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Research Policy xxx (2014) xxx–xxx

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Research Policy

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nd the winner is—Acquired. Entrepreneurship as a contest yieldingadical innovations

oachim Henkela,b,∗, Thomas Røndec,b,1, Marcus Wagnerd,e,2

Technische Universität München, TUM School of Management, Arcisstr. 21, 80333 Munich, GermanyCenter for Economic Policy Research (CEPR), London, UKCopenhagen Business School, Department of Innovation & Organizational Economics, Kilevej 14A, K3.72, 2000 Frederiksberg, DenmarkUniversität Augsburg, Chair in Innovation and International Management, Universitätsstr. 16, 86159 Augsburg, GermanyBureau d’Economie Théorique et Appliquée (BETA), Strasbourg, France

r t i c l e i n f o

rticle history:eceived 16 December 2013eceived in revised form 9 September 2014ccepted 9 September 2014vailable online xxx

eywords:adical innovationntrantncumbent

a b s t r a c t

New entrants to a market tend to be superior to incumbents in originating radical innovations. Weprovide a new explanation for this phenomenon, based on markets for technology. It applies in industrieswhere successful entrepreneurial firms, or their technologies, are acquired by incumbents that thencommercialize the innovation. To this end we analyze an innovation game between one incumbent anda large number of entrants. In the first stage, firms compete to develop innovations of high quality. Theydo so by choosing, at equal cost, the success probability of their R&D approach, where a lower probabilityaccompanies higher value in case of success—that is, a more radical innovation. In the second stage,successful entrants bid to be acquired by the incumbent. We assume that entrants cannot survive ontheir own, so being acquired amounts to a prize in a contest. We identify an equilibrium in which the

cquisitionarkets for technologyame theory

incumbent performs the least radical project. Entrants pick pairwise different projects; the bigger thenumber of entrants, the more radical the most radical project. Generally, entrants tend to choose moreradical R&D approaches and generate the highest value innovation in case of success. We illustrate ourtheoretical findings by a qualitative empirical study of the Electronic Design Automation industry, andderive implications for research and management.

. Introduction

What is the division of labor in the production of innovationsmong large established firms and small entrepreneurial ventures?his fundamental question has attracted the interest of scholars andolicy makers alike, and has spawned a broad literature going backo Schumpeter (1912) and as far as Say (1827). While the evidences somewhat mixed, the overall picture is that incumbent firmsevelop most of the incremental innovations but that entrants playn important role in the creation of breakthroughs (e.g., Scherer

Please cite this article in press as: Henkel, J., et al., And the winner is—AcRes. Policy (2014), http://dx.doi.org/10.1016/j.respol.2014.09.004

nd Ross, 1990; Van Praag and Versloot, 2007). Baumol (2010, p. 25)xplains this as the result of a process where “[T]he giant companiesay account for the major share of the economy’s R&D financing,

∗ Corresponding author at: Technische Universität München, TUM School of Man-gement, Arcisstr. 21, 80333 Munich, Germany. Tel.: +49 89 289 25741;ax: +49 89 28925742.

E-mail addresses: [email protected] (J. Henkel), [email protected] (T. Rønde),[email protected] (M. Wagner).1 Tel.: +45 3815 2573.2 Tel.: +49 931 318 9046.

ttp://dx.doi.org/10.1016/j.respol.2014.09.004048-7333/© 2014 Elsevier B.V. All rights reserved.

© 2014 Elsevier B.V. All rights reserved.

but these better established firms tend to minimize risk by special-izing in incrementally improving the most promising of the radicalinnovations they purchase, license or adapt from the smaller firmsthat created them.”

Early theoretical studies point out that incumbents have weakerincentives than start-ups to invest in R&D in situations where theywould replace their own products (Arrow, 1962) but that theyhave stronger incentives to invest if their market power is threat-ened by entry (Gilbert and Newbury, 1982; Reinganum, 1983).However, there is an important distinction with respect to howthe innovations of start-ups are commercialized. The abovemen-tioned models assume that start-ups enter the product marketand compete with incumbents. Yet, as Baumol (2010) pointsout, a cooperative agreement between an entrant and an incum-bent regarding commercialization, in general should be superiorboth because of increased market power and because entrantstypically lack the broad resource bases of incumbents. Reflect-

quired. Entrepreneurship as a contest yielding radical innovations.

ing this point, some more recent theoretical studies allow fora successful entrant to be acquired by (or to license its inven-tion to) an incumbent (Gans and Stern, 2000; Kleer and Wagner,2013).

dx.doi.org/10.1016/j.respol.2014.09.004


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shadow of acquisition (or, technology licensing) was first analyzedtheoretically by Gans and Stern (2000). They modeled in detailthe negotiations between an incumbent and an entrant over an

ARTICLEESPOL-3052; No. of Pages 16

J. Henkel et al. / Resear

Our paper contributes to this stream of literature. However,ur approach differs in two respects from earlier work. First, weote that in many industries the number of start-ups seeking toe acquired is, for each technological innovation, higher than theumber of start-ups that eventually succeed. In such a market,tart-ups compete to be acquired. Second, with the notable excep-ion of Färnstrand Damsgaard et al. (2009), the previous studieshoose innovation effort—i.e., budget spent—as the players’ choiceariable. However, selecting an R&D project is often a question ofhich path to follow rather than how much to invest. As an illus-

ration, consider Vertex Pharmaceuticals (Pisano et al., 2006). With given R&D budget, the biotech firm had to pick two from fourromising drug candidates, each characterized by its own successrobability, and value in case of success. In addition, the typically

imited financial resources of entrants make it unlikely that theyould achieve more radical innovations by outspending incum-ents. Furthermore, in many industries—among them software andiotechnology—capital requirements in the early phases of R&Drojects are modest, and so budget spent is not the most relevant

ever for innovation radicalness. It is thus a plausible assumptionhat entrants distinguish themselves from incumbents by choosing

ore “radical” R&D approaches with lower success probability andoncomitant higher value in case of success.

In our model, we consider an industry consisting of one incum-ent and N entrants. The firms conduct R&D with the aim ofeveloping an innovation at a fixed cost normalized to zero. Onlyhe incumbent can commercialize an innovation, so the entrants’oal is to be acquired. The firms’ choice variable is the successrobability of their R&D projects, with projects with lower suc-ess probability having a higher value in case of success. All firmsave access to the same R&D possibilities, described by a function

inking the project’s value in case of success to its success proba-ility. In the first stage of the game, firms select their projects; inhe second stage, after the outcomes of the projects are realized,uccessful entrants compete to be acquired by the incumbent.

The main results of our analysis are the following. There alwaysxists an equilibrium in which all entrants choose more radical R&Drojects than the incumbent—i.e., projects with lower success prob-bility, and in case of success, higher value. In this equilibrium, allntrants choose pairwise different strategies; competition betweenntrants drives the “radicalness” of their innovation in the sensehat a larger number of entrants leads to an increase in the valuen case of success of the most radical innovation project. In turn,o equilibrium exists in which the incumbent chooses the mostadical project. Furthermore, for a specific value function and N ≤ 3e show that the equilibrium in which the incumbent chooses the

east radical project is unique. We show that our key results areobust to changes in the timing of the R&D decisions, the distri-ution of bargaining power in the market for acquisitions, and the

ntroduction of more incumbents. We thus obtain the rather robustesult that, overall, entrants pursue more radical innovations thanhe incumbent. The economic intuition behind this result is relatedo the value of having the second best technology. The incumbentenefits from its technology both when it is best (and it is usedo produce) and when it is second best (and it is used to reducehe price paid for the best technology). Therefore, the incumbentas an incentive to pursue a more incremental technology with aigher success probability than an entrant who only benefits from

ts technology when it is the best one and is acquired.We illustrate this, using a qualitative empirical study of the elec-

ronic design automation (EDA) industry to support our analysis.his industry, which develops software tools for the automated


esign of computer chips, consists of three large incumbentsnd numerous start-ups. It features those characteristics that wessume in our model—start-ups that compete in R&D with eachther and with incumbents, and that need to be acquired if they

PRESScy xxx (2014) xxx–xxx

are successful—and shows outcomes that are predicted by our the-oretical analysis, in particular, start-ups that go for R&D projectswith lower success probability and higher value in case of success.Also in other industries we observe acquisitions that are consistentwith the predictions of our model. The business press reports thatbiotech firm Gilead acquired Pharmasset since the latter had a bet-ter therapeutic concept against Hepatitis C virus (Bloomberg, 2011),and that Bristol-Myers Squibb acquired Inhibitex in the same mar-ket in order to improve its own offering (Wall Street Journal, 2012).We will discuss the applicability of our results to other industry inmore detail in the concluding section.

Our results that entrants originate more radical innovationsseem in line with the literature. Yet, they are based on a funda-mentally different mechanism than the findings in earlier studies:essentially, on the existence of a market for technology (e.g. Aroraet al., 2001; Arora and Gambardella, 1994; Gans and Stern, 2003;Lamoreaux and Sokoloff, 1999) between entrants and incumbents.In our model, the fact that entrants produce more radical innova-tions derives from the assumptions that (a) firms choose innovationprojects characterized by success probability (rather than effort orinvestment), and (b) entrants, if successful, need to be acquired inorder to commercialize their innovations. The incumbent neithercannibalizes its own product when innovating nor does it protect anexisting market. Our model also makes predictions that differ fromthose of established models—in particular, that entrants choosepairwise distinct strategies and that the expected value of the mostsuccessful innovation increases with the number of entrants. Moregenerally, our approach suggests that the existence of a market fortechnology—whether technologies or entire firms are traded in thismarket—plays an important role in explaining the stylized facts inthe innovation and entrepreneurship literatures.

The remainder of the paper is structured as follows. In thefollowing section, we review the relevant literature. In Sections3–5 we introduce and analyze the model, and perform robustnesschecks and extensions. Section 6 provides a qualitative empiricalstudy of the EDA industry to illustrate our analysis. In Section 7 wesummarize and discuss our findings and conclude the paper.

2. Literature review

There is broad evidence from a number of high-technologyindustries that acquisitions of small, innovative target firmsfrequently pursue the goal of gaining technology access and of pre-empting technology competition (Hall, 1990; Lerner and Merges,1998; Bloningen and Taylor, 2000; Lehto and Lehtoranta, 2006;Grimpe and Hussinger, 2008, 2009).3 In line with our analysis,Granstrand and Sjolander (1990) show that start-up innovationsare more radical than those of incumbents, and they suggest adivision of scientific labor between entrants and incumbents thatestablishes their roles as targets and acquirers. This view is sup-ported by Lindholm (1996), who shows that small firms take activesteps to increase their odds of being acquired. A weak positionin complementary assets on the side of the entrant increases thegains from trade of technology, and well-established intellectualproperty rights and involvement of professional intermediaries arefound to increase the likelihood that these gains are realized byentrant and incumbent (Gans et al., 2002; Hsu, 2006).

R&D competition between entrants and incumbents in the


3 It should be noted, though, that Desyllas and Hughes (2008) attribute less impor-tance to innovation-related variables, finding that from a target perspective theycontribute little to explaining acquisition by a large firm.


