International Journal of Industrial Organization 31 (2013) 527–537

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International Journal of Industrial Organization

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R&D competition versus R&D cooperation in oligopolistic markets withevolving structure☆

H. Dawid a, M. Kopel b, P.M. Kort c,d,⁎a Department of Business Administration and Economics and Center for Mathematical Economics, Bielefeld University, Germanyb Department of Organization and Economics of Institutions, University of Graz, Austriac Department of Econometrics and Operations Research & CentER, Tilburg University, The Netherlandsd Department of Economics, University of Antwerp, Belgium

☆ Wewould like to thank the editor, Ulrich Doraszelski,for their detailed comments on an earlier version of the paGerman Science Foundation (DFG) under grant DA 763/4-(NWO) under grant 464-11-104, and COST Action IS110geography of economic systems: models, tools and packnowledged.⁎ Corresponding author at: Department of Economet

University, P.O.Box 90153, 5000 LE Tilburg.E-mail address: Kort@uvt.nl (P.M. Kort).

0167-7187/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.ijindorg.2013.09.003

a b s t r a c t

a r t i c l e i n f o

Article history:Received 5 March 2013Received in revised form 25 July 2013Accepted 17 September 2013Available online 16 October 2013

JEL classification:C73L13O33

Keywords:R&DCompetitionCooperationProduct innovationCapital accumulationDifferential game

This paper considers investment behavior of duopolistic firms subject to technological progress. It is assumedthat initially both firms offer a homogeneous product, but after a stochastic waiting time they are able toimplement a product innovation. Production capacities of both firms are product specific. It is shown thatfirms anticipate a future product innovation by under-investing (if the new product is a substitute to theestablished product) and higher profits, and over-investing (in case of complements) and lower profits,compared to the corresponding standard capital accumulation game. This anticipation effect is stronger in thecase of R&D cooperation. Furthermore, since due to R&D cooperation firms introduce the new product at thesame time, this leads to intensified competition and lower firm profits right after the new product has beenintroduced. In addition, we show that under R&D competition the firm that innovates first, overshoots in new-product capacity buildup in order to exploit its temporary monopoly position. Taking into account all theseeffects, the result is that, if the new product is neither a close substitute nor a strong complement of theestablished product, positive synergy effects in R&D cooperation are necessary to make it more profitable forfirms than R&D competition.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

In many industries R&D cooperation is a pervasive phenomenon(see e.g. Hagedoorn (2002) and Roijakkers and Hagedoorn (2006)). Akey challenge incumbent firms face is whether new productdevelopments, which open new additional submarkets that influencethe demand of established products, should be carried out jointly withcompetitors on the market. Examples for such R&D cooperationsinclude the Global Hybrid Cooperation between GM, Daimler, Chrysler,and BMW for the development of hybrid cars, the cooperation between

and two anonymous reviewersper. Financial support from the1, theDutch Science Foundation4: ‘The EU in the new complexolicy evaluation’ is gratefully

rics & OR, and CentER, Tilburg

ghts reserved.

Sony and Samsung for the development of TFT-LCD screens, or thecooperation between Lenovo and NEC to develop tablet computers.1

On the other hand, several of the innovations opening new submarketswere introduced by incumbents who did not engage in R&Dcooperation, like the introduction of MP3 players by Apple. Animportant difference between the case of MP3 players and previousexamples is that MP3 players are complements to the establishedproduct (PCs) rather than substitutes. Furthermore, the degree ofdifferentiation between the two products in the MP3 example seemsto be larger than in the previous three examples, so that the linkagebetween the two markets seems weaker.

1 It should be noted that in all three examples the new products are substitutes to theexisting ones. To illustrate, one of the main producers on the PC and tablet market,Samsung Electronics, stated that it expects the global personal computer market to shrinkby 5% in 2013 as consumer demand continues to shift to mobile devices such astablet computers (see India Times (2013; http://www.indiatimes.com/pc-and-laptop/samsung-global-pc-sales-to-reduce-by-5_-57356.html)).

528 H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

Based on these observations, the paper addresses the followingresearch questions:

• Under which circumstances do incumbents have incentives tocooperate in the new product development?

• How are the investment patterns before and after the emergence ofthe new sub-market influenced by cooperation/non-cooperation inthe innovation project?

In the literature the issue of R&D cooperation has attracted substan-tial interest. Influential theoretical contributions include D'Aspremontand Jacquemin (1988), Choi (1993), and Goyal and Joshi (2003). Thelarge literature based on these papers relies on static models, butin order to capture the main implications of R&D cooperations inindustry settings like the ones discussed above, a dynamic frameworkis needed.2 In particular, firms' investment incentives are influencedby the expected future introduction of new products. Furthermore, theinduced changes in investment patterns of competitors influence alsothe current profitability of investments in the established product.However, the few dynamic analyses of R&D cooperation (see Martin(2002), Miyagiwa and Ohno (2002), Erkal and Piccinin (2010), Celliniand Lambertini (2009)) do not study interdependencies with existingproducts. Also, all these contributions focus on R&D cooperation withrespect to process innovation.3

This paper addresses several issues that are not covered in theliterature so far. First, we explicitly model the effects of R&D cooperationon the behavior of firms on established markets. This allows us toexamine how the linkage between the established and the new productaffects incentives for R&D cooperation. Second, we explicitly study howthe behavior of incumbents with respect to the established product isinfluenced by future new product introductions. To capture the resultinganticipation effectwe focus on capacity dynamics, thereby contributing tothe literature on dynamic oligopolistic competition (e.g. Jun and Vives(2004), Besanko and Doraszelski (2004), Besanko et al. (2010a,b)).4

Third, in a dynamic setting we explicitly take into account that R&Dcooperation for product innovation has a synchronizing effect on productintroduction dates across competitors. Fourth, in addition to the pureknowledge sharing aspect, which leads to the synchronization effect, wealso model potential synergies generated by R&D cooperations (see e.g.Link et al. (1996) or Link (1998) for empirical evidence for the existenceof synergies in R&D cooperations). This feature of the model allows usto understand under which circumstances positive synergy effects arenecessary to give firms an incentive to cooperate in R&D.

