments decrease the marginal cost of the bidder firmand as a result, the profitability of the acquisition is affected positively.In contrast, the reduction in the target’s marginal cost, through R&Dinvestments, increases the acquisition price that the bidder firm has topay and subsequently, the profitability of the acquisition is affected neg-atively. The target’s strategic behavior, to invest in R&D in order tomaximize the acquisition price that will receive from the bidder, sug-gests that in case of acquisition participants overinvest in R&D againstof avoiding the duplication of effort. On the other hand, the profitabil-ity of the acquisition is affected negatively by the reduction in the totaloutput, presicely as in the case of merger, due to the increased concen-tration. Our analysis suggests that the positive effects of the bidder’sR&D dominate the negative effects of the target’s strategic behaviorand the higher concentration if and only if, the efficiency of the R&Dtechnology is γ < 3.02.Note that in order for the acquisition to be profitable, the efficiency

of the R&D technology has to be higher (that is lower γ) than thecorresponding in case of merger. Intuitively, it is the target’s R&Dinvestments, in order to maximize its acquisition price, that reduce theprofitability of the acquisition and demand the higher R&D efficiency inorder the negative effects of the reduced output to be dominated.

5 Extensions

Our basic model is rather stylised, so it is natural to check the robustnessof our results. Let us, therefore, explain how results may change whenwe extend our basic model in three different directions.

5.1 Incorporating R&D spilloversSo far in our analysis we have incorporated cost reducing R&D invest-ments, following d’Aspremont and Jacquemin (1988), but we have ab-stained from taking into account the spillovers of R&D activities. How-ever, in d’Aspremont and Jacquemin (1988) words, “R&D externalitiesor spillovers imply that some benefits of each firm’s R&D flow withoutcompensation to other firms and this may cause free-riding behavior andunderinvestment problems”.10

10Recent empirical evidence establish the existence of R&D spillovers (for a survey,see De Bondt, 1996).

15

In this part of the paper, we incorporate R&D spillovers in our for-mal model, considering that the magnitude of spillovers is exogenouslygiven and industry-wide. Subsequently, we add a third determinant,the free-riding effects of R&D, on the profitability of the merger (acqui-sition). Incorporating R&D spillovers, firm i’s cost function takes theform Ci = (c − xi − δx−i)qi + γx2i /2, with x−i =

P∀j 6=i xj the sum of

competitors’ R&D investments that leak to firm i without compensation,due to the spillovers of R&D activities and 0 ≤ δ ≤ 1, the magnitude ofthe spillovers. The higher the values of δ, the more fierce the free-ridingand underinvestment. Analysis of pure-strategy subgame-perfect Nashequilibria leads to the following proposition.

Proposition 3 Merger (Acquisition) is the subgame perfect equilibriumif and only if γ < 5.27 and δ < 0.43 (γ < 3.02 and δ < 0.33).

Recall that, assuming that δ = 0 in our basic model, we have foundthat the merger (acquisition) emerges in the subgame perfect equilib-rium if and only if γ < 5.27 (γ < 3.02). Incorporating spillovers, we findthat the positive effects of the R&D investments dominate the negativeeffects of the higher concentration, and thus the merger (acquisition)strategies emerge endogenously in equilibrium, if and only if the free-riding effect is be weak, given a minimum level for the efficiency of theR&D technology.Intuitively, the higher the spillovers, the more fierce the underinvest-

ment and subsequently, the more efficient that the R&D technology hasto be in order the positive effects of the cost efficiencies to dominate thenegative effects of the higher concentration and thus make the merger(acquisition) profitable. The critical spillover rate in case of acquisitionis lower than the corresponding in case of merger. This result indicatesthat the strategic behavior of the target firm, that reduces the prof-itability of the acquisition, demands the free-riding effect to be weaker,compared with the corresponding in case of merger, in order the acqui-sition to be profitable.

5.2 The case of differentiated productsIn our previous analysis, we have examined the case of a homogeneousgood. Let us now examine an industry that consists of three firms, eachproducing one brand of a differentiated product. Firm i produces brandi in quantity qi. Demand for the differentiated product is characterisedby a symmetric demand system, where the inverse demand functionfor brand i is given by pi = a − qi − bq−i with q−i =

P∀j 6=i qj. The

parameter b ∈ (0, 1) denotes the extent of product differentiation. Ifb → 0 the brands are regarded as (almost) unrelated, whereas b → 1

16

corresponds to the case of (almost) homogeneous goods. We furtherassume that the post-integration firm produces two brands (1 and 2),making it ‘larger’ than either of the pre-merger firms, while the outsider(firm 3) continues to produce one brand (3). Analysis of pure-strategysubgame-perfect Nash equilibria for the case of Cournot competitionleads to the following proposition.