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(i) If two or more entrants have higher realized R&D values thanthe incumbent, then the incumbent acquires the entrant with the

5 When the incumbent negotiates with the most successful entrant, its threatpoint, or (maximum) willingness to pay, is the difference in value between the bestand the second best projects. This is also the negotiable surplus since the entrant’s(minimum) willingness to receive is zero. Our approach to modeling the negotiation



nnovation and showed how the acquisition price depends cruciallyn the strength of intellectual property protection and on the pos-ibility of the entrant to enter the product market. This, in turn,etermines the two firms’ payoffs from and incentives to conduct&D. Kleer and Wagner (2013) model competition between smallnd large firms for an exclusive patent, assuming R&D efficiencydvantages for small firms and exploitation advantages for largerms. Among other things they derive, and confirm empirically,hat acquisitions increase overall innovation output. Also Phillipsnd Zhadnov (2013) assume differences between small and largerms with respect to their costs of production and of R&D. Firmsave the binary choice to conduct R&D or not. The authors find thatoth small and large firms attempt to innovate when acquisition isossible; however, with increasing size firms may find it preferableo buy successful small innovators. Compared to these studies, weocus less on the subtleties involved in technology bargaining andssume a simple, competitive market for technology. This allows uso set up a tractable model where the type of R&D project chosen byhe incumbent and multiple entrants can be analyzed, and whereompetition between entrants affects their choices of strategy.

Our paper is related also to the well-established literature thattudies the choice of the “risk-return” profile of R&D projects, eithern terms of the success probability, the variance in the return, orhe correlation to competitors’ R&D projects. This approach has, forxample, been used to study the clustering of firms in geographicalnd product space (Gerlach et al., 2005, 2009), the efficiency of theortfolio of R&D projects in a competitive market (Bhattacharyand Mookherjee, 1986; Dasgupta and Maskin, 1987), the optimalelection of R&D projects (Ali et al., 1993; Cabral, 1993), and the per-istence of market dominance (Cabral, 2002). Closest to our setup,ärnstrand Damsgaard et al. (2009) consider the choice of successrobability by an entrant and an incumbent firm. They show that ifhe entrant incurs a higher cost of commercializing an innovationhan the incumbent, then this induces the entrant to pursue a moreadical R&D project.

. The model

We consider an industry consisting of one incumbent firm (I)nd N ≥ 1 entrants. All firms conduct R&D with the aim to develop

product for a new market segment. Only the incumbent can mar-et an innovation, so the entrants’ goal is to be acquired by thencumbent.4 Firms choose an R&D project from a given set of combi-ations of success probabilities and values in the case of success. Toeep the analysis tractable and in line with our motivation, we focusn success probability as the only choice variable rather than alsoncluding the level of R&D investment. That is, costs are identicalor all firms and normalized to zero.

We assume that firm i (i = I, 1,. . ., N) chooses a project character-zed by a success probability pi from [0, 1]. The random variablesescribing success or failure of the N + 1 firms are independentlyistributed. A successful project results in an innovation of value(pi) if it is commercialized by the incumbent. If a project is not

uccessful, its value is zero. We call �(·) the “value function” andssume it is differentiable and strictly decreasing. Given that anyrm for a given p will prefer the project with the highest value

n case of success, the function �(·) can be interpreted as describ-ng the set of undominated projects. At this technological frontier,ower success probability implies higher rewards in case of success.


urthermore, we assume that (i) p�(p) is concave and (ii) p�(p)akes on a maximum at some p, p ∈ (0, 1). For a given set of suc-ess probabilities pI, p1,. . ., pN, let ˘ i denote player i’s expected

4 If not acquired by the incumbent, the entrants do not have the choice to enterhe market and compete with the incumbent as in Rasmusen (1988).

PRESScy xxx (2014) xxx–xxx 3

payoff. Notice that all firms are assumed to have the same R&Dpossibilities. Hence, if the incumbent and the entrant make differ-ent R&D choices, it is not due to intrinsic differences in their R&Dcapabilities. The expected value of the most valuable innovation,denoted by E[Vmax], is a function of the N + 1 success probabili-ties chosen by the incumbent and the entrants. We assume thatE[Vmax] is strictly concave such that there exists a unique combina-tion of success probabilities (modulo symmetry among the firms)maximizing E[Vmax].

We employ the value function of �(p) = 1 − p to illustrate ourresults. This function fulfills the requirements defined above, withp�(p) and E[Vmax] being concave, and p�(p) assuming its maximumat p = 0.5. For this specific case, we can furthermore prove severaluniqueness results that are elusive for the general case.

In the main analysis, we assume that all firms take their R&Ddecisions simultaneously. Upon choice of R&D decisions, Naturemoves and R&D outcomes are realized. In the final stage—Stage 2in the simultaneous game, Stage N + 2 in the sequential game—theincumbent may acquire an entrant. In the acquisition stage, theentrants simultaneously make price offers to the incumbent, whicheither uses its own project or accepts the best offer.5 Alternatively,the acquisition can be thought of as involving only the entrant’sinnovation, not the entire firm. To keep the model solvable, weassume that the acquisition happens in a single step, withoutstaged investments or toehold purchases. Finally—not modeledexplicitly—products are sold and profits in the market are realized.

4. Solving the model

In this section, we prove the existence of an equilibrium in whichthe incumbent picks the least radical project, and show that thisequilibrium is welfare optimal; and prove the non-existence ofequilibria in which the incumbent chooses the most radical project,and for the specific value function of �(p) = 1 − p show that theabove-mentioned equilibrium is unique. We proceed in three steps.We solve the game backwards by initially examining the acquisi-tion stage. Then, we turn to the R&D choices of the firms. We firstlook at a model with one incumbent and two entrants in order toillustrate the mechanisms of the model and to provide economicintuition for our results. Finally, we generalize our results to morethan two entrants.

4.1. The acquisition stage

The incumbent acquires a maximum of one entrant since it canuse the technology of only one of the entrants. We denote the valueof firm i’s realized R&D outcome by �i, �i ∈ {0, �(pi)}.

Lemma 1.


allocates all negotiation power to the entrant in the bilateral bargaining, in the sensethat it can capture the incumbent’s willingness to pay completely. Notice that thisdoes not imply that the incumbent is left with no gains from trade: if there is morethan one entrant, the competition among the entrants implies the incumbent canappropriate a surplus corresponding to the value of the second best project. Moregenerally, the allocation of bargaining power is less critical in our framework (as weshow formally in Section 5.2) since we do not study entrants’ nor incumbent’s R&Dinvestments (as, e.g., Gans and Stern, 2000)—which obviously are strongly affectedby the surplus sharing rule—but rather their choice of success probabilities.


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highest realized value (j) at a price of (�j − �k), where k is theentrant with the second-highest realized value.

(ii) If only one entrant (j) has a higher realized value than the incum-bent, then the incumbent acquires this entrant at a price of(�j − �I).

iii) If no entrant has a higher realized value than the incumbent, thenthe incumbent makes no acquisition.

roof. Follows from standard Bertrand competition logic.

.2. The R&D stage

.2.1. One incumbent and two entrantsWe start by looking at an industry with two entrants (N = 2).

ssuming without loss of generality that p2 ≤ p1 and using Lemma, the profit function of the incumbent is:

I(pI) =

⎧⎪⎨⎪⎩

p2p1�(p1) + p2(1 − p1)pI�(pI) + (1 − p2)p1pI�(pI) + (1

p2pI�(pI) + (1 − p2)pI�(pI) + p2(1 − pI)p1�(p1)

pI�(pI) + (1 − pI)p2p1�(p1)

If the realized values of the entrants’ technologies are higherhan the realized value of the incumbent’s technology (situationsepresented by summands containing the factor p2p1 in the abovequations), the entrants are competing to be acquired. Then, thencumbent acquires the entrant with the most valuable technol-gy (entrant 2, since we assume p2 ≤ p1) at a price that secures thencumbent a profit equal to the value of the other entrant’s technol-gy (i.e., �(p1)). In all other circumstances, the incumbent’s profitorresponds to the value of its own technology. This happens eitherecause the incumbent acquires the only entrant with a superiorechnology at a price that leaves the incumbent indifferent betweencquisition and no acquisition, or because there is no entrant with

more valuable technology to acquire.An entrant only makes a profit if it has developed the technology

f the highest realized value. It follows from the analysis of thecquisition stage summarized in Lemma 1 that the expected profitf entrant i is Pr[Acquisition] · E[Acquisition price] where:

[Acquisition price]=�(pi)−E[Value of the second best technology

|i’s technology is best], (2)

r[Acquisition]

= pi · Pr[No technology of higher value than �(pi) exists]. (3)

The profit function of entrant i (shown for i = 1) requires dis-inguishing six cases depending on the relative sizes of p1, p2, andI:

1(p1) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

p1(1 − p2)(1 − pI)�(p1) + p1p2(�(p1) − �(p2)) + p1(1 −p1(1 − pI)(1 − p2)�(p1) + p1pI(�(p1) − �(pI)) + p1(1 −

(1 − p2)p1(1 − pI)�(p1) + (1 − p2)p1p2(�(p1) − �(pI))

(1 − p2)(1 − pI)p1�(p1)

(1 − pI)p1(1 − p2)�(p1) + (1 − pI)p1p2(�(p1) − �(p2))

(1 − p2)(1 − pI)p1�(p1)

We focus on an equilibrium in which p∗2 ≤ p∗

1 ≤ p∗I . The existence

f other equilibria is discussed below. Maximizing profits yields therst-order conditions (FOCs) characterizing the equilibrium:


∂˘I(pI)∂pI

= [p2(1 − p1) + (1 − p2)p1 + (1 − p2)(1 − p1)] · [�(pI)

+ pI�′(pI)] ⇒ FOC : �(p∗

I ) = −p∗I �′(p∗

I ) (5)


(1 − p1)p1�(pI) : p2 ≤ p1 ≤ pI

: p2 ≤ pI ≤ p1

: pI ≤ p2 ≤ p1

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I(�(p1) − �(pI)) : p1 ≤ p2 ≤ pI

(�(p1) − �(p2)) : p1 ≤ pI ≤ p2

: p2 ≤ p1 ≤ pI

: p2 ≤ pI ≤ p1

(4)

∂˘1(p1)∂p1

= [(1 − p2) + (1 − pI) + (1 − p2)pI] · [�(p1) + p1�′(p1)]

− (1 − p2)p1�(p1) ⇒ FOC : �(p∗1) = −p∗

I �(p∗I )

= −p∗1�′(p∗

1) (6)

∂˘2(p2)∂p2

= [(1−p1)+(1−pI)+p1+(1−p1)pI] · [�(p2) + p2�′(p2)]

− p1�(p1) − (1 − p1)p1�(pI) ⇒ FOC : �(p∗2) − (p∗

1�(p∗1)

+ (1 − p∗1)p∗

I �(p∗I )) = −p∗

2�′(p∗2) (7)

The left-hand side (LHS) of the incumbent’s first-order condi-tion (5) is the value of the own technology in case of success, whichcorresponds to the marginal benefit from increasing the successprobability (in circumstances where the value of the incumbent’sown technology determines its profit). The right-hand side (RHS)of the same equation represents the marginal cost (in the formof reduced technology value in case of success) of increasing thesuccess probability. The two first-order conditions (6) and (7) char-acterizing p∗

1 and p∗2 can be interpreted in a similar manner. The LHS

is the expected acquisition price, which is the marginal benefit fromincreasing the success probability conditional on an acquisition tak-ing place. The RHS is the reduction in the value of the technology,and thus in the acquisition price that constitutes the marginal costof increasing the success probability conditional on acquisition.6

Comparing the LHS of Eqs. (6) and (7) to that of (5) shows the addi-tional terms that reflect how the existence of a second successfultechnology weakens the respective entrant’s bargaining positionand pushes it to pursue riskier projects.