We consider a dynamic oligopoly model, where incumbent firmsoffer an established homogeneous product. At some ex-ante unknownpoint in time the range of products is enlarged, because one or severalof the competing firms obtain the option to introduce a new product,which is vertically and horizontally differentiated from the existingproduct. Capacities cannot be (fully) transferred between the productionof different products. Therefore, the introduction of the new productreduces (in case of substitutes) or increases (in case of complements)the value of the existing capacities. The firms' objectives are tomaximizetheir total discounted profits by optimally selecting their investments inproduction capacities for the different products they offer. Firms canenter an R&D cooperation with the competitor in order to develop the

2 The importance of a dynamic perspective on oligopoly markets has been stressed inCabral (2012, p.278), who argues that, “… dynamic oligopoly models are an area wheremuch work needs to be done and much work can be done.”, and further, “… dynamicoligopoly models provide considerable value added with respect to static models.”

3 Exceptions are Cellini and Lambertini (2002), who consider a differential gamewherefirms over time influence the degree of differentiation of their products, and Bourreau andDogan (2010), who focus on the complementarity between the degrees of cooperation inproduct and process innovation.

4 For the examples of the emergence of new submarkets mentioned above, costs ofcapacity expansion are relevant factors. To illustrate, in 2010 and 2011 Samsung investedheavily in production capacity for parts needed to produce tablet PCs. Another examplerelates to the main battery supplier for Toyota Hybrid cars, which has expanded itsproduction capacity by a factor of more than eight in the 2000s.

new product. Entering such a cooperation reduces the expected timeuntil thefirm can introduce the newproduct because thefirmgets accessto the R&D results of thepartner and the cooperationmight also generatesynergies in the R&D activities. The drawback of such a cooperation isthat the partner will be able to introduce the new product at the sametime, thereby intensifying market competition.

The developed model has the form of a piecewise deterministicdifferential game with different modes. In the initial mode none of thefirmshas introduced the newproduct. An introduction of a newproductresults in a switch to a new mode opening a broader range ofinvestment possibilities for the innovating firm.

The characterization ofMarkov Perfect Equilibria (MPE) of the gameleads to the following answers to our research questions. Although themodel abstracts from explicit cooperation costs and knowledgespillover considerations, R&D cooperation has implicit costs due tostrategic interactions on the market. We identify two main effectsresponsible for these costs: i) R&D cooperation implies that after a suc-cessful innovation, the new product is available for market introductionto all cooperation partners. Hence, competition in the new submarketemerges immediately after the introduction of the new product (wedenote this as the synchronization effect). ii) In case the new product isa complement to the established one, the anticipation of the eventualintroduction of the new product induces an increase in investment incapacities of the established product already prior to the new productintroduction. The increased investment brings the price for theestablished product closer to the competitive level, thereby reducingfirm profits. This anticipation effect is stronger if firms cooperate inR&D, since the expected innovation time is shorter. This results inadditional implicit costs of R&D cooperation.

If the new product is neither a close substitute nor a strongcomplement of the established product, in the absence of synergiesfrom R&D cooperation the overall implicit costs outweigh the gains ofcooperation. These gains consist not only of reduction of expectedinnovation time, but also of a reduction in capacity adjustment costsfor the new product (adjustment cost effect). We show that under R&Dcompetition the (intertemporally optimal) capacity trajectory of theinnovator is non-monotonic. Directly after the new product introduc-tion, the innovator builds up the corresponding capacity to exploit thetemporarymonopoly position. After the competitor has also introducedthe new product, the innovator scraps parts of this installed capacity tokeep product prices at a sufficiently high level. The costs associatedwithsuch ‘overshooting’ of capacity build-up are avoided in case of R&Dcooperation, because there we observemonotone capacity adjustmentson both markets after the innovation.

Another main insight from our dynamic analysis is that the anti-cipation of the market introduction of a substitute to the establishedproduct acts as a collusion device. If firms expect that a substitute fortheir current productwill be introduced, the expected return fromcurrentcapacity investment decreases. Hence, such expectations lead to lowercapacities and a higher price for the established product. This moves theprice closer to the monopoly price and increases current total industryprofits compared to a situation without such an anticipation.

The paper is organized as follows. The next section presents themodel. This is followed by a characterization of the Markov PerfectEquilibria of the game in Section 3. Section 4 discusses the economicimplications of our analysis and Section 5 concludes.

2. The model

We consider a duopoly where both firms, denoted Firm A and FirmB, have initial capacities K1f(0) (f= A,B) available for production of anestablished product, denoted as product 1. At t=0 both firms start aninnovation project aiming at the development of a new differentiatedproduct (product 2). The completion time of the innovation project offirm f is denoted by τf, = A,B. The project might be carried outindependently or jointly. In the case of independent R&D, which we

R&D CooperationR&D Competition

1m

2m

3m

4m 1m

2m

3m

4m

compλcoopλ

compλ

compλ

compλ

Fig. 1. Transition rates between the different modes under R&D competition and R&Dcooperation.

529H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

will refer to as R&D competition, both firms in general have differentproject completion times. The new product becomes available only tothe firm which has finished its project at that time. Completion timesare exponentially distributed with arrival rate λcomp N 0 and inde-pendent across firms. In order to focus the analysis on the capacitydynamics of both firms, the distribution of the project completiontimes is assumed to be exogenous.

Alternatively, in the case of R&D cooperation, the firms engage in ajoint innovation project, whose completion time τcoop is exponentiallydistributed with arrival rate λcoopN 0. At this completion time, the newproduct becomes available for both firms to produce. Since in the R&Dcompetition case the minimal completion time min[τA,τB] is expo-nentially distributed with arrival rate 2λcomp, we assume λcoop to begreater than or equal to this value. We interpret λcoop− 2λcomp≥ 0 asthe degree of synergies that arise due to cooperation of the two firms.

In order to be able to producepositive quantities of this newproduct,the firms have to build up production capacities, where initial capacitiesare K2f(0)=0, f=A, B. At the same time they can adjust their capacitiesfor the established product. Production capacities here involve physicalcapital at production facilities as well as the specific know-how, supplychains, and distribution channels. Production capacities are specific tothe production of either the established or the new product.5

It is assumed that both firms at each point in time fully exploit theirproduction capacities.6 Prices are given by the linear inverse demandsystem

p1 tð Þ ¼ 1− K1A tð Þ þ K1B tð Þð Þ−η K2A tð Þ þ K2B tð Þð Þ; ð1Þ

p2 tð Þ ¼ 1þ θ−η K1A tð Þ þ K1B tð Þð Þ− K2A tð Þ þ K2B tð Þð ÞÞ: ð2Þ

This type of inverse demand system can be derived from a represen-tative consumer model with a quality-augmented version of thestandard quadratic utility function (see Symeonidis (2003), Vives(1999)). The parameter η determines the degree of horizontal dif-ferentiation, where−1bηb1. The parameter θ≥0measures the degreeof vertical differentiation between the two products, where it isassumed that the new product is of higher or equal quality. We assumethat production costs are linear, and for reasons of simplicitywe assumethatmarginal production costs for both products are normalized to zero.

