Knowledge Sharing and Competition in a Bio-tech Consortium

Transcription

1 Knowledge Sharing and Competition in a Bio-tech Consortium Hervouet Adrien Trommetter Michel March 17, 2017 Very Preliminary Abstract This article deals with a current research project, namely the Amaizing project. The goal of this research project is to create an innovation process in biotechnology. In this aim, rms must share their knowledge. However, private rms are not only in a cooperative framework but also in competition on the market and knowledge sharing increases spillover eects. Indeed, if a rm shares its knowledge it takes the risk that their competitors will develop a new variety that could compete strongly its own product. Therefore, there is a tradeo between the value of the innovation obtained by the research project and the intensity of competition. Furthermore, a wide heterogeneity between rms in this sector exists. Indeed, some of them compete internationally whereas others only locally. As a consequence their expectations and their actions could be dierent. A theoretical model is developed where rms, in a rst stage, choose whether they share their knowledge and, in a second stage, compete in a Cournot duopoly. The model shows that a high competition between rms decreases the knowledge sharing and large rms keep knowledge sharing with higher competition than small rms. Key words: Knowledge sharing, R&D cooperation, Horizontal Dierentiation, Spillovers Speaker and corresponding author, GAEL, INRA, CNRS, Grenoble INP, Univ. Grenoble- Alpes, 38000, Grenoble, France, Tel.: , adrien.hervouet@grenoble.inra.fr GAEL, INRA, CNRS, Grenoble INP, Univ. Grenoble-Alpes, 38000, Grenoble, France, michel.trommetter@grenoble.inra.fr 1

2 1 Introduction Innovation is crucial for many rms to create new products and preserve their market share, but it is also expensive and uncertain. To minimize risks and costs associated with innovation, rms can cooperate during the R&D stage. The advantages of cooperation are abundant, particularly rms in cooperation are able to share R&D cost, knowledge and cooperation can lead to commercializing inventions. Moreover spillover increases with cooperative behavior (Branstetter and Sakakibara, 2002; Gomes-Casseres et al., 2006). As a consequence, a rise of R&D cooperation appears during 90s and they stay currently widespread (Hagedoorn, 2002; Letterie et al., 2008; Tomasello et al., 2016). Furthermore, public authorities promote also public and private cooperation in R&D. Indeed, private rms are able to turn public laboratory and university discoveries into commercializing applications. In the biotechnology sector, plant variety creation plays a key role. Indeed, it provides a considerable contribution to the agricultural sector by improving yields, reducing losses coming from pests and diseases, reducing consumption of water and chemical products and also meeting the food industrial expectations in terms of characteristics provided by crops (e.g. the quality of the our from dierent variety of wheat). In this paper, a particular and current research project is analyzed, namely the Amaizing Project. This project incorporates public laboratories and eight private companies in biotechnology, essentially rms specialized in plant variety innovation. The research project has a main goal: provide a process innovation useful for private companies. This innovation will allow private rms to create new varieties of maize that will resist to cold temperature and consume less water and nitrogen. In this aim, private rms should not just share their R&D cost but also their genetic resources and the result of dierent experimentations. Indeed, the more private rms share their knowledge, the more the innovation provided by the research project will be signicant. In fact, this project need the largest number of genetic resources to be ecient. In France, similar consortium exist such as Breedwheat, Rapsodyn and Peamust where knowledge plays also a key role. Internationally, 2

3 the non-prot organization International Service for the Acquisition of Agri-Biotech Application (ISAAA) creates public/private partnership with knowledge sharing to develop agriculture in developing countries. More generally, knowledge sharing is crucial in many collaboration in high-tech industries (Samaddar and Kadiyala, 2004). However, private rms are rarely only in a cooperative framework but also in competition on the market and knowledge sharing increases spillover eects. Indeed, if a rm shares its knowledge it takes the risk that their competitors will develop a new variety that could compete strongly its own product. Therefore, there is a tradeo between the value of the innovation obtained by the consortium and the intensity of competition. Furthermore, a wide heterogeneity between rms in this sector exists. Indeed, some of them compete internationally whereas others only locally. As a consequence their expectations and their actions could be dierent. Transnational companies require less this research project than local rms. Actually, local rms have more diculties to invest in biotechnology than transnational companies due to the high cost of R&D. In fact, rms in bio-tech spend more than ten percent of their revenues in R&D. Therefore, a rm with a higher market share has a great advantage to conduct R&D compared to her rivals. In parallel, if an international company obtains technologies of a small company, there is a risk that she could monopolize the whole market share of the small company. Consequently, small companies could also hesitate to share their knowledge. Thus, two problematics emerge of this consortium: - Does the risk of a higher competition deteriorate the knowledge sharing that is crucial for R&D collaboration? - What is the impact of an asymmetry in the size of bio-tech rms on knowledge sharing? Our research questions are linked to the literature on R&D cooperation and knowledge sharing. Many authors, study these problematics starting with Katz (1986) and d'aspremont and Jacquemin (1988). They modeled R&D cooperation 3