The first-order conditions can be solved recursively, and it fol-lows that p∗

2 < p∗1 < p∗

I = p. We prove below for the more generalcase of N entrants that these success probabilities constitute anequilibrium, which involves showing for each firm that the profitfunction has a global maximum at the equilibrium success prob-ability given the R&D choices of the other firms. Note that ourassumptions do not force the firms to pick differing R&D projects.Rather, this asymmetry arises endogenously.


6 The first-order condition for entrant 1, Eq. (6), has a parallel with the modelsby Färnstrand Damsgaard et al. (2009) and Haufler et al. (2012). In these models,[p�(p)]’, evaluated at p1, needs to be equal to an entry cost, while in our model itneeds to equal the expected value of the incumbent’s project. The latter can thus beinterpreted as a sort of entry hurdle.


ARTICLE ING ModelRESPOL-3052; No. of Pages 16

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Fig. 1. Firms’ payoffs when deviating from equilibrium, for N = 2 and �(p) = 1 − p.

As an illustration, consider the value function of �(p) = 1 − p.his function fulfills the requirements defined above, with p�(p)eing concave and assuming its maximum at p = 0.5. The equi-

ibrium actions for the incumbent and entrants are, respectively,∗I = 0.5, p∗

1 = 3/8 = 0.375, and p∗2 = 39/128 ≈ 0.305. Fig. 1 illus-

rates the firms’ payoffs as a function of their success probabilityiven the equilibrium choices of the other firms. Note that the pay-ff functions are kinked (but continuous) where the focal firm’success probability equals the (equilibrium) value of one of the two


ther firms (with the exception of ˘ I(p), which is differentiable at = p∗

2).7

7 The kinks in the entrants’ profit functions appear for the following reason: oncen entrant (1, say) chooses a higher success probability than the other entrant2), entrant 2 is no longer considered a competitor of entrant 1 at the acquisitiontage; an acquisition of 1 only occurs conditional on entrant 2 being unsuccessful.his increases the expected acquisition price, and thus, the marginal benefit fromncreasing the success probability conditional on acquisition. (The profit functions continuous where the focal entrant’s success probability equals the equilibriumuccess probability of one of the other firms, because the increase in the acqui-ition price is offset by a decrease in the acquisition probability.) The kink in thencumbent’s profit function at pI = p∗

1 is caused by a decrease in the marginal costf increasing the success probability as it becomes entrant 1’s technology, rather


In this equilibrium all entrants aim for more radical innova-tions than the incumbent. This finding is in line with observationsfrom the EDA industry as well as with established results in theliterature. Note, however, that it is not based on the cannibal-ization effect since the incumbent is not present initially in themarket segment considered. Instead, it derives from the fact thatthe incumbent but not the entrants, is able to market the innovationat hand. In particular, unlike the entrants, the incumbent also bene-fits from having the second most valuable technology in the marketbecause it improves its bargaining position when negotiating withthe entrant that developed the project of highest realized value. Theentrants, on the other hand, are in a different situation because theycan only make profits by being acquired if they have developed thehighest quality project. This creates a strong incentive for them topursue a project of high potential value but low success probabil-ity in order to have the most valuable technology. The equilibriumoutcome where the incumbent pursues a less radical project thanall entrants thus reflects the difference in the value of being secondbest in the market. A crucial assumption for this result is that therecan be competition in the market for acquisitions, a point we willelaborate upon in Section 5.1.

Another notable feature of the equilibrium is that the ex-antesymmetric entrants choose asymmetric success probabilities inequilibrium. By choosing a success probability that is sufficientlydifferent from the ones chosen by the other firms in the indus-try, an entrant avoids the risk of ending up in a situation where itfaces tough competition at the acquisition stage from a firm thatoffers a technology of the same, or a very similar value. Thus, dif-ferentiation in terms of success probability-return choices softenscompetition in much the same way as does differentiation in theproduct space; see Gerlach et al. (2009) for further discussion of thispoint.

Turning to the welfare properties of the equilibrium, considera hypothetical social planner who maximizes total welfare. Sincethe identity of the firm that develops the most valuable technol-ogy does not affect total welfare, the social planner maximizes theexpected value of the technology brought to the market (subject tothe condition p2 ≤ p1 ≤ pI):

MaxpIp1p2 {p2�(p2) + (1 − p2)p1�(p1) + (1 − p2)(1 − p1)pI�(pI)},(8)

which yields the first-order conditions (5)–(7). It followsimmediately that the firms’ equilibrium R&D choices are welfare-maximizing. Hence, in a market that fits our model assumptions,there is no market failure with respect to the type (i.e., success level)of innovation that firms pursue.8 The intuition behind this some-what surprising result is twofold. First, it is optimal from a welfarepoint of view to have a firm choosing p. This firm picks the technol-ogy with the highest expected value, providing a fall-back option incircumstances where the other, more ambitious R&D projects fail.In the equilibrium considered, this role is played by the incumbent.


Second, an entrant only makes a profit if it has the best technology,and its profit is the difference in value relative to the second besttechnology, see Eq. (2). This also corresponds to the incrementalsocial value of the project; i.e., the welfare lost if this technology did

than the incumbent’s own technology that determines the price at which entrant 2is acquired if all R&D projects are successful.

8 Regarding the number of firms that enter in a free-entry equilibrium, assuming afixed cost of entering, welfare optimality depends on the role played by the marginalentrant. If the marginal entrant is the one choosing the lowest success probability,its profit corresponds exactly to the social value that it creates. The equilibrium thenis also welfare maximizing in terms of the number of active firms. However, if theexpected profit of the marginal entrant is greater than this—e.g., equal to the averageprofit among the entrants—then the equilibrium is characterized by excessive entry.


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ot exist. Since the profit that an entrant earns from an R&D projects equal to the project’s social value, private and social incentivesre aligned. Therefore, the entrants make the welfare maximizing&D decisions. We discuss the robustness of this result in Section.4.

.2.2. One incumbent and N entrantsWe now turn to the case of N entrants. Since most results and

ntuitions carry over from N = 2, our focus here is on the addi-ional insights that the general analysis provides. All proofs are inppendix.

emma 2. There is no equilibrium in pure strategies in which two orore firms choose the same success probability.

Having established that firms play asymmetric strategies inquilibrium, we turn to the main analysis. First, re-label the N + 1rms in such a way that p0≥· · ·≥pN .

efinition 1. Set h0 = 0, and define {p0, . . ., pN} and {h1, . . ., hN+1}ecursively as follows:

k :=pk−1�(pk−1) + (1 − pk−1)hk−1 for k = 1, . . ., N + 1 (9)

(pk) + pk�′(pk):=hk for k = 0, . . ., N (10)

Notice that hk equals the expected value of the highest realizedalue among firms 0, 1,. . ., k − 1, and that social welfare is equal toN+1.

emma 3. The success probabilities {p0, . . ., pN} have the followingroperties:

(i) p = p0 > p1 > · · · > pN > 0;ii) {p0, . . ., pi}, i ≤ N, maximize the expected value of the best technol-

ogy among i + 1 R&D projects. In particular, {p0, . . ., pN} maximizesocial welfare.

We are now ready to present the main result of the theoreticalnalysis.

roposition 1.

(i) There exists an equilibrium in pure strategies in which firms makethe welfare maximizing R&D choices. Renumbering the entrants,the incumbent chooses p∗

I = p0 and entrant k chooses p∗k

= pk ,k = 1,. . .,N. This is the unique equilibrium (modulo symmetryamong the entrants) in which the incumbent chooses the highestsuccess probability.

(ii) For N ≥ k the equilibrium value of pk is independent of N.iii) Expected payoffs are highest for the incumbent. For the entrants,

they decrease with k. That is, ˘ I > ˘1 > · · · > ˘N.

Proposition 1 shows that the results obtained for N = 2 generallyold. There exist an equilibrium in which the incumbent chooses

higher success probability than all N entrants, where the firmshoose pair-wise different success probabilities, and where the R&Dhoices are welfare maximizing.

Proposition 1 allows for comparative statics with respect tohe number of entrants. Parts (i) and (ii) show that increasinghe number of entrants from N to N + 1 neither changes the R&Dhoice of the incumbent nor the R&D choices of entrants 1 to. However, a more radical R&D project with a lower successrobability is added by entrant N + 1 to the industry portfolio of&D projects. That is, increasing the number of entrants not only

eads to a higher probability that some innovator will succeed at


ll but also pushes the limit of the highest attainable innovationalue.

The finding that the incumbent does not change its R&D choicen the face of market entry contrasts in an interesting way with


the results in Gans and Stern (2000) showing that an incumbentbehaves differently (invests less) in the face of entry—anticipatingthe opportunity to acquire a successful entrant—from a monopolist.

As the competition among entrants intensifies, the entrants arepushed to pursue increasingly radical R&D projects to mitigatecompetition. Still, part (iii) of the proposition shows that these moreradical projects are less profitable in expectation. If there is a fixedcost, e.g., of doing R&D for the entrants, there would then be a limitto the number of firms that the market can support.

Proposition 1 is in line with the empirical observation thatentrants tend to pursue innovation projects with lower successprobability but higher value in case of success, than incumbents.This result would be moot if also equilibria with any other order ofsuccess probability levels existed, in particular with the incumbentchoosing the highest-risk project (p1 > · · · > pN > pI). The follow-ing proposition shows that the latter type of equilibrium can beexcluded.

Proposition 2. There is no equilibrium in pure strategies in whichthe incumbent chooses a project with lower success probability thanall entrants.

The logical next step would be to formulate and prove a propo-sition about the existence or non-existence of equilibria in whichthe incumbent chooses some intermediate risk level, that is, withp1 > · · · > pI > · · · > pN. We conjecture that no such equilibria existbut we cannot prove it in full generality. However, we can provethe statement for the specific value function introduced above,�(p) = 1 − p, and for the cases of N = 2, N = 3.

Proposition 3. Let the value function be given by �(p) = 1 − p.Then, (i) for N = 2 there is no equilibrium in pure strategies inwhich p1 > pI > p2. The unique equilibrium is characterized by pI = 0.5,p1 = 0.375, and p2 ≈ 0.305.

(ii) For N = 3 there is no equilibrium in pure strategies in whichp1 > pI > p2 > p3, and no equilibrium in which p1 > p2 > pI > p3. Theunique equilibrium is characterized by pI = 0.5, p1 = 0.375, p2 ≈ 0.305,and p3 ≈ 0.274.

Proposition 2 establishes, for the case of general �(p) and N,that in equilibrium the incumbent never chooses the highest-riskproject. For the specific case of �(p) = 1 − p and N ≤ 3, Proposition 3shows that the incumbent always chooses the project with lowestrisk. Overall thus, the mere definition of entrants as firms that needto be acquired in order to commercialize their innovation generatesthe result that entrants focus on riskier but in case of success, morevaluable or more radical projects.