Proposition 4 Merger (Acquisition) is the subgame perfect equilibriumif and only if γ < 5.27 and b > 0.4 (γ < 3.02 and b > 0.55).

Recall that, assuming that b = 1 in our basic model, we have foundthat the merger (acquisition) strategies emerge endogenously, if γ <5.27 (γ < 3.02). Considering differentiated products, we find that themerger (acquisition) is the subgame perfect equilibrium if and only if theproducts are quite differentiated, given a minimum level for the efficiencyof the R&D technology.This result is explained as follows: The total output in the industry

decreases as products become more homogenous in al cases: no-merger(merger), no-acquisition (acquisition). In our model, the more unre-lated (b→ 0) the brands are, the larger the difference between the pre-and the post-merger (acquisition) total output and thus, the strongerthe pressure on the profitability of the merger (acquisition) due to theconcentration effect. Subsequently, the deviation from the no-merger(no-acquisition) will be profitable, if the products are not very differ-entiated, given that the R&D technology exceeds a minimum level ofefficiency.11 In case of acquisition, the difference between the pre- andthe post-acquisition total output is larger than the corresponding in caseof merger and thus, in order for the acquisition to emerge endogenously,the products must be more homogenous, compared with the case of themerger.12

5.3 The case of a myopic target firmWe now restrict our attention on a special feature of the no-acquisition(acquisition) equilibrium. In our basic model we have assumed that

11Our result contradicts with Lommerud and Sorgard (1997), who find that in atriopoly with two merger candidates, where the number of brands in a choice variable,the profitability of the merger increases in the degree of product differentiation.12According to the case of Bertrand competition, in a differentiated products in-

dustry, Deneckere and Davidson (1985) find that a merger is always profitable. Weexamine the case where firms undertake process innovations R&D investments jointlywith the decision for merger (acquisition) and the above result is reinforced, regard-less the type of horizontal integration (merger or acquisition).

17

when the bidder firm deviates from the no-acquisition (acquisition) equi-librium, the target firm optimally responses by readjusting its R&D in-vestment in favor of maximizing the net acquisition price that the bidderfirm will pay for the acquisition transaction to be held. This can be thecase of a non-myopic target firm. If we rather consider a myopic targetfirm that does not readjust its R&D investment, results obtained for thecase of Cournot competition with homogenous products are reinforced.The only difference is that in order for the no-acquisition (acquisition) toemerge endogenously, the R&D technology has to be more efficient thanit has to be in case of a non-myopic target.13 Intuitively, when facing amyopic target, the bidder firm invests more than it invests in case of anon-myopic one and subsequently, the R&D technology has to be moreefficient in order the deviation from the no-acquisition (acquisition) tobe profitable.

6 Welfare analysis

In this section we deal with the antitrust issues of our analysis. Compe-tition authorities are concerned primarily with horizontal mergers due tothe potential price increase and allocative inefficiencies that they cause.In order to assess the overall effects of mergers it is necessary to makeexplicit the policy goals of merger regulation. In the policy debate, theconsumer surplus and the social welfare are the most frequently men-tioned.The seminal analysis of Williamson (1968) advocated the social wel-

fare approach in merger analysis. Antitrust authorities, when decidingwhether or not to approve a merger, have to compare the deadweightlosses due to price increases after merger with the internal efficienciesthat are generated. Farrell and Shapiro (1990), examine a variant of thelatter approach according to which, mergers have to be assessed on thebasis of their effects on consumers and competitors jointly. If mergersyield a net positive external effect, they should be allowed, even if theeffect on consumers alone is negative. In a recent contribution, Nevenand Roller (2004), comparing the above objectives in a political econ-omy framework, conclude that neither standard dominates and that thechoice of a standard that an antitrust agency is held accountable to isaffected by the precise political economy environment that it may be

13Analysis of pure-strategy subgame-perfect Nash equilibria discloses that the ac-quisition (no-acquisition) is the subgame perfect equilibrium if and only if γ < 2.12(γ > 2.12).