4 in a Cournot framework where in a rst stage, rms cooperate by maximizing the joint prot for the choice of R&D and, in a second stage, rms compete by maximizing their own prot for the commercialization of their products. The spillover plays a role by lowering the production cost. D'Aspremont and Jacquemin (1988) nd that, with few rms and high spillovers, R&D cooperation is interesting for rms. Katz (1986) shows that high competition decreases eective R&D whereas strong spillover increases eective R&D. Moreover, when the R&D plays a role on the output, cooperation could reduces incentives to conduct R&D because it helps its rivals. Dierent authors improved this elds by introducing asymmetry, dynamics, absorptive capacities and knowledge (Katz and Ordover, 1990; Kamien et al., 1992; Motta, 1992; Suzumura, 1992; Ziss, 1994; Salant and Shaer, 1998; Petit and Tolwinski, 1998, Cellini and Lambertini, 2009; among others). In this literature an interesting paper for the problematics highlight above is Sakakibara (2003). He integrates in the model of d'aspremont and Jacquemin (1988), beside the R&D eort, complementary knowledge as Cohen and Levinthal (1989). Before the maximization of the prot by the R&D eort and quantities, competitors has to choose the level of the knowledge sharing ratio. The model suggests that cooperation when rivals control complementary knowledge increases the endogenous spillover ratio and R&D eorts. In all this elds, spillover does not play a direct role on the degree of competition what is crucial for questions presented above. An original modeled, initially developed by Samaddar and Kadiyala (2004) and modied by Ding and Huang (2010), takes into account the R&D eort and the knowledge sharing. They also made a dierence between current research creation and prior knowledge. Unlike the previous articles, competitors are in a Stackelberg framework, with a leader and a follower, for the decisions of the R&D eort and the knowledge sharing. However, in this theoretical model, the stage of competition does not exist. The main result of these two articles is that leader would participate only if it marginal gain is high enough comparing to the elasticity of current research creation. 4

5 Network theory is an other eld working on cooperative R&D. Goyal and Gonzales (2001) and Goyal and Joshi (2003) build a theoretical model with a Cournot competition where R&D and spillovers reduce the unit cost as D'Aspremont and Jacquemin (1988). They highlight that, in a Cournot competition with homogeneous goods, R&D eort is negatively inuenced by cooperation. In this literature, empirical works try, in particular, to test whether similarity between rms increases cooperative behavior. Cantner and Graf (2006), Hanaki et al. (2010) and Tomasello et al. (2016) use patent statistics to test the eect of similarity. Cantner and Gra (2006) employ citation data and found a positive eect. Tomasello et al. (2016) obtain also a positive impact but they use categories of patent (IPC classication) instead of citations. Conversely, Hanaki et al. (2010) nd a negative eect with subcategories of patents. This dierent result can be from an issue with the variable of similarity in these articles. Indeed, two rms can have many similarities and then obtain patents in the same category. Simultaneously, these two rms may produce complementary outputs and would not compete in the same market. For example, in bio-tech sector, a rm can innovate on the genome and sell directly this innovation to the other rm that will create a new variety of crop. Therefore, the incentives to cooperate would be important. Nevertheless, these two rms could produce substitutes products and then compete in the same market. In this situation, rms have probably less incentives to cooperate because higher spillovers involve by cooperation could increase competition. To address the highlighted problematics, a theoretical model is developed where two rms work together in a R&D cooperation. In the rst stage they have to choose whether they share their knowledge. In the second stage, they compete in a Cournot duopoly. To represent the intensity of competition between these two rms, plant varieties are not perfectly homogeneous. The innovation provided by the research project allows bio-tech rms to create a new variety that requests less water and less chemical products to grow up. Therefore, the cost for farmers is decreasing and, as a consequence, their willingness to pay for these varieties rise. Thus we assume that the innovation increases the demand. The level of the innovation depends on the 5