5. Robustness checks and extensions

In this section, we consider different variations of the modelin order to explore the robustness of the results obtained and toidentify the key assumptions of the model. It is assumed throughoutthat N = 2.

5.1. The importance of competition in the market for acquisitions

The fact that the acquisition price of an entrant depends on thedifference in value from the second best technology is clearly essen-tial for our results since it drives both the entrants’ incentive tochoose a radical project to push up the acquisition price, and theincumbent’s incentive to choose a project with a high expectedvalue to minimize the acquisition price.


To illustrate the importance of this assumption, consider asimple variation of the model where the successful firms areequally likely to be granted an exclusive patent that preventsthe other firms from marketing their technologies. This removes


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ompetition at the acquisition stage as maximally one technologyan be marketed.

Using Lemma 1, the expected profit of firm i can then be writtens:

i(pi) = pi

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(11)

here i, j, k ∈ {I, 1, 2} and i /= j /= k. It follows immediately that therexists a unique and symmetric equilibrium in pure strategies inhich p∗

I = p∗1 = p∗

2 = p. Unlike the traditional patent race litera-ure that envisions firms competing for one patent, our results relyhus on the assumption that competing technologies can co-existnd compete in the market. In many instances, this assumption islearly more plausible than that of the patent race winner obtain-ng a monopoly. Certainly in complex technology industries suchs ICT and mechanical engineering it is generally relatively simpleo invent around a patent. And even in discrete technologies suchs drugs and chemicals the scope of patents is often too narrowo allow an innovator excluding competing technologies (see, e.g.,ternitzke, 2013). More generally, our results point to the beneficialelfare effects of technology competition on ex-ante R&D choices,hich provide an additional argument for optimal patents beingarrow but sufficiently long-lived to provide firms with incentiveso do R&D (Gilbert and Shapiro, 1990).

.2. Generalized bargaining game

Consider a bargaining game at the acquisition stage where aake-it-or-leave-it offer is made, with probability b, by the incum-ent rather than the entrants. Notice that this bargaining gamencompasses the one considered in our main model as a specialase (b = 0) but allows for a more equal distribution of bargainingower between the incumbent and the entrants.

roposition 4. Suppose, for N = 2, that the incumbent makes a take-t-or-leave-it offer to the entrants with probability b, 0 ≤ b ≤ 1, and thentrants make competing offers to the incumbent with the complemen-ary probability. Then, there exists an equilibrium in pure strategies inhich the success probabilities chosen by the firms are identical to

hose described in Proposition 1.

Proposition 4 confirms that the different R&D choices of incum-ent and entrants are driven by the difference in the value of havinghe second best technology rather than the specific form of theargaining game.

.3. Two incumbents and one entrant

In our main model, there is one incumbent that controls accesso the market. The following proposition shows that our qualita-ive results are robust to an increase in the number of firms withccess to the market. We will refer to firms with market access asincumbents” but these could equally well be firms that are active


n a neighboring market and that face a negligible entry cost. Hence,he analysis can be thought of as a comparative static exercise inhich the (infinite) entry costs of the two entrants are removed

uccessively.The setup is as follows. First, all firms choose the success prob-

bility of their R&D project. After the R&D outcomes are realized,he incumbents compete to acquire the entrant (if an entrant existsnd is successful). Finally, the incumbents compete in the product


market.9 The incumbent in possession of the best technologyafter the acquisition stage earns profit equal to the difference invalue between the best and the second best technology. All otherincumbents earn zero profits.

Proposition 5. Suppose that there are two incumbents and oneentrant. Then, there exists a unique equilibrium in pure strategiesin which the firms choose the success probabilities described inProposition 1. In this equilibrium, the entrant chooses the lowest suc-cess probability (p2) and the incumbents choose the higher successprobabilities (p0 and p1).

When there are two incumbents, the incumbents choose differ-ent success probabilities in equilibrium in order to avoid competingall profits away, either in the product market (if the entrant isunsuccessful) or in the acquisition market (if the entrant is suc-cessful). More importantly, Proposition 5 shows that the entrantchooses a more radical project than the incumbents. This againreflects the value to the incumbents of having the second best tech-nology which induces them to go for less radical projects than theentrant who needs to have the best technology to make a profit.Notice also that our results are slightly stronger in the case of twoincumbents and one entrant because we are able to show unique-ness of the equilibrium for the general function �(p).

Finally, it can be shown that if all three firms are incumbents,the only equilibrium in pure strategies is one where the firms playp0, p1, and p2. The incentive of the firms to differentiate themselvesin terms of success probability-return thus exists independent ofhow many firms have market access. However, our analysis showsthat if there are entrants without direct market access, these tendto be the ones pursuing the more radical innovation projects inequilibrium.

5.4. Sequential moves

Real-world R&D decisions are often best modeled as simul-taneous moves as above, since it is plausible that firms have tomake irreversible R&D decisions before observing their competi-tors’ choices. Notwithstanding this, there may exist situationsin which firms discover market opportunities at rather differentpoints in time such that the R&D choices of early movers becomeobservable to followers before the latter make their own R&D deci-sions. In analyzing the sequential-move game, we restrict ourselvesto N = 2. First, we analyze a game where the incumbent moves first,then entrant 1, and finally entrant 2. A general value function isassumed here. Afterward, we consider all possible orders of movesfor the value function �(p) = 1 − p. All proofs of the results in thissubsection are available from the authors upon request.

Turning to the first part of the analysis, the following lemmadescribes the equilibria of the subgames starting after the incum-bent has chosen its success probability.

Lemma 4. Consider the Nash equilibria of the subgames starting afterthe incumbent has chosen pI. Then, (i) entrant 1 chooses the successprobability that maximizes the welfare resulting from the innovationsof the incumbent and of entrant 1 conditional on pI; (ii) entrant 2chooses the success probability that maximizes the welfare resultingfrom the innovations of all firms conditional on pI and p1.

The profit of entrant 2 coincides with the social value of its


innovation, as discussed above, which leads it to take the welfaremaximizing R&D decision. Entrant 1 has to consider the reaction ofentrant 2 when deciding on its R&D project. It is optimal for entrant

9 The assumption that the incumbents do not acquire each other can be justifiedby the presence of an antitrust authority that prohibits mergers and acquisitionsthat serve only to reduce competition and do not bring efficiency gains.


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than an entrant who only benefits from its technology when it isthe best.

The results in Propositions 1 and 7 contrast in an inter-esting way, and illustrate the challenges involved in testing

10 For each order of moves, we numerically determine the approximate equilib-rium values with eight different sets of starting values. In the first set, each variablevaries between 0.01 and 0.99; in the later sets, these intervals are successivelyreduced in order to zoom in on the equilibrium values, with interval widths of1.5e−6 in the final set. For each set, each of the three variables (p1, p2, pI) takes on1000 equidistant values. The inner loop of the 109 iterations per set yields the bestresponse of the last mover to the choices made by the first and the second movers;the middle loop, the best response of the second mover to the choice made by thefirst mover, taking the last mover’s reaction into account; and the outer loop, the



to choose a profitable R&D project with high success probabil-ty, and it foresees that entrant 2 will choose a more radical R&Droject with lower success probability. Hence, entrant 1 will onlyake a profit if entrant 2 fails. Ideally, entrant 1 would like to pick

project that maximizes entrant 1’s expected profit when entrant fails, and that minimizes the success probability that entrant 2hooses. It turns out that there is no conflict between these twobjectives. By choosing the welfare maximizing success probabil-ty conditional on pI, entrant 1 maximizes its expected profit whenntrant 2 fails and maximizes the competitive pressure that entrant

experiences, thereby pushing entrant 2 to choose a more radical&D project with a low success probability.

We define the success probabilities p1 and p2 by p1�′(p1) +(p1) = pI�(pI) and p2�′(p2) + �(p2) = p1�(p1) + (1 − p1)pI�(pI),

espectively. Furthermore, we define pI implicitly by pI�(pI) +1 − pI)p�(p) = p1�(p1) + (1 − p1)pI�(pI). With these definitions,e can put down:

roposition 6. The equilibrium success probabilities of theequential-move game with the order of moves given by I, 1, 2 coincideith those of the simultaneous-move game if the following conditionolds for all pI ≤ pI :

d2(p�(p))dp2

∣∣∣∣p=p2

≤ − (1 − p1)(�(p1) − pI�(pI))1 − p2

.

Expressed verbally, the condition requires that the function�(p) is sufficiently concave. For �(p) = 1 − p, e.g., it is fulfilled.he intuition behind Proposition 6 is the following. When choos-ng the success probability of its R&D project, the incumbent faces

trade-off. On the positive side, pI = p maximizes the expectedrofit of the incumbent when one or none of the entrants suc-eeds in developing an innovation because in these circumstanceshe incumbent earns pI�(pI). At the same time, however, pI =

˜ maximizes the competitive pressure that the entrants face,nd so minimizes the best response success probabilities of thentrants as well as the surplus that the incumbent can extractrom the entrants’ R&D activities. For both (counteracting) effects,he first-order condition is fulfilled at pI = p. One can show that,f the condition in Proposition 6 is fulfilled, the direct effect ofI on the value of the incumbent’s R&D project dominates thendirect effect on the entrants’ R&D choices, such that the solu-ion pI = p to the first-order condition indeed corresponds to a

aximum.In the derivation of Proposition 6, we have assumed that the

layers are forward looking, following the logic of subgame perfec-ion. Due to the recursive construction of the Nash equilibrium ofhe simultaneous-move game, myopic firms (i.e., firms that do notonsider the effect of their choice on firms moving later in the game)ould choose the same success probabilities in the sequential-ove game as when moves are simultaneous. Furthermore, one

an show that also for a game in which the incumbent movesrst and then all entrants move simultaneously Proposition 6olds.

For the case that not the incumbent but one of the entrantsoves first, one might expect that this firm moves closer to p

which maximizes the expected project value). It might even pick aess radical project than the incumbent. Surprisingly, however, thisoes not seem to be the case. For N = 1 and a general profit function,he incumbent picks p irrespective of the order of moves since itsxpected profit, pI·�(pI), is independent of p1. Hence, the entrant


ill pick its best response to pI = p even if it moves first. While general proof is elusive, numerical simulations for �(p) = 1 − p,

= 2, show robustness of the simultaneous-move outcome whenlayers move sequentially:


Numerical Result 1. Let the value function be given by �(p) = 1 − pand let N = 2. Then, the players’ equilibrium actions in a sequen-tial game are identical to those in the simultaneous-move game,irrespective of the order of moves. That is, pI = 0.5, p1 = 3/8 = 0.375,p2 = 39/128 = 0.3046875.

Within the numerical precision of 1e−8, the values of pI, p1,and p2 that were determined in the respective final round ofiterations are identical to those stated in Numerical Result 1, nomatter whether the incumbent moves second or third (the case ofI moving first is covered by Proposition 6).10

Notice that the analyses in this subsection point to a first-mover advantage for entrants. Given that the firms pick thesame R&D projects as in the simultaneous-move game, Proposi-tion 1 shows that entrant 1 earns higher expected profits thanentrant 2.