Investment costs are assumed to be linear–quadratic and symmetricacross firms, i.e., C Iif tð Þ� � ¼ biIif tð Þ þ cIif tð Þ2

2 , where Iif(t) denotes theinvestment of firm f∈ {A,B} for product i=1,2 at time t. The parameterbi≥0 is the unit price of capacity for product i and cN0 is the adjustmentcost parameter. We allow for disinvestment of firms and hence Iif (t)may be any real number for any t taking into account the non-negativity of the capacities. Investments (or disinvestments) incapacities to produce the new product are only possible at t if the newproduct has become available at some τ≤ t. To capture this constraintformally we define four modes of the game (see Dockner et al. (2000),Chapter 8 for a general description of multi-mode differential gamesreferred to as ‘Piecewise deterministic games’). The first mode, labeledas m1, corresponds to the periods where the new product has notbecome available yet. In the modes m2 and m3 the new product isavailable only to one of the two firms, where in mode m2 firm A

5 It could be argued that in many industries capacities built for the production of theestablished product can be partly transferred to the production of the new product.Relaxing our assumption that capacities are completely product specific along these lineswould however not alter our qualitative conclusions as long as a sufficiently large fractionof established market capacities is lost when transferred to the production of the newproduct. Moreover, in the examples like flatscreen TVs mentioned in the Introduction,the production processes for the established and the new product are based on verydifferent technologies. In such situations the capacities devoted to the established producttypically can hardly be transferred to the production of the new product.

6 The assumption that capacities are fully used by firms has been adopted in large partsof the literature, see for example Goyal and Netessine (2007) for an extensive discussionand related references.

innovates first, whereas firm B is the innovation leader in mode m3.One of these two modes always occurs under R&D competition in thetime interval betweenmin[τA,τB] andmax[τA,τB]. Under R&D cooperationnone of these modes can occur. Instead, with R&D cooperation there is adirect transition from mode m1 to mode m4, where both firms haveaccess to the new product. Also under R&D competition, mode m4 iseventually reached after the second firm has completed its innovationproject. See Fig. 1 for a graphical summary of these transitions.

In mathematical terms we define a Markov process m(t) on the setM := {m1,m2,m3,m4} with m(0)=m1 and the transition rates given inFig. 1. The restrictions on investment are then captured by theconstraints

I2 f tð Þ ¼ 0 ∀t s:t: m tð Þ ¼ m1; f ¼ A;B:I2B tð Þ ¼ 0 ∀t s:t: m tð Þ ¼ m2I2A tð Þ ¼ 0 ∀t s:t: m tð Þ ¼ m3

ð3Þ

Overall there are four relevant capacities, which evolve according tothe state dynamics

Kif ¼ Iif ; i ¼ 1;2; f ¼ A;B; ð4Þ

with initial conditions

K1 f 0ð Þ ¼ Kini1 f ≥0; K2 f 0ð Þ ¼ 0; f ¼ A;B: ð5Þ

Capacities have to be non-negative and are bounded above by some(large) value Kif ; i ¼ 1;2; f ¼ A;B . For simplicity no depreciation ofcapital is considered.

Each of the two firms chooses its investments in order to maximizeits discounted profits net of investment costs over an infinite horizon.Denoting by r N 0 the discount rate, the objective functions of the twofirms are given by

J f ¼ IE�Z ∞

0e−rt

h1− K1A þ K1Bð Þ−η K2A þ K2Bð Þð ÞK1 f

þ 1þ θ−η K1A þ K1Bð Þ− K2A þ K2Bð Þð ÞK2 f−b1I1 f−c2I21 f−b2I2 f−

c2I22 fidt�;

ð6Þ

subject to (3), (4), (5), where the expectation is taken with respect tothe stochastic processm(t).

We assume that firms use stationary Markovian feedback strategiesand focus on behavior under aMarkov Perfect Equilibrium (MPE). Sincethe precise definition of such an equilibrium in ourmulti-mode conceptis not completely standard we provide an exact definition of an MPE inthe Appendix A. We rely in our analysis on the concept of a Markov-Perfect Equilibrium rather than on alternatives like Open-Loop NashEquilibria (OLNE) because we believe that the level of commitment offirms assumed under OLNE (each firm has to commit at time t=0 toits investment pattern for the entire infinite time horizon) is notappropriate for the problem under consideration here.

530 H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

3. Characterization of the Markov perfect equilibria

We characterize the Markov-perfect equilibria of the describeddynamic capacity game using a dynamic programming approach. Aspointed out in Dockner et al. (2000), for multi-mode games the valuefunctions of the players depend not only on the states, but also on themode of the game. Formally, the value function of firm f = A,B is amapping V f : 0;K1

� �2× 0;K2� �

×M→R , where in mode m1 the valuefunctions only have to be determined on the subset of the state spacewhere K2A = K2B =0 and in mode m2 (m3) only on the subset whereK2B=0 (K2A=0). The Hamilton–Jacobi–Bellman (HJB) equations differbetween modes. In particular in mode m1 we have under R&Dcompetition

r V f K1 f ;0;K1g ;0;m1

� ¼ max

I1 f

"1− K1A þ K1Bð Þð ÞK1 f−b1I1 f−

c2I21 f

h iþ ∂V f �;m1ð Þ

∂K1 fI1 f

þ∂V f �;m1ð Þ∂K1g

I�1g þ λcomp V f �;m2ð Þ−V f �;m1ð Þ�

þ λcomp V f �;m3ð Þ−V f �;m1ð Þ� #

;

f ; g ¼ A;B; g≠ f :