6 knowledge sharing. The highest level of innovation occurs when both rms share their knowledge. If only one rm shares her knowledge, the level of the innovation is lower and the lowest level arises when both rms do not share their knowledge. At the same time, we assume that spillovers, implied by sharing knowledge, involve two eects. In fact, sharing knowledge brings the risks that competitor can include one technology of the other rm in its products. As a consequence, there is more similarity between both products and then more competition. Simultaneously, this technology can be sought by new farmers. Therefore, spillovers involve a positive impact by increasing the demand and a negative impact by raising the competition. If only one rm shares her knowledge, this rm will face more competition without an higher demand because she will not obtain the competitor technology whereas its competitor will access to a greater demand 1. The theoretical model shows two interesting results. The more the competition is, the less competitors share their knowledge. In fact, if two rms are in high competition there will not be enough incentives for them to share their knowledge than two rms nearly monopolist. An example of this result on bio-tech rms specialized in plant variety creation is Limagrain and KWS. These two rms cooperate more intensively in the North American market where they were not in competition with the creation of a joint venture (AgReliant). Furthermore, we found that a large rm keeps knowledge sharing with higher competition than a small rm. Indeed, transnational rms can cannibalize local rms whereas local rms have not such power on transnational rms. As a consequence, knowledge sharing is riskier for 1 To give an other explanation of our assumption an example can be made where two varieties have dierent characteristics. Plant variety 1 has characteristics a, b and c whereas plant variety two has c, d and e. If both rms share their knowledge, they can grab a characteristic of the plant variety of the competitor to insert it into their own plant variety. Therefore, after the research project, the plant variety 1 resist to pest a, b, c and d and the plant variety 2 resist to pest b, c, d and e. The two plant varieties becomes more homogeneous than before, as a consequence, the competition becomes stronger because more farmers are indierent between plant varieties one and two (negative spillover). Simultaneously, plant variety one and two has more characteristics, then more farmers can be interested by these varieties at a higher value (positive spillover). If only one rm shares its knowledge, the plant variety of this rm will not obtain a characteristic of the plant variety of the competitor whereas the plant variety of the competitor will capture one more characteristic (eg. a, b, c and d vs. c, d and e). Therefore, the competition will increase for both varieties but at a lower level and only the rm that do not share its knowledge will obtain an higher demand. 6

7 a small entity than a large entity in our framework. Lastly, the positive and the negative spillovers have negative impacts on the knowledge sharing because they incites rms to let only competitors share their knowledge. The paper is organized as follows. In section 2 the model is presented. Section 3 shows the results of the model when rms are similar. Section 4 explores the impacts of heterogeneous rms. Section 5 concludes. 2 The Model We consider a two-step model with two types of agent: two mono-product bio-tech rms and risk neutral farmers. In the rst step both rms choose whether they share their knowledge. The knowledge sharing provides useful resources that make it possible to create an interesting innovation. If both rms share their knowledge, the value of the innovation is given by the parameter ω. The innovation parameter increases the demand through the willingness to pay of farmers. If only one rm shares her knowledge, then the value of the innovation will be ω 2 = ω 2 2. When not any of rms decide to share their knowledge the value of the innovation is normalized to zero such that ω 3 = 0. The parameter ω will increase the demand of farmers. Furthermore, knowledge sharing involves two spillovers: a negative one increasing the competition, δ, and a positive one increasing the demand of farmers, λ. Compare to d'aspremont and Jacquemin (1988) spillovers are not coming from R&D investment and do not aect the unit cost of production. Here, we call spillovers the externalities provided by sharing a part of the prior knowledge 3. For competitors, sharing prior knowledge could increase the degree of competition between rms for the reason that a competitor could use this knowledge to compete stronger the sharing rms in her demand segment. Inversely, the innovation, ω, will have similar impacts 2 A later discussion will be held in the paper on the impact of an higher or a lower value of ω 2 3 As explained by Samaddar and Kadiyala (2004) there is a dierence between prior knowledge and current knowledge. Current knowledge is provided by the R&D cooperation (the innovation) whereas prior knowledge is the stock of knowledge provided by rms (a knowledge created before the collaboration). Samaddar and Kadiyala (2004) show examples of R&D cooperation becoming useless due to the lack of cooperation in the sharing of prior knowledge. 7