5.5. R&D investment as the decision variable

The choice variable that has been most frequently used inanalyses of R&D competition is R&D investment. For the pur-pose of comparison, let us consider a variant of the model whereR&D investment rather than R&D success probability is the choicevariable.

In order to formalize this notion, we assume that firm i choosesan R&D intensity �i, which results in an innovation of value �(�i)and 0 with probability p(�i) and 1 − p(�i), respectively, i = 1, 2, I. Thecorresponding R&D cost is represented by an increasing and con-vex function c(�i). Additional R&D investment increases the successprobability and/or the value of an innovation. That is, p′(�i) ≥ 0 and�′(�i) ≥ 0 with at least one strict inequality (notice that firms can-not trade off success probability against value). We make a fewadditional concavity assumptions, which are specified in the proofof Proposition 7.

Proposition 7. Suppose that the firms choose the level of R&D invest-ment. Then, there exists a unique equilibrium in pure strategies inwhich the firms choose pairwise different investment levels and inwhich the incumbent invests more than the entrants.

In industries in which the key choice variable is R&D invest-ment, our model thus predicts that the most valuable technologiescome from incumbent firms. The incumbent invests more than theentrants, which translates into a higher success rate and a morevaluable technology in case of success.11 The reason why no equi-librium exists in which an entrant invests more than the incumbentis again related to the value of having the second best technology:Since the incumbent benefits from its technology both when it isbest and second best, it has a stronger incentive to invest in R&D


first mover’s best strategy, taking the other players’ reactions into account. A detailedaccount of the numerical analysis is available from the authors upon request.

11 More precisely, it translates into a success rate and a technology value in caseof success, that are at least as good as those of the entrants, and where at least one(success rate, technology value) is strictly better than those of the entrants.


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mpirically whether incumbents or entrants conduct the mostadical R&D. Indeed, our analysis shows that the answer tohis question may depend on something as subtle as the key&D decision variable in the industry (more generally, on the

nterplay among R&D investment, success probability, and pos-ibly further choice variables) and that not controlling for thisariable may bias results. Regarding welfare, one can showhat the investment choices are welfare maximizing if andnly if investment into R&D only increases the value of theechnology (but not the success probability). In general, how-ver, the incumbent puts greater weight on its own technologyhan would a hypothetical social planner because it is notble to appropriate the full value of the entrants’ technolo-ies. This results in an equilibrium where the incumbent investsoo much and the entrants invest too little from a welfareerspective.

. Innovation and acquisition in the EDA industry

.1. Industry background

The EDA industry is a sub-segment of the semiconductorndustry, providing tools that support the (automated) design ofntegrated circuits.12 Historically hardware-based, involving ded-cated workstations for computer-aided design, it evolved into aoftware-based industry in the 1980s. EDA firms provide a largeet of tools to aid chip designers in transforming an abstract logi-al representation of an integrated circuit into a structure that cane manufactured physically. These tools cover a complex processrom chip design to testing. It can be subdivided into a numberf subprocesses, each focused on one special aspect of design andesign testing. The EDA industry is characterized by high indus-ry concentration, with 68% of the 2009 revenues being generatedy the three largest firms (Solid State Technology, 2010), and by

larger number of small firms entering the industry yearly whichltimately are either acquired by one of three large incumbentsr go out of business. The number of start-ups and young firmsas risen continuously, to over 400 firms in 2005 (Desai, 2005;

Suppli, 2010; Solid State Technology, 2010). Industry turnover wasore than $4 billion (bn) in 2009 (compare the total revenue of

hip manufacturers of $230 bn). The industry grew on average 3%ear on year until 2006 when growth slowed somewhat, leadingo a decline of 4.5% from 2008 to 2009 (Solid State Technology,010).

.2. Interviews

Our qualitative empirical study is based on semi-structurednterviews with industry experts and the larger EDA companies.his approach has been applied in similar exploratory researchettings and is also advocated methodologically (e.g., Miles anduberman, 1994). Through our interviews, we study whether or not

tart-ups, in particular those that are later acquired by large incum-ent firms, pursue more radical innovations than incumbents.he questions in the interview guideline are derived partly fromhe extant literature (Henderson, 1993; Christensen and Bower,996) and partly from our own knowledge of the industry and thehenomenon under study. In the interviews, we put a particularmphasis on entrants’ and incumbents’ relative innovation perfor-


ance, the drivers of performance differentials, facts and figuresegarding acquisitions of entrants by incumbents, and the reasonsor these acquisitions, in particular those related to innovation.

12 A brief description of innovation in the EDA industry is also contained in Kleernd Wagner (2013).


The interview guideline was adjusted as the research progressedin order to maximize the insights gained from succeeding inter-views. From December 2005 to January 2008, eight interviews (10interviewees) were carried out with senior professionals and sci-entists with detailed knowledge of the EDA industry. The list ofinterviewees comprises representatives from the two largest andsome smaller EDA firms, industry consultants, and academics fromAmerica and Europe. Each interview lasted between 30 min and2 h. Three interviews were conducted over the phone or by email,the remainder were face to face. Interviews were subsequentlytranscribed and the written material was then analyzed. Two inter-views were conducted in German, so interview quotes have beentranslated into English.13

6.3. Drivers of innovation in the EDA industry

In the EDA industry, new requirements for innovation andimprovement of technological products emerge on a regular basis.This need, identified from the interviews, is driven by two essentialfactors: the International Technology Roadmap for Semiconductors(ITRS) and the cumulative nature of technological change, pairedwith the highly cyclical nature of the semiconductor industry(Levy, 1994). For example, during the most severe downturn in2000–2001, R&D expenditure in the industry dropped significantlyand has still not fully recovered. Semiconductor firms tried tomitigate this reduction by putting heavy pressure on suppliers,including those of EDA tools, to innovate in order to reduce cost. Asa first stylized fact of the analysis, we note the continuously increas-ing requirements for EDA tools, and hence permanent demand forinnovation in the EDA industry.

6.4. Sources of innovation in the EDA industry

Each emerging innovation need in the EDA industry is usu-ally addressed by several start-ups and the incumbents, which inparallel try to develop a solution to these needs. However, as welearned from our interviews, the incumbents often fail to addressthese needs in a systematic manner, as illustrated by the follow-ing statement: “An example here is in logic simulation. Synopsys,Cadence, and Mentor [the three largest firms in the EDA industry] allacquired their current generation of simulators to replace their existingproducts. In all cases, smaller companies came up with better algo-rithms that made their simulators significantly faster than those of thelarge companies. In all cases, the larger companies tried to compete bycreating new simulators themselves prior to making their respectiveacquisitions, but failed.” Hence, with incumbents failing to innovatesuccessfully, opportunities emerge for start-ups with better per-forming products. According to our interviewees, and illustratedby the above quote, these start-ups are frequently acquired by thelarger incumbents. Such acquisitions, in turn, may trigger height-ened acquisition efforts by competing incumbents in order to catchup.

As we argue below, the relative success of start-ups comparedto incumbents derives partly from the fact that, unconstrainedby existing customers and existing products, start-ups are free topursue more radical innovations. This freedom attracts talentedengineers, which in turn further increases the odds of start-upsto prevail in the competition with incumbents: “It usually remains


logical difference. While these people certainly can be hired by largeEDA companies . . . these people . . . go and start a new company. This

13 Further details of each interview (date, duration, interviewee’s function, typeof organization employing the interviewee) are available from the authors uponrequest.


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tarves the larger company of the knowledge and talent while pro-oting the potential success of the new venture.” This observation

s in line with the work of Holmström (1989) who argues largerms introduce control and bureaucracy to minimize the cost of

ncentivizing production activities but in the process screen outore entrepreneurial individuals. As a stylized fact, we note that

oth, entrants and incumbents innovate but that incumbents oftenail to develop a solution of satisfactory quality—or any solution atll—and in this case usually acquire start-ups.

.5. Type of innovation pursued

It emerges from the interviews that entrants generally chooseiskier innovation projects. Interviewees suggested a number ofeasons for this. These in part relate to the obstacles identified in theiterature on disruptive innovation (Christensen and Bower, 1996;hristensen, 1997), namely, that incumbents often are forced to

ocus on large existing customers: “So they [large incumbents] areelying on start-ups, which then are starting from scratch . . . so theyan apply very new methodology with very new techniques withouteing restrained by all [existing] customers or all the methodology.”

At the same time, the nexus of new knowledge in the indus-ry often resides in the small start-ups, as the following statementlearly shows: “The current way is that the know-how, the innovationn terms of software, is mostly generated in small firms. . . The share ofmployees who in the larger EDA firms are really innovative should bemall.”

Fitting with these statements is the observation that largencumbents generally have a weak track record of developing newechnologies in-house but are rather successful at further devel-pment of an existing project, i.e., at carrying out incrementalnnovation. On closer inspection, it is clear that not only does muchf the innovation in the EDA industry emerge out of start-ups butlso that in terms of quality, small firms pursue more radical inno-ation projects—a characteristic that is negatively correlated to theevel of probability of project success. This was confirmed by sev-ral interviewees, stating, e.g., “. . . but there [in small firms] . . . haso be a radical core, I would say, otherwise it is not possible” and “. . .he radical stuff is always done by the start-ups.” Hence as a stylizedact, entrants pursue more radical innovation projects than incum-ents, i.e. they pursue innovation projects that are both more likelyo fail, and in case of success, are more valuable than those pursuedy incumbents.

.6. The fate of entrants in the EDA industry

The increasingly complex combination of different tools usedor chip design (the “design flow”) makes it increasingly likelyhat entrants will be acquired and will become integrated intohe design flow of one of the three large vendors, as succinctlyescribed by one interviewee: “It [acquisition] is getting more com-on because the tools are getting more complex. . . . You need more

f a ‘solution’ nowadays. You can’t just come out with one point tool,


ou need to come out and have at least a solution to a subsegment ofhe problem.”14

Hence, it seems that entrants can succeed in the long run onlyf they are acquired. Our interviews support this conjecture, indi-ating that if acquisitions are not the only way to survival, they

14 A start-up’s innovation constituting a particular tool in the design flow is com-lementary to the existing other tools in this flow offered by incumbents. However,e found no indication of a complementary interaction between an incumbent’s

nd a start-up’s innovations. It is the substitutive relationship between innovationsor the same type of tool that matters.


certainly are the most prevalent. This is partly because beingacquired is financially attractive to start-ups since initial publicofferings (IPOs) are less predictable, and also venture capital-ists aiming for a profitable exit always consider the option of atrade sale. Several interviewees confirmed this view, stating that“for most of these small companies’ the dream is to be bought bysomebody big” and “the success path is to be acquired by a bigcompany.”

Next to these push factors, a number of pull factors were alsoidentified in the interviews. One interviewee pointed to the impor-tant role of complementary assets such as a strong internationalsales force: “. . . with their sales network which of course then [afteracquisition] explodes compared with the small firm, because they[large incumbents] are already everywhere in Asia, Europe, and else-where and they get just another product to sell. And they get worldwidesales support when they need it. . . . They [small firms] eventually breakdown because of a lacking sales network and demand for applicationservices which they cannot provide anymore with their own humanresources.” Even more to the point, one entrepreneur stated: “Thegoal is always to be acquired. [. . .] The more successful we are, themore urgent it becomes to be acquired.”