ð7Þ

Intuitively, the expression in the square brackets on the first line ofthe right hand side stands for the instantaneous profit of producingthe established product. The next two terms capture the effects ofchanges of the capacities of the established product of firm f and itscompetitor. The last two terms deal with the value function effects ofthe appearance of the new product on the market (i.e. the potentialjumps from mode m1 to mode m2 or mode m3). For R&D cooperationwe obtain

r V f K1 f ; 0;K1g ;0;m1

� ¼ max

I1 f

"1− K1A þ K1Bð Þð ÞK1 f−b1I1 f−

c2I21 f

h iþ ∂V f �;m1ð Þ

∂K1 fI1 f

þ ∂V f �;m1ð Þ∂K1g

I�1g þ λcoop V f �;m4ð Þ−V f �;m1ð Þ� #

; f ; g ¼ A;B; g≠ f :

ð8Þ

The HJB equation is similar to (8) with the exception that in case thenew product arrives it is simultaneously adopted by both firms (i.e. themode jumps from m1 to m4). In mode m2 we have for the innovatorfirm A

r VA K1A;K2A;K1B;0;m2ð Þ

¼ maxI1A;I2A

�h1− K1A þ K1Bð Þ−ηK2Að ÞK1A

þ 1þ θ−K2A−η K1A þ K1Bð Þð ÞK2A−b1I1A−c2I21A−b2I2A−

c2I22Ai

þ ∂VA �;m2ð Þ∂K1A

I1A þ∂VA �;m2ð Þ

∂K1BI�1B þ

∂VA �;m2ð Þ∂K2A

I2A þ λcomp VA �;m4ð Þ−VA �;m2ð Þð Þ�:

ð9Þ

The instantaneous profit offirmA is given on thefirst two lines of theright hand side, where firm A now also receives profits from the newmarket. There are three relevant capital stocks whose dynamics has tobe taken into account by firm A. The final term on the right hand sidecaptures the value function effect of firm B becoming active on the

new product market (i.e. jump fromm2 tom4) at a yet unknown futurepoint in time. For the laggard firm B we obtain

r VB K1A;K2A;K1B;0;m2ð Þ

¼ maxI1B

�1− K1A þ K1Bð Þ−ηK2Að ÞK1B−b1I1B−

c2I21B

þ ∂VB �;m2ð Þ∂K1A

I�1A þ ∂VB �;m2ð Þ∂K1B

I1B þ∂VB �;m2ð Þ

∂K2AI�2A þ λcomp VB �;m4ð Þ−VB �;m2ð Þð Þ

�:

ð10Þ

The only difference to Eq. (9) is thatfirm B does notmake any profitsyet with the new product. Symmetric equations arise in mode m3,where firm B is the innovator and firm A is the laggard. Finally, inmode m4 the HJB-equation reads

r V f K1A;K2A;K1B;K2B;m4ð Þ

¼ maxI1 f ;I2 f

"1− K1A þ K1Bð Þ−η K2A þ K2Bð Þð ÞK1 f

þ 1þ θ− K2A þ K2Bð Þ−η K1A þ K1Bð Þð ÞK2 f−b1I1 f−c2I21 f−b2I2 f−

c2I22 f

þ ∂V f �;m4ð Þ∂K1 f

I1 f þ∂V f �;m4ð Þ

∂K1gI�1g þ

∂V f �;m4ð Þ∂K2 f

I2 f þ∂V f �;m4ð Þ

∂K2gI�2g

#;

f ; g ¼ A;B; f≠g: ð11Þ

This is a standard HJB for a capital accumulation game where eachfirm produces two products. Considering the first order conditions, itfollows directly from these equations that the equilibrium investmentstrategies are of the form

I�if K;mð Þ ¼ 1c

∂V f K;mð Þ∂Kif

−bi

!i ¼ 1;2; f ¼ A;B;m ∈ M;

with K=(K1A,K2A,K1B,K2B). Since the game is symmetric with respect tothe two firms, wewill concentrate on the characterization of symmetricMarkov-perfect equilibria. Due to the linear quadratic structure of thegame the following form for the value functions can be assumed:

V f K;m4ð Þ ¼ α4 þ β4K1 f þ χ4K1g þ 4K2 f þ ϕ4K2g þ φ4K21 f þ γ4K2

1g

þ ι4K22 f þ κ4K2

2gþμ4K1 f K1gþ ν4K1 f K2 f þσ4K1 f K2g

þω4K1gK2 f þ ψ4K1gK2g þ ξ4K2 f K2g ;

VA K1A;K2A;K1B;0;m2ð Þ ¼ α2A þ β2

AK1A þ χ2AK1B þ 2

AK2A þ φ2AK

21A þ γ2

AK21B

þ ι2AK22A þ μ2

AK1AK1B þ ν2AK1AK2A þω2

AK1BK2A;

VB K1A;K2A;K1B;0;m2ð Þ ¼ α2B þ β2

BK1B þ χ2BK1A þ ϕ2

BK2A þ φ2BK

21B þ γ2

BK21A

þ κ2BK

22A þ μ2

BK1AK1B þ ψ2BK1AK2A þ σ2

BK1BK2A;

V f K1A;K2A;0;0;m1ð Þ ¼ α1 þ β1K1 f þ χ1K1g þ φ1K21 f þ γ1K2

1g þ μ1K1AK1B;

with f, g= A, B, f≠ g. The value functions in mode m3 are completelysymmetric to those in mode m2 with reversed firm roles and αf

3=αg2,

βf3=βg

2,… for f, g=A, B, f≠g.In order to determine the coefficients of these value functions we

follow a standard approach by inserting the equilibrium investmentrules and the quadratic value functions for the different modes intothe HJB-equations. In particular, for the case of R&D competition thevalue functions for all four modes are inserted into (7) and (9)–(11),whereas for the case of R&D cooperation the value functions formodes m1 and m4 are inserted into (8) and (11). Comparing thecoefficients of the capital stock terms of different degrees yields 41nonlinear equations in 41 unknowns under R&D competition and 21nonlinear equations in 21 unknowns under R&D cooperation. Solvingthese systems is facilitated by the fact that they can be solvedrecursively, starting with mode m4 and then proceeding to modes m2

and m1. In all results to be presented below it has been checked that(globally) stable steady states exist in all modes, which implies thattransversality conditions are satisfied.

comp

coopcomp

V

VV −

η

Fig. 2. The relative difference in game values between R&D competition and R&Dcooperation when no synergies from cooperation are present.