8 in the following theoretical model than the model of d'aspremont and Jacquemin (1988). Indeed, the eect of an innovation reducing the unit cost or increasing the demand has the same consequences (Spence, 1984). After the choice of sharing knowledge, rms will compete in a Cournot duopoly with dierentiated goods. To represent this heterogeneity, we assume that the goods are not perfect substitutes, the level of substitution between both goods is γ. We dene a quadratic utility function for farmers as Singh and Vives (1984) U = α 1 q 1 + α 2 q 2 (β 1 q β 2 q γq 1 q 2 )/2, (1) which leads to a linear demand system p 1 = α 1 β 1 q 1 γq 2, (2) p 2 = α 2 γq 1 β 2 q 2 The farmers surplus will be CS = U p 1 q 1 p 2 q 2, the rm prot Π i = p i q i c i q i and the welfare is the addition of the consumer surplus and the rm prots W = CS + 2 i=1 Π i. To obtain positive demand and to the problem makes sense we assume, as Singh and Vives, that α i > 0, β i > 0, β 1 β 2 γ 2 > 0 and α 1 β 2 α 2 γ > 0. Notice that with γ > 0, goods are substitutes but if γ = 0 then both rms become monopolist. Moreover, if γ < 0 goods turn into complementary and if γ = β 1 = β 2 they would be perfect substitutes. In order to obtain the most proper resolution possible, we made some simplication. Elasticity parameters, β i, are normalized to unity 4. Consequently, equilibrium quantity and price will be equal and the constraint on γ becomes γ ]0, 1[ (non perfect substitutes). Moreover, the only dierence between rms will be the market size parameter α i. Unit costs, c i, are normalized to zero. In fact, in this sector (plant variety creation), each rm has a similar unit cost because they all have to comply with the regulation (commercial rules, norms,...) on the specicity of each new and 4 This simplication will not have an impact on the further main results of the paper. 8

9 old products. Lastly, we assume that the xed cost to develop the innovation in the cooperation is equally shared between partners and is normalized to zero 5. Thus, the return on investment is always positive whatever the level of the R&D xed cost. As a consequence, the welfare will be simply equal to the farmers utility (W = U). The model is resolved by backward induction. Thus, we rstly resolved the Cournot competition. To be done, parameters involved by the sharing knowledge activity have to be added to the farmers utility and inverse demand. Actually, four situations are possibles - case A: both rms share their knowledge, - case B: only rm 2 shares her knowledge, - case C: only rm 1 shares her knowledge, - case D: no one shares its knowledge. In case A, the innovation, ω, and the positive spillover, λ, provided by the sharing knowledge increase the market size respectively by raising the willingness to pay and the number of farmers interested by this product. Moreover, the negative spillover, δ, increases the degree of competition represented by the degree of substitutability. Therefore, farmers utility and inverse demands are U A = (α 1 + ω + λ)q 1 + (α 2 + ω + λ)q 2 (q q (γ + δ)q 1 q 2 )/2, p A 1 = α 1 + ω + λ q 1 (γ + δ)q 2, p A 2 = α 2 + ω + λ (γ + δ)q 1 q 2, (3) where (γ + δ) ]0, 1[. In case B only the rm two shares her knowledge. Thus, the consortium obtains a lower innovation, ω, than in case A. Moreover, the positive 2 spillover plays only a role on the demand of the rm one because rm two are not able to use the knowledge of rm one to increase her own demand. The negative spillover continues to exist for both rms but at a lower level, we assume that is divided by two ( δ ), than in case A. Indeed, even if only rm two gives her knowledge, the 2 larger substitutability between products plays for both rms. Thus, farmers utility 5 In the Amaizing consortium, private companies nance it to similar amounts. 9