One interviewee described how incumbents exploit the inno-vative activity of start-ups, in his statement capturing the centralmessage of our model: “The vast majority of start-ups in EDA fail,as they do in most industries. In some sense, this encourages bigcompanies to only look outside to acquire new technologies—it’scheaper to let the cash efficient start-ups figure out how to design theproduct and build the market, suffering real failures in many cases,than it is to do it inside the large company.” In sum, we can putdown as a stylized fact that a large share of successful entrantsin the industry are—and almost always need to be—acquired,and that incumbents rely to some extent on this source of newtechnology.

Summarizing, the EDA industry fits both the assumptions madein our model and the key predictions derived from it, ratherwell. While there are several factors that influence the firms’ R&Dstrategies, the fact that incumbents “are relying on start-ups” andon the possibility of acquisition clearly contributes to makingentrants the predominant source of radical innovations in the EDAindustry.

7. Discussion and conclusion

New entrants to a market are characterized by various fea-tures, among them organizational flexibility, lack of establishedcustomer relationships, and the absence of existing products. Allthese features contribute to explaining why innovations, in par-ticular radical innovations, are more likely to come from start-upsthan from incumbents. Yet, one important explanation for this ismissing from this list. Defining entrants solely as firms that need tobe acquired in order to commercialize their innovations, our modelgenerates—based on a different mechanism to earlier studies—thefamiliar result that entrants are more likely to produce radicalinnovations. Essentially, the existence of a market for technologybetween entrants and incumbents drives the former to pursue rad-ical innovations. More precisely, since firms are modeled to choosenot research investment but rather the success probability of theirinnovation project, we find that the incumbent aims at more cer-tain innovations of lower value, while entrants pursue projects thatare less likely to succeed but which, in case of success, will bemore valuable. Furthermore, the higher the number of start-ups


and the stronger the competition among them, the more valuablethe most radical project pursued. Also, entrants pick projects withpairwise different success probabilities—a prediction of our modelthat differs from those of existing ones.


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hritcteiieeepcacioiga

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The qualitative empirical study of the EDA industry has con-rmed that our model assumptions are realistic. The EDA industry

s characterized by few incumbents and numerous start-ups. Bothncumbents and start-ups perform R&D, but the latter generallyeed to be acquired in order to survive in the long run. How-ver, for each type of technology, an incumbent would—with someimplification—only acquire one start-up, so those developing sim-lar technology compete to be acquired. While some of the existingxplanations for entrants’ superiority in developing radical innova-ions also seem to apply to the EDA industry, the fact that innovationor start-ups has the character of a contest with acquisition as therize, clearly contributes to the pursuit of radical innovation bytart-ups.

Although our empirical study focuses on this one industry, thepplicability of our theoretical results is broader. First, severalther software-based industries are similar to EDA in that largencumbents provide system products, and therefore we expect ouresults to also hold in these industries. Second, the pharmaceu-ical industry could also fit our framework. Here, smaller biotechrms supply new technologies and products to large pharmaceu-ical firms which then do the final testing and trials, go throughhe approval process, and commercialize the products. Also, Cabral2003) cites evidence from the biotechnology industry where onef the two winners in the race for artificial human insulin wascquired. He shows also that the contestants chose approacheshat differed in relation to their radicalness rather than theirffort levels. The cases of Gilead acquiring Pharmasset (Bloomberg,011) and of Bristol-Myers Squibb acquiring Inhibitex (Wall Streetournal, 2012), mentioned in the Introduction, provide further sup-ort for our results from the biotech industry.

Inevitably, our analysis builds on simplifying assumptions andas limitations that need to be considered when applying theesults. First, we explored the robustness of the equilibrium in var-ous ways, but we are not able to demonstrate the uniqueness ofhe equilibrium in full generality. Second, we provide a robustnessheck regarding the number of incumbents in Section 5.3 (withwo incumbents and one entrant) but do not address the gen-ral case of several incumbents and entrants, as found in the EDAndustry. We conjecture that our main result—the entrants pick-ng more radical projects—remains robust, since it relies on thentrants’ need to be acquired rather than on the number of acquir-rs. Furthermore, we conjecture that, if the number of entrantsxceeds that of the incumbents, the radicalness of the most radicalroject increases with the number of entrants, since it is based onompetition between the entrants. Third, we made the simplifyingssumption that entrants need to be acquired in order to commer-ialize their innovations. In reality, even in industries such as EDAt cannot be fully excluded that some entrant is successful on itswn in the long run. However, if the probability of such an events small enough, our model should be a good approximation. Still,eneralizing our model along these dimensions is an interestingrea for future research.

Market dynamics are multifaceted, in particular the interplayetween incumbents and new entrants. With its focus on successrobability as a choice variable, entrants’ need to be acquired, andompetition between a large number of entrants, we believe thatur study contributes important new aspects to this variegatedicture.

cknowledgments


We are grateful to two anonymous reviewers, Carliss Baldwin,arc Gruber, Holger Patzelt, Olav Sorenson, and three anonymous

eviewers for the Academy of Management Meeting for help-ul comments on earlier versions of this paper. Thanks also to


participants in seminars and workshops at the Academy of Man-agement Meeting, Advances in Industrial Organization (Vienna),Catolica-Lisbon, DRUID Summer Conference 2010, EPFL Lausanne,Harvard Business School, Industrieökonomischer Ausschuss of theVerein für Socialpolitik, Technische Universität München, Univer-sität der Bundeswehr München, and WHU Vallendar. Errors andoversights are ours alone.

Appendix.

Proof of Lemma 2. Assume there is an equilibrium in which twoor more firms pick the same success probability. Renumber firms,including I, such that p0 ≥ · · · > pk = · · · = pk+m > · · · ≥ pN. We denotepk = · · · = pk+m by p. At least one of firms k to k + m is an entrant, andwe order the firms such that firm k is an entrant. Using hk defined inDefinition 1, we can write firm k’s profit function in case of a smalldeviation to larger or smaller values of p as follows (with ε > 0):

˘k(p + ε) = (p + ε)

(N∏

i=k+m+1

(1 − pi)

)(1 − p)m(�(p + ε) − hk),

˘k(p − ε) = (p − ε)

(N∏

i=k+m+1

(1 − pi)

)((1 − p)m(�(p − ε) − hk)

+ (1 − (1 − p)m(�(p − ε) − �(p)).

Differentiating with respect to ε and calculating the limit of εgoing to zero from above, we obtain:

d˘k(p + ε)dε

∣∣∣∣ε

+−→0

=(

N∏i=k+m+1

(1 − pi)

)(1 − p)m(�(p)+p�′(p)−hk)

d˘k(p − ε)dε

∣∣∣∣ε

+−→0

= −(

N∏i=k+m+1

(1 − pi)

)((1 − p)m(�(p)

+p�′(p) − hk) + (1 − (1 − p)m)p�′(p))

A necessary condition for the candidate equilibrium to exist isthat both of the above terms are non-positive. However, if [d˘k(p +ε)]/dε|

ε+−→0

≤ 0, this implies that (d˘k(p − ε))/dε|ε

+−→0> 0,

because (1 − (1 − p)m)p�′(p) < 0. Hence, an equilibrium of the typespecified in the proposition cannot exist.

Proof of Lemma 3. To start the induction argument, notice thath1 = p0�(p0) > h0 = 0, which implies that p0 > p1 due to concav-ity of p�(p). Assume that hk > hk−1 > · · · > h0 and that p0 > p1 >· · · > pk. Now, using (9), one can derive that hk+1 = hk + pk(�(pk) −hk). Since (i) hk is the expected value of the best project amongprojects 0, 1, . . ., k − 1, (ii) �(p) is decreasing in p, and (iii) pj > pk

for all j < k, it follows that �(pk) > hk. Hence, hk+1 > hk. This, in turn,implies that pk > pk+1, which proves part (i) of Lemma 3.

Consider an R&D portfolio consisting of i + 1 projects wherethe projects have been renamed such that p0 ≥ p1 ≥ · · · ≥ pi. Theexpected value of the best project is:

E[Vmax] =i∑

m=0

pm�(pm)i∏

j=m+1

(1 − pj)

Maximizing E[Vmax] yields the first-order conditions (10), whichproves part (ii) of the lemma.


Again by induction we now show that pk > 0 and hk <[p�(p)]′p=0 ≡ �(0) for all k. It is true for the base case: p0 = p > 0,and h0 = 0 by definition. Assume it is true for k − 1. Then hk is aweighted average of �(pk−1) and hk−1, both of which are less than


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kp

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(0). Thus, also hk is less than �(0), from which pk > 0 followsecause it is defined through the condition [p�(p)]′p=pk

= hk.

roof of Proposition 1. The proof proceeds as follows. First (a),tarting from the assumption that pI > p1 > · · · > pN in the sought-or equilibrium, we characterize the equilibrium candidate, showhat it exists, and show that no player k has an incentive to devi-te to some p′

k∈ [p∗

k−1, p∗k+1]. Having thus shown “local” stability of

he equilibrium candidate, we then also show (b) that “non-local”eviations that change the order of p’s (i.e., deviations from pk toome p′

k< p∗

k+1 or p′k

< p∗k−1) are not attractive.

Now, ˘ I consists of three additive terms that capture the caseshat (a) two or more entrants are successful (first terms), (b) exactlyne entrant is successful (second term), and (c) no entrant is suc-essful (third term):

I =N∑

j=2

j−1∑k=1

pjpk�(pk)N∏

m = k + 1

m /= j

(1 − pm) + pI�(pI)N∑

j=1

pj

×N∏

m = 1

m /= j

(1 − pm) + pI�(pI)N∏

j=1

(1 − pj)

Deriving the incumbent’s first-order condition yields (10) with = 0, and it follows that p∗

I = p0 = p. For entrant k, the expectedrofit can be written as follows:

k = pk

⎛⎝ N∏

j=k+1

(1 − pj)

⎞⎠ (�(pk) − hk),

here hk is defined in Definition 1. Deriving entrant k’s first-orderondition yields (10) with k > 0, and it follows that p∗

k= pk. This

roves that the success probability characterized in Proposition constitutes an equilibrium, except for showing that “non-local”eviations are not profitable.

Assume now that k deviates from p∗k

to some higher successrobability p′

ksuch that p′

k∈ [p∗

m, p∗m−1], where m < k. This deviation

hanges the shape of k’s profit function (since now there are m − 1ther start-ups whose value in case of success is less than or equalo k’s, as opposed to k − 1 before the deviation), and as a result thepplicable first-order condition becomes (10) with k replaced by m.hus, when k deviates to some p′

k∈ [p∗

m, p∗m−1], then the best it can

o is to deviate to pm (since by the FOC, this is the optimal choice of′k

within this interval). We now show that even this deviation to′k

= pm results in lower expected profit than p∗k

= pk. First, p′k

= p∗m

annot be (locally) optimal since, as we show in Lemma 2, there islways an incentive to deviate to slightly smaller or larger valuesf p when two players choose identical actions. But due to the FOC,here can be no incentive to deviate from p∗

m to slightly larger valuesf p (since the optimal choice of p′

kin [p∗

m, p∗m−1] is p∗

m). Hence, thereust be an incentive to deviate to slightly smaller values of p. That

s, there exists some p′k∈ [p∗

m+1, p∗m) resulting in greater profit than

′k

= p∗m. Applying this argument iteratively finally shows that some

′k

in [p∗k+1, p∗

k−1) is more attractive than any p′k

= p∗k−1. Hence, no

rofitable deviation exists for k to values of p′k

larger than p∗k−1. A

imilar argument establishes that there is no profitable deviationo some p′

k∈ [p∗

m+1, p∗m], where m > k.