531H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

4. Economic analysis

In what follows we address the economic questions posed in theIntroduction by carrying out a numerical analysis. We depart from thefollowing default set of parameters

λcomp ¼ 0:05;λcoop ¼ 0:1; θ ¼ 0; b1 ¼ b2 ¼ 0; c ¼ 5; r ¼ 0:04;

where we will present robustness checks of the qualitative findingswith respect to variations of these parameters at the end of the sectionand in Appendix B. Without loss of generality we always assume thatthe price of capital is normalized to zero, i.e. bi=0. In the default settingwe have λcoop = 2λcomp, which means that we consider a scenariowithout R&D synergies. Results differ qualitatively between the caseswhere the new product is a substitute or a complement to theestablished product. Hence, we always separately discuss results forpositive (η = 0.5) and negative (η = −0.5) values of the degree ofhorizontal differentiation. In the default setting we consider the casewhere the new product is of equal quality to the established one(θ = 0). In Section 4.3 and in Appendix B we show that results arequalitatively similar if the new product is assumed to be also verticallydifferentiated.

In all the analyses, the initial levels of the capital stocks of theestablished product are set to the steady state levels arising in theMarkov-perfect equilibrium of the standard capital accumulationgame where both firms produce only the established product forever.In some of our discussion below we will refer to this capacity level asthe no-innovation benchmark. Setting such initial conditions can beinterpreted in a way that before the start of the R&D project(s) firmsignored the possibility of new products being introduced into themarket.

0 2 4 6 80.35

0.36

0.37

0.38

0.39

0.40

t

CoopB

CoopA KK 11 =

CoopB

CoopA KK 11 =

CompB

CompA KK 11 =

CompB

CompA KK 11 =

((a)

Fig. 3.Dynamics of (a) capital stocks and (b) instantaneous profits inmodem1 under R&D coopehorizontal black line refers to the no-innovation benchmark. (For interpretation of the referen

4.1. Incentives for R&D cooperation

To examine the incentives of firms to engage in R&D cooperation,Fig. 2 considers the relative difference of the value functions of thefirms under R&D competition and under R&D cooperation evaluatedat the initial capital stocks. It can be clearly seen that in the absence ofsynergies there is no incentive to cooperate for almost all values of thehorizontal differentiation parameter η. This is quite remarkable giventhat we do not assume that cooperation induces any explicit costs forthe firms. Furthermore, it can be seen that the relative advantage ofR&D competition crucially depends on the degree of horizontaldifferentiation. In particular, for a large part of the η-interval (−1,1)R&D competition is more attractive the smaller the horizontal dif-ferentiation parameter η is. Although certainly many factors notcaptured in our model also influence actual cooperation decisions offirms, still this finding is qualitatively consistent with the examplesdiscussed in the Introduction. In particular, in the three exampleswhere the new product is a substitute to the established one (hybridengines, TFT-LCD screens, tablet PCs), R&D cooperations occur. However,no cooperation is observed in the MP3–PC example, where the relation-ship between the products is complementary.

To better understand the factors driving cooperation incentives,three effects have to be considered:

(i) Anticipation effect,(ii) Synchronization effect,(iii) Adjustment cost effect.

Below we discuss each of these effects in detail.

4.1.1. Anticipation effectTo explain the anticipation effect, the dynamics of production

capacities for the established product prior to the introduction of thenew product has to be considered. Fig. 3 shows the dynamics ofproduction capacities for the old product and instantaneous profitsof the firms in the periods before the new product is introduced(i.e. during mode m1). It can be seen that starting the R&D projectsinfluences the capacity levels for the established product even beforethe newproduct is introduced. In particular, both under R&Dcooperationand R&D competition the firm invests less if the anticipated new productis a substitute. The reason is that the firm takes into account that after theintroduction of the new product the revenue generated by one unit ofcapital stock of the established product will decrease. This reduces thevalue of the capital stock already before the new product arrives.Hence, the firms invest less in mode m1 compared to the no-innovationbenchmark. Due to this underinvestment the price of the establishedproduct moves closer to the monopoly price and the instantaneouspayoffs of both firms go up compared to the no-innovation benchmark.

0 2 4 6 80.080

0.085

0.090

0.095

0.100

0.105

t

CoopB

CoopA FF 11 =

CoopB

CoopA FF 11 =

CompB

CompA FF 11 =

CompB

CompA FF 11 =

b)

ration (blue) andR&Dcompetition (purple) for η=0.5 (solid) and η=−0.5 (dashed). Theces to color in this figure legend, the reader is referred to the web version of this article.)

532 H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

If the new product is a complement to the established product, itsanticipated introduction has a positive effect on the value of theestablished product's capital stock. Therefore, firms invest more (priorto the new product introduction) compared to the no-innovationbenchmark. This leads to lower prices and lower instantaneous payoffs.

Comparing the dynamics under R&D competition and R&D coopera-tion we see that the size of the anticipation effect in mode m1 is largerunder R&D cooperation than under competition. The reason is thatunder R&D cooperation the change of the value of the establishedproduct's capital stock due to the anticipated innovation is larger. Inthe case of substitutes we get a larger reduction in the value for thefollowing two reasons. First, under R&D cooperation both firms intro-duce the new product at τcoop. This implies a stronger price decreasefor the established product compared to R&D competition. In the lattercase only one firm introduces the new product at the time when thenew product first reaches the market. Second, under R&D cooperationfor each firm the expected time until it introduces the new product islower than under competition. Once the firm offers both products, thevalue of the established product's capital stock further decreases dueto a cannibalization effect. Analogous arguments show that in the caseof complements the overinvestment is larger under R&D cooperationbecause the value of the established product's capital stock increasesmore under R&D cooperation compared to R&D competition. It shouldbe noted that the presence of synergies enhances the difference in thesize of the anticipation effect between the cases of R&D cooperationand R&D competition, because the expected time to the new productintroduction is then shorter under R&D cooperation.

For complements this results in lower payoffs under cooperation inmode m1, whereas for substitutes it is the other way round. As canalso be seen in Fig. 3, the size of the anticipation effect and of theresulting difference between R&D cooperation and competition is largerfor complements than for substitutes.