10 and inverse demands become U B = (α 1 + ω 2 + λ)q 1 + (α 2 + ω 2 )q 2 (q q (γ + δ 2 )q 1q 2 )/2, p B 1 = α 1 + ω 2 + λ q 1 (γ + δ 2 )q 2, p B 2 = α 2 + ω 2 (γ + δ 2 )q 1 q 2, (4) where (γ + δ ) ]0, 1[. The case C is symmetric to the case B. Farmers utility 2 and inverse demands are given by U C = (α 1 + ω 2 )q 1 + (α 2 + ω 2 + λ)q 2 (q q (γ + δ 2 )q 1q 2 )/2, p C 1 = α 1 + ω 2 q 1 (γ + δ 2 )q 2, p C 2 = α 2 + ω 2 + λ (γ + δ 2 )q 1 q 2. (5) In Case D, there is no longer knowledge sharing. Therefore, all parameters involved by the knowledge sharing are equal to zero. We can write farmers utility and inverse demands as U D = α 1 q 1 + α 2 q 2 (q q γq 1 q 2 )/2, p D 1 = α 1 q 1 γq 2, p D 2 = α 2 γq 1 q 2. (6) In the rst step, rms have a perfect information on all equilibrium prices, quantities and prots for all cases. The non cooperative Nash game of knowledge sharing is reported in Table 1. Since rms are rational, perfectly informed and prot maximizing, they choose whether they share their knowledge according to the level of their prots. Table 1 Knowledge sharing game shares knowledge Firm 1 does not share knowledge shares Π A 1 Π B 1 Firm knowledge Π A 2 Π B 2 2 does not share Π C 1 Π D 1 knowledge Π C 2 Π D 2 10

11 The Table 2 summarizes all the parameters of the model that will be used in the following sections. Table 2 Parameters q j i p j i α i ω γ δ λ Quantity of rm i in case j Price of rm i in case j Market size (willingness to pay) value of the innovation degree of competition negative spillover (on competition) positive spillover (on demand) 3 Homogeneous Firms This section explores the impact of the innovation and spillovers involve by the knowledge sharing of two symmetric rms α 1 = α 2 = α. Results provided by the Cournot competition in step two are displayed in Table 3. In the Case A, where both rms share their knowledge, the innovation and the positive spillover increase equilibrium quantities, prices, prots, farmers surplus and the welfare. On the contrary, the negative spillover and the degree of competition have negative impacts. It could seem curious that a higher competition decreased the welfare. In fact, if both rms are in monopoly (γ = 0), then each rm has his own demand. When products become non perfect substitutes, the competition increases (γ > 0), simultaneously both rms can take a part of the demand of their competitor. A part of the demand of each rm is shared by both rms. Thus, the parameter of competition, γ, can not increase alone. Here, the positive and negative spillovers represent both impacts of a higher competition. Since rms one and two are symmetric, results of the Cournot competition are also symmetric for quantities and prot in the case B and C. Parameters keep the same inuence except for the positive knowledge. Indeed, equilibrium quantity and 11

12 price and the prot of the rm that share her knowledge decline with respect to the positive spillover ( qb 2 = 1 1 ). However, the positive spillover maintains λ 4+2γ+δ 4 2γ δ a positive impact on the farmers surplus and the welfare. Moreover, its positive inuence on the prots of the rm that does not share her knowledge is greater than in the case A ( qb 1 > qa 1 ). In other words, the rise of the prot in the case B for λ λ the rm 1 is sharper than in the case A. Table 3 Payos for similar rms q1 A q2 A Π A 1 Π A 2 CS A W A q1 C q2 C Π C 1 Π C 2 CS C 1 2 W C α+ω+λ q B 2α+λ+ω 2+γ+δ 1 + λ 4+2γ+δ 4 2γ δ α+ω+λ q B 2α+λ+ω 2+γ+δ 2 λ 4+2γ+δ 4 2γ δ (α+ω+λ) 2 Π B (2α(4 2γ δ)+ω(4 2γ δ)+8λ) 2 (2+γ+δ) 2 1 (4 2γ δ) 2 (4+2γ+δ) 2 (α+ω+λ) 2 Π B (2α(4 2γ δ) (2γ+δ)(2λ+ω)+4ω) 2 (2+γ+δ) 2 2 ( (4 2γ δ) 2 (4+2γ+δ) 2 ) (α+ω+λ)2 (1+γ+δ) CS B 1 (2α+λ+ω) 2 2(2α+λ+ω)2 + λ2 + 2λ2 (2+γ+δ) γ+δ (4+2γ+δ) 2 4 2γ δ (4 2γ δ) 2 (α+ω+λ)2 (3+γ+δ) W B (2α+λ+ω)2 + (2α+λ+ω)2 + λ2 λ 2 (2+γ+δ) 2 2(4+2γ+δ) (4+2γ+δ) 2 8 4γ 2δ (4 2γ δ) 2 2α+λ+ω λ q D α 4+2γ+δ 4 2γ δ 1 2+γ 2α+λ+ω + λ q D α 4+2γ+δ 4 2γ δ 2 2+γ (2α(4 2γ δ) (2γ+δ)(2λ+ω)+4ω) 2 Π D α 2 (4 2γ δ) 2 (4+2γ+δ) 2 1 (2+γ) 2 (2α(4 2γ δ)+ω(4 2γ δ)+8λ) 2 Π D α 2 ( (4 2γ δ) 2 (4+2γ+δ) 2 ) 2 (2+γ) 2 (2α+λ+ω) 2 2(2α+λ+ω)2 + λ2 + 2λ2 CS D α2 (1+γ) 4+2γ+δ (4+2γ+δ) 2 4 2γ δ (4 2γ δ) 2 (2+γ) 2 (2α+λ+ω)2 + (2α+λ+ω)2 + λ2 λ 2 W D α2 (3+γ) 2(4+2γ+δ) (4+2γ+δ) 2 8 4γ 2δ (4 2γ δ) 2 (2+γ) 2 In order to solve the rst step of the model, threshold values have to be found. These thresholds will indicate when a rm want to share her knowledge whether the other rm share also her knowledge. Knowing that rms are symmetric, thresholds are similar for rm 1 and 2. Therefore, the rst thresholds is for Π A 1 > Π B 1 and Π A 2 > Π C 2 such that rms want to share their knowledge when the other shares it λ < (4 2γ δ)((2 + γ)ω αδ) 4γ(2 + γ) + 4(2 + γ)δ + δ 2, (7) where the right hand side of this inequality is denoted λ 1. The second threshold is for Π C 1 > Π D 1 and Π B 2 > Π D 2 such that rms want to share their knowledge when the other do not λ < (4 2γ δ)((2 + γ)ω αδ) 2(2 + γ)(2γ + δ) (8) 12