Finally, we need to show that for the incumbent also, a non-local


eviation cannot be profitable. Assume that the incumbent devi-tes from p∗

0 to some p′I such that p′

I ∈ [p∗m+1, p∗

m], 0 < m. To simplifyxpressions, denote by S the number of successful projects amongntrants m + 1 to N. Also, define P(S) as the probability of exactly S


successful projects among entrants m + 1 to N and E(˘I |S) as theincumbent’s profit conditional on S. Furthermore, we introducehk+1 = hk + p∗

k+1(�(p∗k+1) − hk) and h0 = 0 where hk is the expected

value of the best project among entrants {1, 2,. . ., k}. It follows fromLemma 3 that hk≥hk. Using the above notation, the incumbent’sexpected profit when deviating to p′

I can be written as:

˘I =N−m∑j=2

P(S = j)E(˘I |S = j) +

⎛⎝1 −

N−m∑j=2

P(S = j)

⎞⎠⎛⎝�(p′

I)p′I

+ (1 − p′I)

⎛⎝P(S = 1)hm + P(S = 0)

m∑j=1

pjhj−1

m∏k=j+1

(1 − pk)

⎞⎠⎞⎠ .

The first term in ˘ I is the incumbent’s expected profit whenmore than two projects of higher value than �(p′

I) succeed. The sec-ond term is the expected profit in the complementary case wherethe incumbent either obtains a profit equal to the value of its ownproject if successful, or the value of the second-best project amongentrants 1 to m. Maximizing the incumbent’s expected profit withrespect to p′

I yields:

�(p′I) + p′

I�′(p′

I) − P(S = 1)hm − P(S = 0)m∑

j=1

pjhj−1

m∏k=j+1

(1 − pk).

Since p′I ≤ p∗

m, it follows from concavity of p�(p) that �(p′I) +

pI�′(p′I)≥hm, and we have:

�(p′I) + pI�

′(p′I) − P(S = 1)hm − P(S = 0)

m∑j=1

pjhj−1

m∏k=j+1

(1 − pk)≥hm

− P(S = 1)hm − P(S = 0)m∑

j=1

pjhj−1

m∏k=j+1

(1 − pk)

= P(S = 1)(hm − hm) + P(S = 0)m∑

j=1

pj(hm − hj−1)m∏

k=j+1

(1 − pk)

+

⎛⎝1 − P(S = 1) − P(S = 0)

m∑j=1

pj

m∏k=j+1

(1 − pk)

⎞⎠hm > 0,

where the last inequality follows from hm > hm, hm > hj−1 >

hj−1 for j − 1 < m, and∑m

j=1pj

∏mk=j+1(1 − pk) ≡ 1 −

∏mk=1(1 − pk) <

1. Therefore, the optimal deviation for p′I ∈ [p∗

m+1, p∗m] is p′

I =p∗

m. A similar argument shows that the optimal deviation forp′

I ∈ [p∗m, p∗

m−1] is p′I = p∗

m−1. Hence, as ˘ I is continuous at p′k

= p∗m,

p′I = p∗

m−1 results in greater profit for the incumbent than p′I = p∗

m.Applying this argument iteratively shows the incumbent has noincentive to deviate to some p′

I ≤ p∗1. Hence, p∗

I = p0 and p∗i

= pi fori = 1,. . ., N constitute an equilibrium. Finally, a social planner max-imizes the expected highest value of the projects, E[Vmax]. Then, itfollows from Lemma 3 that the equilibrium R&D choices are welfaremaximizing, which proves part (i) of the proposition.

In order to prove part (ii), we proceed in three steps. First, itfollows from Lemma 3 that p∗

k−1 maximizes hk given the choicesof the other firms. Hence, hk decreases when entrant (k − 1)’s suc-cess probability is continuously decreased from p∗

k−1 to p∗k. This,

in turn, implies that the decrease in pk-1 increases the expected


profit of entrant k. Finally, as ˘k = ˘k−1 for pk−1 = p∗k, ˘∗

k< ˘∗

k−1in equilibrium in which pk−1 = p∗

k−1. It only remains to also showthat ˘∗

I < ˘∗1. To see this, note that ˘∗

I ≥p�(p), since this is thevalue that the incumbent can secure without any acquisition, and


ING ModelR

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sH

Pprvfel

oc

P

(

Piaeocai

˘

∗ ∗

˘1(p1) =⎪⎩ p1(�(p1) − p∗2�(p∗

2)) if p∗E ≤ p1 < p∗

2

p1(�(p1) − p∗2�(p∗

2)) if p1 ≤ p∗2 < p∗

E



ince it will only acquire an entrant if doing so increases its profit.ence, ˘∗

1 < p∗1�(p∗

1) < p�(p) ≤ ˘∗I , which completes the proof.

roof of Proposition 2. Consider the candidate equilibrium with1 > p2 > · · · > pN > pI. Define A as the expected value of the highestealized value among the entrants 1, . . ., N − 1, and B as the expectedalue of the second-highest realized value among all entrants. Itollows from these definitions that A > B. We can now write thexpected payoffs of the incumbent and of entrants 1 and N as fol-ows:

˘1 = p1�(p1)(1 − pI)N∏

k=2

(1 − pk)

˘N = pN(1 − pI)(�(pN) − A)

˘I = pI�(pI) + (1 − pI)B

The resulting first-order conditions are:

�(p1) + p1�′(p1) = 0

�(pN) + pN�′(pN) = A

�(pI) + pI�′(pI) = B

Since p�(p) is concave and increasing in p for p < p, the first-rder conditions are fulfilled for p = p1 > pI > pN . Hence, thereannot exist an equilibrium in which p1 > p2 > · · · > pN > pI.

roof of Proposition 3.

(i) Analytically solving the system of first-order conditions forthe candidate equilibrium with p1 > pI > p2 yields the uniquesolution of p1 = 0.5, pI ≈ 0.461, and p2 ≈ 0.308. This, however,turns out not to be an equilibrium. For example, deviating from0.5 to 0.4 increases firm 1’s expected payoff from approxi-mately 0.0931 to approximately 0.0972. Thus, there exists noequilibrium with p1 > pI > p2. Together with Proposition 2 andProposition 3 this proves that the only equilibrium is given bypI = 0.5, p1 = 0.375, and p2 ≈ 0.305.

ii) Solving the system of first-order conditions for the candidateequilibrium with p1 > pI > p2 > p3 yields the unique solution ofp1 = 0.5, pI ≈ 0.445, p2 ≈ 0.307, and p3 ≈ 0.260. However, deviat-ing from 0.5 to 0.4 increases firm 1’s payoff from approximately0.0712 to approximately 0.0724. Note that, due to the needto calculate the roots for the higher-order polynomials, theequilibrium had to be calculated numerically. Regarding thesecond part of the statement, starting with the assumptionthat p1 > p2 > pI > p3 and (numerically) solving the system offirst-order conditions leads to a unique solution, which how-ever, does not fulfill the above sequence of inequalities: p1 = 0.5,p2 ≈ 0.375, pI ≈ 0.414, and p3 ≈ 0.264. That is, there is no equi-librium in which p1 > p2 > pI > p3. Together with Proposition 1and Proposition 2 this proves that the only equilibrium is givenby pI = 0.5, p1 = 0.375, p2 ≈ 0.305, and p3 ≈ 0.274.

roof of Proposition 4. Suppose that at least one of the entrantss successful such that the incumbent has an interest in makingn acquisition. If the incumbent makes the offer, it acquires thentrant with the most valuable technology at an acquisition pricef zero. Instead, if the entrants make the offers, the equilibrium out-ome at the acquisition stage is as described in Lemma 1. Considern equilibrium where p∗

2 ≤ p∗1 ≤ p∗

I . Then, the profit function of thencumbent can be written as:⎧ ∗ ∗ ∗ ∗ ∗


I(pI) =⎪⎨⎪⎩

bE[Vmax] + (1 − b)(p2p1�(p1) + (1 − p2p1)pI�(pI)) if p2 ≤

bE[Vmax] + (1 − b)(pI�(pI) + (1 − pI)p∗2p∗

1�(p∗1)) if p∗

2 ≤

bE[Vmax] + (1 − b)(pI�(pI) + (1 − pI)p∗2p∗

1�(p∗1)) if pI <


where E[Vmax] = pk�(pk) + (1 − pk)pj�(pj) + (1 − pk)(1 −pj)pi�(pi) for pi≥pj≥pk for pi≥pj≥pk is the expected value ofthe best technology. The profit functions of the entrants aregiven by the profit function in Eq. (4) multiplied by (1 − b). If theincumbent chooses p∗

I = p0, it follows immediately from the proofof Proposition 1 that the entrants choose p∗

1 = p1 and p∗2 = p2 in

equilibrium.For p∗

2 ≤ p∗1 ≤ pI , the first-order condition of the incumbent is

given by:

∂˘I(pI)∂pI

= 0 ⇔ �(pI) + pI�′(pI) = 0,

which implies that p∗I = p0 is a local maximum. Consider a deviation

to some p′I ∈ [p∗

2, p∗1]. Then, the first-order condition is given by:

�(p′I) + p′

I�′(p′

I) − b(1 − p∗2) + p∗

2(1 − b)1 − p∗

2bp∗

1�(p∗1) = 0

Notice that (a) [b(1 − p∗2) + p∗

2(1 − b)]/(1 − p∗2b) < 1, and (b)

p∗1�(p∗

1) < p∗I �(p∗

I ) as p∗I = p. Hence, the incumbent’s first-order

condition is satisfied for some pI > p∗1, which implies that ˘I(pI)

is increasing in pI for p∗2 ≤ pI < p∗

1. Finally, since ˘I(pI) is continu-ous at pI = p∗

1, it follows that pI = p∗1 = p0 yields higher profit for the

incumbent than any p∗2 ≤ pI < p∗

1. A similar argument establishesthat there does not exist a profitable deviation to some pI < p∗

2. Thisproves the existence of the candidate equilibrium.

Proof of Proposition 5. Consider a game with two incumbentsand one entrant. Denote the incumbents by 1 and 2 and the entrantby E.

Lemma A.1. Suppose that there are two incumbents and one entrantand that the realized value of incumbent j’s project (�j) is greater thanor equal to the realized value of incumbent i’s project (�i), �j ≥ �i.

(i) If the realized value of the entrant’s project (�E) is greater thanor equal to �j, then incumbent j acquires the entrant at a priceof �E − �j. The two incumbents compete in the market, and theprofits of incumbent j and i are �j − �i and 0, respectively.

(ii) If �E is less than �j but greater than or equal to �i, then incumbentj acquires the entrant at a price of 0. The two incumbents competein the market, and the profits of incumbent j and i are �j − �i and0, respectively.

(iii) If �E is less than �i, then no acquisition takes place. The two incum-bents compete in the market, and the profits of incumbent j and iare �j − �i and 0, respectively.