18

operating in.14 15

Thus, for the purposes of our analysis, we assume that there existsan antitrust authority that can approve or forbid a merger. The au-thority’s objective is the total surplus and subsequently, a merger willbe approved if it is optimal from the point of view of the social welfare.The appropriate measure of welfare consists of two parts: consumers’surplus and firms’ profits. Thus, social welfare is defined as:

SW =1

2(QI)

2 + 2ΠI , I = n, m, a (27)

12(QI)

2indicates consumers’ surplus and 2ΠI indicates overall indus-try profits. n, m and a correspond to the no-merger (no-acquisition),merger and acquisition respectively.Using results in equilibrium from the previous sections, the corre-

sponding social welfare for every case are as follows:

SWn =(60γ2 − 27γ) (a− c)2

2 (3− 8γ)2(28.1)

SWm =4γ (a− c)2

9γ − 4 (28.2)

SWa =(4608γ4 − 11345γ3 + 9387γ2 − 2592γ) (a− c)2

32 (9− 26γ + 18γ2)2(28.3)

The non-negativity constraints imply: SWn > 0 if γ > 0.45, SWm >0 if γ > 0, SWa > 0 if γ > 0.69. Thus, should the antitrust authorityapprove the merger (acquisition)? In order to answer this question, wecompare social welfare under no-merger (SWn) with the correspondingin case of merger (SWm) and in case of acquisition and we summarizeour findings in the following proposition:

Proposition 5 The antitrust authority will approve the merger (acqui-sition) if γm < 3.12 (γa < 2.87).

14Roller at al. (2001) mention that although economists argue that one shouldfocus on total welfare, and therefore focus on the allocative inefficiency (or deadweightloss) caused by the merger, competition authorities, in most countries, are primarilyconcerned with the distributional effects of price increases, focusing on consumerssurplus.15Recent empirical findings by Gugler et al. (2003), suggest that the nearly 18,000

horizontal mergers that were actually completed across the world during 1981-1998,resulted in profits increases and output decreases and subsequently, these mergerswere welfare reducing.

19

We shall now proceed to explain how we came to these results. Thereare two effects on social welfare. According to the first one, R&D in-vestments decrease the marginal cost and the price of the final good.Subsequently, the demand for the final good increases and firms expandtheir output. Thus, consumers’ surplus and firms’ profits are affectedpositively. However, the integration (through either a merger or an ac-quisition) of the two competitors increases the concentration in the mar-ket, raises the industry price and reduces total output. As a result,consumers’ surplus decrease although industry profits increase. We findthat the positive effect of R&D investments dominates the negative ef-fect due to the higher concentration, and subsequently SWm > SWn,only if the efficiency of the R&D technology exceeds a minimum level,that is, if γm < 3.12. In this market, although a merger from triopoly toduopoly increases market concentration, it also increases social welfareand should be approved. The reason is that the efficiency gains in theform of reduced marginal costs dominate the dead weight loss associatedwith increased concentration.In the same lines, in case of an acquisition, we find that SWa > SWn

if γa < 2.87. Thus, the level of efficiency that guarantees the approval ofthe acquisition is higher (γa > γm) than the corresponding in case of amerger. The reason for that lays in the target firm’s strategic bahaviorthat reduces the profitability of the acquisition and subsequently, theR&D technology has to be more efficient in order the positive effects ofthe R&D investments on social welfare to dominate the negative effects ofthe higher concentration. Note that the efficiency of the R&D technologythat ensures the approval of the merger (acquisition) by the antitrustauthority is higher than the corresponding efficiency that guaranteesthe profitability of the merger (acquisition).Our previous analysis offers some direct policy implications. We ar-

gue that policy-makers should move towards the subsidization of R&Dinvestments for firms that are about to integrate either through a mergeror an acquisition. The subsidization of R&D increases both consumerssurplus and firms profits and as a result, social welfare is affected pos-itively. Policy-makers should also encourage the formation of M&A inR&D intensive industries given that the efficiency of the R&D technologyexceeds a minimum level.

7 Concluding remarks

Although horizontal M&A and technological innovations have been con-sistently used as vehicles for firms’competitiveness strengthening in therapidly changed business environment, the literature for the role of R&Dinvestments on the decisions for firms’ integration is scarce.

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We fil this gap by studying how process innovations R&D invest-ments induce the endogenous emergence of profitable horizontal M&A.Our key result indicates that an horizontal integration emerges endoge-nously if the efficiency of the R&D technology exceeds a minimum levelwhich ensures that the positive effects of the R&D investments dominatethe negative effects of the post-integration higher market concentration.In our model, the strategic behavior of the target firm in the acquisitionprocess, that makes it more expensive for the acquiring firm to bringabout a profitable acquisition, demands the efficiency of the R&D tech-nology to be higher, than the corresponding in case of merger, for anacquisition transaction to be profitable. Thus, we prove that incentivesfor a merger differ from incentives for an acquisition and thus, thesetwo types of horizontal integration should not be treated as identical, atleast when competing firms invest in process innovations. Our analysisalso reveals that horizontal M&A have positive effects on social welfare,given that a minimum efficiency of the R&D technology is ensured.

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