13 where the right hand side of this inequality is denoted λ 2. λ 1 and λ 2 are positive for (2 + γ)ω αδ > 0. We assume that the innovation is high enough such that ω > αδ. For the constraint values on γ and δ ((γ + δ) [0, 1]), λ (2+γ) 1 is lower than λ 2. This last result leads to the following Proposition Proposition 1 - For λ < λ 1 Both rms share their knowledge - For λ 1 < λ < λ 2 There is a multiple equilibrium: one rm share her knowledge - For λ > λ 2 Both rms do not share their knowledge Proof 1 - For λ < λ 1 : Π A 1 > Π B 1, Π A 2 > Π C 2, Π C 1 > Π D 1 and Π B 2 > Π D 2 - For λ 1 < λ < λ 2 : Π A 1 < Π B 1, Π A 2 < Π C 2, Π C 1 > Π D 1 and Π B 2 > Π D 2 - For λ > λ 2 : Π A 1 < Π B 1, Π A 2 < Π C 2, Π C 1 < Π D 1 and Π B 2 < Π D 2 The Proposition 1 shows that the more λ is high, the less likely rms will share their knowledge. The eect of other parameters on the threshold values, λ 1 and λ 2, conducts to the Proposition 2 Proposition 2 - The innovation ω has a positive impact on the sharing knowledge. - The positive spillover λ, the negative spillover δ, the degree of competition γ and the market size parameter α have a negative impact on the sharing knowledge. Proof 2 Partial derivatives of λ 1 and λ 2 with respect to δ, γ and α (ω) are negatives (positives). Thus, a rise of δ, γ and α (ω) decrease (increase) the space of parameter values where rms choose to share their knowledge. As a consequence, the more the competition is strong between two rms, the less they will share their knowledge. Moreover, if the knowledge is heavily strategic and 13