Proof. Follows from standard Bertrand competition logic.

Using Lemma A.1, it is now possible to write down the expectedprofit of the firms as a function of the chosen success probabili-ties. Consider first a candidate equilibrium where P∗

E ≤ P∗2 ≤ p∗

1. Theprofit functions can be written as:

˘E(pE) =

⎧⎪⎨⎪⎩

pE(�(pE) − p∗2�(p∗

2) − (1 − p∗2)p∗

1�(p∗1)) if pE ≤ p∗

2 ≤ p∗1

(1 − p∗2)pE(�(pE) − p∗

1�(p∗1)) if p∗

2 < pE ≤ p∗1

(1 − p∗1)(1 − p∗

2) − pE�(pE) if p∗2 ≤ p∗

1 < pE⎧⎪⎨ (1 − p∗2)p1�(p1) if p∗

E ≤ p∗2 ≤ p1


p1 ≤ pI

pI < p∗1

p∗2 ≤ p∗

1


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b

chtCs

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tttd

caps

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pTSyit

sp

˘

˘

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alcpei

Ptfi

i i i idecreasing in the R&D intensity �i, the first-order conditions implythat �∗

I > �∗2 > �∗

1 in equilibrium.Finally, we need to show that there does not exist a profitable,

non-local deviation for any of the firms. If the incumbent deviatesto some �∗

2 > �′I≥�∗

1, the profit function remains the same as the′ ∗ ∗ ′



2(p2) =

⎧⎪⎨⎪⎩

(P2(�p2) − p∗1�(p∗

1)) if p∗E ≤ p2 ≤ p∗

1

(1 − p∗1)p2�(p2) if p∗

E ≤ p∗1 < p2

p2(�(p2) − p∗1�(p∗

1)) if p2 ≤ p∗E < p∗

1

Using Definition 1, the first-order conditions can for pE ≤ p2 ≤ p1e written as:

∂˘1(p1)∂p1

= 0 ⇔ �(p1) + p1�′(p1) = h0 ⇔ p∗1 = p0

∂˘2(p2)∂p2

= 0 ⇔ �(p2) + p2�′(p2) = h1 ⇔ p∗2 = p1

∂∏

E(pE)

∂pE= 0 ⇔ �(pE) + pE�′(pE) = h2 ⇔ p∗

E = p2

Following the arguments in the proof of Proposition 1, the suc-ess probabilities constitute an equilibrium only if the firms do notave an incentive to make a non-local deviation (i.e., a deviationhat changes the relative ranking of the firms’ success probabilities).onsider first deviations by E. Suppose that the entrant choosesome p∗

2 < pE ≤ p∗1. Then, the first-order condition is given by

(pE) + pE�′(pE) = p∗1�(p∗

1).

The first-order condition is satisfied for p∗2 = pE , which implies

hat ˘E(pE) is decreasing in pE for p∗2 < pE ≤ p∗

1. Since ˘E(pE) is con-inuous at p∗

2 = pE , it follows that PE = P∗E = p2 yields higher profit

han any P∗2 < PE < P∗

1. A similar argument establishes that thereoes not exist a profitable deviation to some P∗

2 ≤ P∗1 < PE .

We consider only non-local deviations by incumbent 1 but itan be shown in a similar manner that there does not exist a profit-ble deviation for incumbent 2. Suppose that 1 chooses some P∗

E ≤1 < p∗

2. Then, the first-order condition characterizing the optimaluccess probability is given by:

(p1) + p1�′(p1) = p∗2�(p∗

2)

It follows from Lemma 3 part (ii) that p∗2�(p∗

2) < p∗1�(p∗

1) =˜�(p). Hence, the first-order condition holds for some p∗

2 < p1.herefore, ˘1(p1) is increasing in p1 in the interval considered.ince ˘1(p1) is continuous at p∗

2 = p1, it follows that p1 < p∗1 ≤ p0

ields higher profit than any p∗E < p1 ≤ p∗

2. Finally, it can be shownn a similar manner that there does not exist a profitable deviationo some p1 < p∗

E ≤ p∗2. This proves the existence of the equilibrium.

In order to show that this is the unique equilibrium in puretrategies, consider first a candidate equilibrium in which p∗

2 <∗E ≤ p∗

1. Then, using Lemma A.1, the profit functions are given by:

E(pE) = (1 − p∗2)pE(�(pE) − p∗

1�(p∗1))

1(p1) = (1 − p∗2)p1�(p1)

2(p2) = p2(�(p2) − p∗1�(p∗

1))

Maximizing profit shows that the incumbents choose p∗1 = p0

nd p∗2 = p1. The entrant also chooses p∗

E = p1 in the candidate equi-ibrium. However, it follows from the first part of the proof that thisannot constitute an equilibrium, because then there would exist arofitable deviation for the entrant to p∗

E = p2. A similar argumentstablishes that there cannot exist an equilibrium in pure strategiesn which p∗ ≤ p∗ ≤ p∗ .


2 1 E

roof of Proposition 7. We make some assumptions to ensurehat investment increases expected R&D performance and that therst-order conditions characterize an equilibrium:


Assumption A.1. p(�i)�(�i) is concave in �i, c(�i) is convex in �i,and p(�i)�(�i) − c(�i) takes on a global maximum for some �i = �.

Assumption A.2. p′(�i) ≥ 0 and �′(�i) ≥ 0 with at least one strictinequality, implying that p(�i) �(�i) is strictly increasing in �i,.

Assumption A.3. 0 ≤ p(�i) < 1 for all �i ≥ 0 and p(�i) is concave in�i.

Assumption A.4. c(0) = c′(0) = 0 and c(�i) is sufficiently convex toensure that the second-order conditions associated to the firms’ max-imization problems are satisfied.

Consider the candidate equilibrium in which �∗I ≥�∗

2≥�∗1. Then,

expected profits of the firms can be written as:

˘I(�I, �∗1, �∗

2) = p(�I)�(�I) + (1 − p(�I))p(�∗1)p(�∗

2)�(�∗1) − c(�I),

˘2(�∗I , �∗

1, �2) = (1 − p(�∗I ))p(�2)(�(�2) − p(�∗

1)�(�∗1)) − c(�2),

˘1(�∗I , �1, �∗

2) = p(�1)(1 − p(�∗I ))(1 − p(�∗

2))�(�1) − c(�1).

The corresponding first-order conditions are:

∂˘I

∂�I= 0 : p′(�∗

I )�(�∗I ) + p(�∗

I )�′(�∗I ) − c′(�∗

I )

= p′(�∗I )p(�∗

1)p(�∗2)�(�∗

1)︸︷︷︸A1

,

∂˘2

∂�2= 0 : p′(�∗

2)�(�∗2) + p(�∗

2)�′(�∗2) − c′(�∗

2)

= p(�∗I )(p′(�∗

2)�(�∗2) + p(�∗

2)�′(�∗2))︸︷︷︸

B1+ p′(�∗

2)(1 − p(�∗I ))p(�∗

1)�(�∗1)︸︷︷︸

B2

,

∂˘1

∂�1= 0 : p′(�∗

1)�(�∗1) + p(�∗

1)�′(�∗1) − c′(�∗

1)

= p(�∗I )(p′(�∗

1)�(�∗1) + p(�∗

1)�′(�∗1))︸︷︷︸

C1+ p′(�∗

1)(1 − p(�∗I ))p(�∗

2)�(�∗1)︸︷︷︸

C2+ p(�∗

1)(1 − p(�∗I ))p(�∗

2)�′(�∗1)︸︷︷︸

C3

.

Under the assumption that �∗I > �∗

2 > �∗1, the right-hand side of

the first-order condition associated with the incumbent’s problemis less than the right-hand side of the first-order condition associ-ated with entrant 2’s problem, because B1 > A1 (due to AssumptionsA.2 and A.3) and B2 > 0 (due to Assumption A.2). This, in turn, isless than the right-hand side of the first-order condition associ-ated with entrant 1’s problem, because C1 > B1 (due to AssumptionA.1), C2 > B2 (due to Assumptions A.2 and A.3), and C3 > 0 (due toAssumptions A.2 and A.3). It follows from Assumption A.1 thatp(� )�(� ) − c(� ) is concave in � . Hence, as the left-hand sides are


one derived above. Hence, ˘I(�I, �1, �2) is increasing in �I for all�∗

2 > �′I≥�∗

1. Also, as the incumbent’s profit function is continuousat �∗

2 = �′I , it follows from the analysis that �∗

I = �′I gives rise to

higher profit for the incumbent than any �′I such that �∗

2 > �′I≥�∗

1.


ING ModelR

ch Poli

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˘

p

e�˘bapan

sp

ataon�n

R

A

A

A

A

B

B

B

B

C

C



Consider instead a deviation to some �∗1 > �′

I . Then, the profitunction of the incumbent becomes:

I(�′I , �∗

1, �∗2) = p(�∗

1)p(�∗2)�(�∗

1)

+ (1 − p(�∗1)p(�∗

2))p(�′I)�(�′

I) − c(�′I).

The corresponding first-order condition is:

′(�′I)�(�′

I) + p(�′I)�

′(�′I) − c′(�′

I)

= p(�∗1)p(�∗

2)(p′(�′I)�(�′

I + p(�′I)�

′(�′I)︸︷︷︸

D1

.

Compare this first-order condition to the one associated withntrant 1. Since p(�∗

1)p(�∗2) < p(�∗

I ), it follows that D1 < C1 for1 = �′

I . Furthermore, as C2 > 0 and C3 > 0, we conclude thatI(�′

I , �∗1, �∗

2) is increasing in �′I for all �∗

1 > �′I . Also, as the incum-

ent’s profit function is continuous at �∗1 = �I, it follows from the

nalysis that ˘I(�′I , �∗

1, �∗2) has a global maximum at �∗

I = �′I . This

roves that there exists no profitable deviation for the incumbent,nd it can be shown in a similar manner that the entrants also doot have an incentive to deviate in equilibrium.

In order to show that this is the unique equilibrium in puretrategies, consider an equilibrium in which �∗

2 > �∗I > �∗

1. Therofit functions of I and 2 are then:

˘I(�I, �1, �2) = p(�I)�(�I) + (1 − p(�I))p(�1)p(�2)�(�1) − c(�I),

˘2(�I, �1, �2) = p(�2)(�(�2) − p(�I)�(�I)

−(1 − p(�I))p(�1)�(�1)) − c(�2).

The corresponding first-order conditions are:

p′(�I)�(�I) + p(�I)�′(�I) − c′(�I) = p′(�I)p(�1)p(�2)�(�1),

p′(�2)�(�2) + p(�2)�′(�2) − c′(�2) = p′(�2)p(�I)�(�I)

+p′(�2)(1 − p(�I))p(�1)�(�1).

Arguing as above, the right-hand side of the first-order conditionssociated with entrant 2’s problem is greater than the right side ofhe first-order condition associated with incumbent’s problem forny �2 = �I. As the left-hand side is decreasing in the R&D intensityf the firm considered, the two first-order conditions hold simulta-eous for some �2 < �I, which contradicts the initial assumption of∗2 > �∗

I > �∗1. It can be shown in a similar manner that there does

ot exist an equilibrium in which �∗2≥�1≥�∗

I .

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