4.1.2. Synchronization effectAn important implication of R&D cooperation is that the intro-

duction of the new product is synchronized among the two firms. Werefer to this as the synchronization effect. It implies that immediatelyafter the innovation there is duopolistic competition also on the marketfor the new product. Under R&D competition there is always a timeinterval where only one firm is active on the new market. During thisinterval the innovator is gaining a relatively high payoff due to itstemporary monopoly position with respect to the new product. Thelaggard, however, is worse off than it would be in a situation whereboth firms introduce the new product simultaneously. Ex-ante firmsdo not know which will be the first innovator. However, the expectedmarket profit (net of capital adjustment costs) under R&D competitionin the time interval between the two innovation times is higher thanin the duopolistic scenario under R&D cooperation. This is an

η

compf ,SS3

compf ,SS2

coopf ,SS4

compf ,SS3

compf ,SS2

FF

FFF 2

+−+

Fig. 4. Difference between average instantaneous payoffs in the steady state of modesm2/m3 under R&D competition and the steady state of modem4 under R&D cooperation.

implication of the fact that industry profits are larger under monopolythan under duopoly. Fig. 4 illustrates this observation. It compares theaverage instantaneous payoff of a firm in the steady states of modesm2 and m3 with its payoff in the steady state of mode m4. It should benoted that in the steady state no capacity investments occur, whichmeans that investment costs are irrelevant. It can be clearly seen thatin the considered range of the degree of horizontal differentiationindeed the average payoff in the steady states of the asymmetricmodes under R&D competition is larger than the steady state payoff inmode m4, where both firms offer the new product. Furthermore, therelative difference increases as η becomes smaller.

4.1.3. Adjustment cost effectThe adjustment cost effect arises from the difference in the capital

adjustment patterns between the two R&D scenarios.Figs. 5 and 6 show the equilibrium dynamics of the four capital stocks

with R&D competition and R&D cooperation, respectively, under theassumptions that innovations occur exactly at their expected time. Incase of R&D competition we assume that firm A is the first innovator.

Focusing first on the case where the two products are substitutesit can be seen that under R&D competition the innovator reducesinvestment in the established product after the new product isintroduced. Also the innovation laggard does so directly after theintroduction of the new product. This is caused by the increasedcompetition on the market, since the introduction of the new productreduces the price of the established product for a given quantity. Theinnovator has an additional incentive to reduce quantities of theestablished product, because this increases the price of thenewproduct.Once the new product is also introduced by firm B (tNτB), capital stocksquickly converge to the symmetric steady state. Due to the absence ofvertical differentiation (θ=0) the steady state levels of both productscoincide. It should be noted that the dynamics of the capital stocks offirm A have a non-monotonic pattern. During the period where thisfirm is the only producer of the new product (τA b t b τB), it increasesits capacity for the new product and decreases that of the establishedproduct. After the introduction of the new product by firm B, exactlythe opposite dynamics arise. Firm A reduces K2A and increases K1A.This is a reaction to i) the increase in new product capacity of itscompetitor, which reduces the price of the new product, and ii) thedecrease ofK1B, which provides incentives for firmA to expand capacityon the establishedmarket. In thisway the sequential introduction of thenew product by the two firms creates an overshooting pattern ofproduction capacities of firm A.7

Comparing this overshooting pattern with the capacity dynamicsunder R&D cooperation (see Fig. 5(b)) we observe that, contrary tothe case of R&D competition, under cooperation there is no over-shooting of capacities and all capital stocks approach the long runsteady state in a monotonic way. Consequently, total capital adjust-ments costs are smaller under R&D cooperation.

In the case of complements, the introduction of the new producttriggers an increase in the capacity investments of the establishedproducts. This is because the introduction of the new product createsadditional demand for the established product. The symmetric steadystate reached after the introduction of the new product by firm B inthis case induces a larger capacity for the established product than inthe no-innovation benchmark. Like in the case of substitutes, underR&D competition overshooting occurs with respect to the capital stocksof the innovator firm A. In the complements case the capacities for bothproducts increase between τA and τB and then decrease after theintroduction of the new product by firm B. Under R&D cooperation no

7 It should be noted that the observed overshooting effect is not an implication of ourassumption that firms always produce up to capacity. Actually, the overshooting effectwith respect to outputwould be even stronger ifwe drop this assumption, because in sucha scenario firm A could reduce quantities without incurring additional adjustment costsafter the new product has been introduced by firm B.

t

AK2

BK2

AK1

BK1

NoInnovK1

Aτ Bτ

t

BA KK 11 =

BA KK 22 =

NoInnovK1

coopτ(b)(a)

Fig. 5. Equilibrium dynamics of the four capital stocks under (a) R&D competition and (b) R&D cooperation if the new product is a substitute.

t

AK2

BK2

AK1

BK1

NoInnovK1

Aτ Bτ

t

BA KK 11 =

BA KK 22 =

NoInnovK1

coopτ(b)(a)

Fig. 6. Equilibrium dynamics of the four capital stocks under (a) R&D competition and (b) R&D cooperation if the new product is a complement.

η

∗λ

compλ2

Fig. 7. The threshold value λ⁎ for varying degree of horizontal differentiation.

533H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

such overshooting occurs. For this reason also if the new product iscomplementary to the established one, expected capital adjustmentcosts are larger in the R&D competition case.

4.1.4. Adding up the effectsConsidering Fig. 2 we conclude that the synchronization effect (plus

the anticipation effect in case of complements), which favors R&Dcompetition, is dominant. Avoiding synchronization of the time of theintroduction of the new product enhances expected market profits toa sufficient degree so that the extra adjustment costs are more thancompensated. Consequently, firms should decide for R&D competitionin the absence of synergies.

4.2. Impact of R&D synergies

In the discussion so far itwas assumed that R&D cooperation does notgenerate any synergies in the sense that the expected time until the newproduct can be first introduced to the market is the same under R&Dcooperation and R&D competition. As mentioned in the Introduction,empirical work suggests that cooperation between different firms inthe market might lead to synergies in the R&D activities of these firms.In our model positive synergies are captured by assuming thatλcoopN2λcomp holds. In the case of such positive synergies, a fourth effectis added to the three effects just discussed. Under synergies the expectedtime span until the first introduction of the newproduct is shorter underR&D cooperation and hence firms expect the corresponding increase intheir instantaneous payoffs to occur earlier. This makes R&D cooperationmore attractive. We refer to this effect as the synergy effect.