14 involves a risk that the degree of competition could be increased (δ), then rms are discouraged to share their knowledge. Surprisingly, the positive spillover is also an obstacle for the knowledge sharing. In fact, it incites rms to let only the competitor sharing his knowledge. If the positive spillover involves by the sharing knowledge is important, then the competitor prefers also to deny knowledge sharing because only the other rm will benet from it. The negative impact of the market size parameter is specic. In fact, if the value of an innovation is very low compare to the value of the market, therefore it is not interesting to risk a higher competition to obtain it. We made the assumption that the innovation in case B and C is divided by two compared to the case A. Proposition 2 will not change with a lower (ω 2 < ω/2) or a higher (ω 2 > ω/2) innovation but other equilibrium can appear. In fact, when ω 2 < ω/2, multiple equilibrium where both share their knowledge or both do not are existing. And, when ω 2 > ω/2, the space of multiple equilibrium where one of them share his knowledge can be higher. 4 Heterogeneous rms This section analyzes the fact that rms can have a dierent weight such as α 1 α 2 and the consequences on innovation and spillovers involve by the knowledge sharing. Results provided by the Cournot competition in step two are shown in Table 4. Prots are not displayed but they are simply the square of the equilibrium quantities. The eect of parameters on payos when rms are heterogeneous is very similar to the previous section. In fact, in the case A, the only dierence is the change between α 1 and α 2. The market size of the competitor involves a negative impact depending on the level of competition for the prot of the rm. However, both market size parameters play positively on the farmer surplus and the welfare. In the case B and C, the dierence between both rms has an interesting impact. Indeed, the competitor's market size parameter continues to play negatively 14

15 on prot but the rm with the higher market share will be less impacted when she shares her knowledge alone whereas its competitor will be more aected if he is the only one to share his knowledge (negative impact on equilibrium quantities for the rm 1 is α 2 α 1 +λ and for the rm 2 α 1 α 2 +λ ). This result can have a positive 4 2γ δ 4 2γ δ (negative) impact for the choice of knowledge sharing for the rm with a superior (inferior) market size. Table 4 Payos for heterogeneous rms (in terms of market size) q A 1 q A 2 CS A α 2 1(4 3(γ+δ) 2 )+2α 1α 2(γ+δ) 3 +α 2 2(4 3(γ+δ) 2 ) W A 1 4 2(2 γ δ) ( 2 (γ+δ+2) 2 (α1+α1+2(ω+λ)) 2 2+γ+δ 2α 1 α 2(γ+δ)+(2 γ δ)(ω+λ) (2 γ δ)(2+γ+δ) 2α 2 α 1(γ+δ)+(2 γ δ)(ω+λ) (2 γ δ)(2+γ+δ) + 2α1((γ+δ+1)(ω+λ)) 2(γ+δ+2) 2 + (α1+α1+2(ω+λ))2 (2+γ+δ) 2 + 2α2(γ+δ+1)(ω+λ) 2(γ+δ+2) 2 + (α1 α1)2 2 γ δ q1 B α 1+α 2+ω+λ + α1 α2+λ 4+2γ+δ 4 2γ δ q2 B α 1+α 2+ω+λ ( α1 α2+λ 4+2γ+δ 4 2γ δ CS B 1 (α1+α2+ω+λ) 2 2(α1+α2+ω+λ)2 + (α1 α2+λ) γ+δ (4+2γ+δ) 2 4 2γ δ W B (α 1+α 2+ω+λ) 2 + (α1+α2+ω+λ)2 + (α1 α2+λ)2 (4+2γ+δ) 2 2(4+2γ+δ) (4+2γ+δ) 2 q1 C α 1+α 2+ω+λ α2 α1+λ 4+2γ+δ 4 2γ δ q2 C α 1+α 2+ω+λ + ( α2 α1+λ 4+2γ+δ 4 2γ δ CS C 1 (α1+α2+ω+λ) 2 2(α1+α2+ω+λ)2 + (α2 α1+λ) γ+δ (4+2γ+δ) 2 4 2γ δ W C (α 1+α 2+ω+λ) 2 + (α1+α2+ω+λ)2 + (α2 α1+λ)2 (4+2γ+δ) 2 2(4+2γ+δ) (4+2γ+δ) 2 q1 D 2α 1 α 2γ 4 γ 2 q2 D 2α 2 α 1γ 4 γ 2 CS D 4(α 2 1 +α2 2)+2α 1α 2γ 3 3γ 2 (α 2 1 +α2 2) 2(4 γ 2 ) 2 W D α 2 1(12 γ 2 ) 2α 1α 2γ(8 γ 2 )+α 2 2(12 γ 2 ) 2(4 γ 2 ) 2 ) + (α1 α1)2 (2 γ δ) 2 ) 2(α1 α2+λ)2 (4 2γ δ) 2 + (α1 α2+λ)2 2(4+2γ+δ) ) 2(α2 α1+λ)2 (4 2γ δ) 2 + (α2 α1+λ)2 2(4+2γ+δ) + 2(γ+δ+1)(ω+λ)2 2(γ+δ+2) 2 Four thresholds are obtained to resolve the game of knowledge sharing. The rst threshold, T 1, is for Π A 1 > Π B 1. The second, T 2, is for Π C 1 > Π D 1. The third, T 3, is for Π A 2 > Π C 2 and the fourth, T 4, is for Π B 2 > Π D 2. They are presented and analyzed in Annex A. We choose to separate the parameter α 1 to evaluate the consequences of the heterogeneity of rm 1 and 2. Moreover, Annex B provides how are ordered each threshold depending on the value of λ. Since there is four thresholds, six equalities can be found between them. For each equality, a dierent value of λ is obtained and denoted λ z, where z [1, 6]. Each λ z is also described and sorted in Annex B. 15