To explore this issue more deeply, we define by λ⁎ the minimalvalue of the innovation arrival rate such that the firms' value func-tions under R&D cooperation exceed that of R&D competition for all

λcoop≥λ⁎. In Fig. 7 this threshold value is depicted for varying degreesof horizontal differentiation and compared to the value 2λcomp

corresponding to no synergies. Consistent with our discussion above,we observe that for all values of η apart from the extreme degrees ofdifferentiation positive synergies are needed to make R&D cooperationattractive. Since the payoff increase resulting from the introduction ofthe new product is larger for complements than for substitutes, thesynergy effect is more pronounced for negative values of η. Hence, asconfirmed in the figure, particularly high synergies are needed if thetwo products are (not too strong) substitutes. The reason that onlyweak synergies are needed to make R&D cooperation attractive in thecase of close substitutes is that in such a scenario the synchronizationeffect becomes very small. The sole producer of the new product has

η

∗λ

04.0=r

1.0=rcompλ2

η

∗λ5=c

10=c

compλ2

(b)(a)

η

∗λ

0=θ

2.0=θ

compλ2

(c)

Fig. 8. Effect of the changes (a) in the discount rate, (b) in the capital adjustment cost parameter, and (c) in the vertical differentiation parameter on the arrival rate threshold λ⁎.

8 For the welfare comparison we employ the discounted welfare stream

W ¼Z ∞

0e−rt U K1A þ K1B;K2A þ K2Bð Þ−b1 I1A þ I1Bð Þ− c

2I21A þ I21B�

−b2 I2A þ I2Bð Þ− c2

I22A þ I22B� h i

dt;

where

U Q1;Q2ð Þ ¼ Q1 þ 1þ θð ÞQ2−12Q2

1−12Q2

2−ηQ1Q2

is the standard Dixit-Stiglitz utility function giving rise to a linear demand system.

534 H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

very little market power because the new product is almosthomogeneous to the established one. The relatively low values of λ⁎for values of η close to −1 are due to the strength of the adjustmentcost effect in the case of strong complements.

4.3. Robustness

Our discussion of the different qualitative effects resulting from thechoice between R&D cooperation and R&D competition has beenbased on a particular parameter constellation. It is important to checkrobustness of the qualitative statements with respect to variations ofthe key parameters of the model. Such a sensitivity check has beencarried out and to illustrate the robustness of our results we depict inFig. 8 the changes in the λ⁎ curve if the discount rate, the capitaladjustment cost parameter and the degree of vertical differentiation isvaried. A more extensive discussion of the robustness of our findingsis provided in Appendix B.

It can be seen that the qualitative features of this curve, in particularthe inverse U-shape and the requirement for positive synergies foralmost the entire range of η values, stay intact. The fact that higherdiscounting moves the curve downwards can be explained by theincreased relevance of the synergy effect. The expected reduction ofthe arrival time of the innovation caused by an increase of the arrivalrate is valued more if the discount rate is higher. Hence, a smalleradvantage with respect to the arrival rate is needed to make R&Dcooperation as attractive as R&D competition. Also an increase in thecapital adjustment costs leads to a downward shift of the curve, becausethe adjustment cost effect, which favors R&D cooperation, becomesmore pronounced. Finally, it can be seen that an increase in the levelof vertical differentiation of the new product does not seriously affectthe threshold value λ⁎. Increasing θ implies that the innovative productbecomes more profitable. This benefits both R&D cooperation and R&Dcompetition such that the difference between the two modes is notaffected in a significant manner.

4.4. Welfare effects

To conclude our analysis we briefly consider the welfare8 implica-tions of R&D cooperation. Intuition suggests that at any point in timein mode m1, prior to the introduction of the new product, an increaseof the total quantity of the established product, relative to the no-innovation benchmark, is welfare-enhancing. The deviation of theoutput from the no-innovation benchmark in m1 stems from theanticipation effect and, as discussed above, this effect is strongerunder R&D cooperation than under R&D competition. If the newproduct is a substitute of the established one, this reasoning impliesthat R&D cooperation has a negative effect on (instantaneous) welfare,whereas R&D cooperation is welfare-enhancing if the new product is acomplement. Considering the modes after the innovation, it is easy tosee that welfare in modes m2 and m3, where only one firm offers bothproducts, is smaller than in mode m4, where both firms offer bothproducts. This is due to larger total output and smaller capacityadjustment costs in mode m4. Since R&D cooperation leads to a directtransition fromm1 tom4, (instantaneous) welfare after the introductionof the new product is always larger under R&D cooperation than underR&D competition. These qualitative statements have been confirmed bynumerical analysis. This analysis also shows that for the parametersettings considered above, in the case of substitutes the negativewelfare effects of R&D cooperation prior to innovation is dominated

535H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

by the positive effects after innovation such that also in the absence ofsynergies the discounted welfare stream under R&D cooperation islarger than under competition regardless of the degree of differentia-tion. In case of complements R&D cooperation increases welfare beforeand after the innovation. Therefore, also in the complements case theeffect of R&D cooperation on the discounted welfare stream is clearlypositive.

5. Conclusions

This paper analyzes the interplay between capacity dynamics andtechnological progress in an oligopolistic market. We focus on productinnovation and study how anticipated and actual introduction ofnew products influencemarket dynamics. In particular, we characterizethe implications of R&D cooperation in product innovation on theinvestment behavior of established firms in an industry. We identifythree effects, which influence the relative profitability of R&D coop-eration: the anticipation effect, the synchronization effect, and theadjustment cost effect. We show that the sign and the size of theseeffects depend on the degree of product differentiation. We find that,although R&D competition is associated with overshooting of thecapacity dynamics for both products and, in case of substitutes, alsoleads to smaller firm profits than R&D cooperation prior to theinnovation date, still firms prefer not to cooperate in R&D in the absenceof sufficiently strong synergy effects. Given that R&D cooperation ispreferable from a welfare perspective, these insights call for policymeasures stimulating R&D cooperation.

The present paper discusses a framework where the two firmsare completely symmetric. It is therefore worthwhile to discuss theimplications of asymmetries, in particular, the case where one of thefirms has a greater potential to innovate. In such a scenario it is expectedthat the incentive to cooperate is smaller for the firm with the largerarrival rate for the innovation, because it is likely that this firm willcapture the temporary monopoly position when firms compete inR&D. This makes the synchronization effect stronger for that firm. Anextreme case of asymmetries, where one of the incumbents has anarrival rate of zero is analyzed in Dawid et al. (2010).

In order to concentrate the analysis on capacity investment dyna-mics we have assumed in this paper that innovation arrival rates areexogenously given. Therefore, an important extension is to introduceknowledge stocks of the firms into the analysis, which can be increasedby R&D investments, and to assume that arrival rates depend onknowledge stocks (see e.g. Doraszelski (2003)). Since such a formula-tion leads to a differential game which does not have a linear quadraticstructure, numerical methods like collocation will have to be employedin such an analysis. An important issue that can be addressed in such asetting is the impact of market share on the established market on theincentives to invest in product innovation.

Finally, it would be interesting to analyze the impact of the numberof firms being active in the established market. In such a context theimplications of different types of R&D networks on firm profitabilitycould be analyzed under the assumption that firms follow Markov-perfect equilibrium behavior. We leave this as an interesting topic forfuture research.

Appendix A. Definition of a Markov-perfect equilibrium

We define by I the set of all piecewise continuous9 functions from0;K1� �2

× 0;K2� �2

×M to R . Note that due to the fact that we have a

9 In the considered model the restriction of attention to piecewise continuous feedbackstrategies turns out to be innocuous. For standard capital accumulation games withconvex investment costs there exist MPEs with continuous feedback strategies (seeDockner et al. (2000)). This suggests that in our setting MPEs exist where the jumps inthe optimal controls occur only at points in time where the mode of the game changes.

multi-mode game, a Markovian feedback strategy has to depend onthe current states and the current mode. The strategy space of eachfirm is then given by I2.

Defining a Markov-perfect equilibrium in a multi-mode game is notcompletely standard. For a given strategy profile IiB

� i¼1;2

we denote as

PA the (stochastic) optimal control problem firm A faces if the feedbackrules I1B; I2B

� are inserted for (I1B,I2B). Note that after insertion of these

strategies, the right hand side of the state dynamics depends on themode m(t). We define Ξ as the set of all possible realizations of therandom innovation time. Hence in the case of R&D competition wehave Ξ=[0,∞)2, whereas under R&D cooperation Ξ=[0,∞). FollowingDockner et al. (2000) we call a control path uf ¼ u1 f ;u2 f

� �: 0;∞½ Þ×Ξ→

R2, where f∈ {A,B}, feasible if

(i) uf is non-anticipating with respect to the realization of theproject completion time. In the case of R&D competition thismeans that uf t; τA; τBð Þ ¼ euf tð Þ∀tbmin τA; τB½ �;uf t; τA; τBð Þ ¼ euf

t; τAð Þ , for τA =min[τA,τB] and t∈ [τA,τB) and uf t; τA; τBð Þ ¼ euf

t; τBð Þ for τB = min[τA,τB] and t ∈ [τB,τA) for some euf :ð Þ .Analogously for R&D cooperation;

(ii) the piecewise deterministic process (K1A(.), K1B(.), K2A(.), K2B(.),m(.)) is well-defined;

(iii) the constraintsKif≥0 and investment constraints (3) are satisfiedwith probability 1,

(iv) the objective integral is well-defined.

A feasible control path uA∗ is optimal if it maximizes the objective

integral within the set of all feasible control paths. Analogously wedefine the optimal path uB

∗ .

Definition 1. A strategy profile I∗1A; I∗2A; I

∗1B; I

∗2B

� �∈I4 is aMarkov-perfect

equilibrium (MPE) of the game if the following condition holds for eachfirm f=A,B:

• If the feedback strategies (I1f∗ ,I2f∗ ) are applied to the control problem P f

determined by inserting (I1g∗ ,I2g∗ ), g≠ f, then the resulting (stochastic)investment path (I1f∗ (K1A(t;τ), K2A(t;τ), K1B(t;τ), K2B(t;τ), m(t;τ)),I2f∗ (K1A(t;τ), K2A(t;τ), K1B(t;τ), K2B(t;τ), m(t;τ))) coincides with theoptimal path uf

∗(t,τ) with probability 1, where τ = (τA,τB) underR&D competition and τ=τcoop under R&D cooperation.

Appendix B. Robustness checks

To check in how far the shape of the λ⁎-curve is robust with respectto parameter changes other than those considered in Section 4.3 and toverify that the discussed shifts of the λ⁎ curve triggered by parametervariations are not specific to the default set of parameters used inSection 4, in this appendix we reproduce Fig. 8 for two additionalparameter settings. In Fig. 9 the chosen base parameter setting is

λcomp ¼ 0:05; θ ¼ 0:2; b1 ¼ b2 ¼ 0; c ¼ 5; r ¼ 0:04; ð12Þ

whereas in Fig. 10 we use

λcomp ¼ 0:05; θ ¼ 0; b1 ¼ b2 ¼ 1; c ¼ 3; r ¼ 0:04: ð13Þ

In both cases we again consider the effects of variations of theparameters r, c and θ. As can be clearly seen, the qualitative findingsreported in Section 4 are very robust with respect to the choice ofdifferent base parameter settings.

-0.95 -0.5 0.5 0.95

0.1

0.15

η

∗λ

04.0=r

1.0=r

compλ2

-0.95 -0.5 0.5 0.95

0.1

0.15

η

∗λ3=c

6=c

compλ2

(b)(a)

-0.95 -0.5 0.5 0.95

0.1

0.15

η

∗λ

2.0=θ

0=θ

compλ2

(c)

Fig. 10.Effect of the changes (a) in thediscount rate, (b) in the capital adjustment cost parameter, and (c) in the vertical differentiation parameter on the arrival rate thresholdλ⁎under thebase parameter setting (13).

-0.95 -0.5 0.5 0.95

0.1

0.15

η

∗λ

04.0=r

1.0=rcompλ2

-0.95 -0.5 0.5 0.95

0.1

0.15

η

∗λ5=c

10=c

compλ2

(b)(a)

-0.95 -0.5 0.5 0.95

0.1

0.15

η

∗λ

4.0=θ

2.0=θ

compλ2

(c)

Fig. 9. Effect of the changes (a) in the discount rate, (b) in the capital adjustment cost parameter, and (c) in the vertical differentiation parameter on the arrival rate thresholdλ⁎ under thebase parameter setting (12).

536 H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

537H. Dawid et al. / International Journal of Industrial Organization 31 (2013) 527–537

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