16 Results provided by Annex A and B are presented in Figure 1. Furthermore, at λ 1 where T 1 = T 3, replacing λ 1 in T 1 and T 3 leads to the result T 1 = T 3 = α 2. The same result is obtained at λ 2 for T 2 and T 4. Therefore, for values of λ lower (higher) than λ 1 (λ 2 ), α 2 is higher (lower) than T 1 and T 2 and lower (higher) than T 3 and T 4. For values of λ between λ 1 and λ 2, α 2 is larger than T 2 and T 3 and inferior to T 1 and T 4. This results allows to know whether α 1 is superior to α 2 according to the placement of α 1 between thresholds. Figure 1 Comparison of the thresholds The upper part of the Figure 1 shows what thresholds is higher or lower than other thresholds between each λ z. The bottom part shows where α 2 is superior or inferior to thresholds. For example, between zero and λ 1 we know from the upper part that T 4 > T 3 > T 1 > T 2 and from the bottom part that α 2 is higher than T 1 and T 2 and lower than T 4 and T 3. Thus, if α 1 is superior to T 4 and T 3, it will also be higher than α 2. Moreover, when α 1 is superior to T 3, the rm 1 wants to share his knowledge but the rm 2 does not want to share it (see Annex A). If α 1 is between T 3 and T 1, then both rms want to share their knowledge. Lastly, when α 1 < T 1, then α 2 is larger than α 1 and only the rm 2 wants to share his knowledge. The analysis of Nash equilibrium continues in Annex C for all values of λ and leads to Proposition 3. Proposition 3 16

17 - If α 1 and α 2 are close enough For λ < λ 1 Both rms share their knowledge For λ 1 < λ < λ 2 There is a multiple equilibrium: one rm share her knowledge For λ > λ 2 Both rms do not share their knowledge - If α 1 is high enough compare to α 2 Only the rm 1 will share her knowledge - If α 1 is low enough compare to α 2 Only the rm 2 will share her knowledge Proof 3 See Annex C. Corollary 1 The rm with an higher market size has more incentives to share its knowledge than the other rm. Proposition 3 shows that when rms are suciently similar, Nash equilibrium become the same that the situation where rms are exactly the same. In fact, λ 1 and λ 2 are the same except that the parameter α is replaced by the parameter α 2. Therefore, with α 2 = α, then λ 1 and λ 2 are exactly equivalent to the previous section. The dierence between the situation where rms were similar is that when a rm has a suciently large market size compared to her competitor, then she will share her knowledge even in the situation where, previously, no one rm shares his knowledge (λ > λ 2 ). However, in the situation where both rms shared their knowledge, henceforth only one rm shares her knowledge (λ < λ 1 ). Indeed, the rm with a lower demand has less incentives to share her knowledge alone as long as the other rm can obtain a higher part of her demand. As the previous section, parameters of the model have similar impacts on the knowledge sharing. Indeed, when λ < λ 1 there is situation where both rms share their knowledge whereas with λ > λ 2 both rms do not share it. Thus, a rise of 17

18 λ can involves a lower knowledge sharing. Moreover, Proposition 2 stays true. Indeed, λ 1 and λ 2 are similar and the eects of parameters on the other λ z are identical. An other result of the model appears in the case B and C. For a sucient dierence between α 1 and α 2 to be in the case B or C, when only one rm share her knowledge, but if this dierence is not too far, then the rm with the higher market size can lost her leadership in this market. This result is summarized in Proposition 4. Proposition 4 For α 2 < α 1 < α 2 + λ, the rm 1 with an higher demand before the knowledge sharing lost her leadership if she shares her knowledge alone. The prot maximizing behavior leads to this result due to a higher prot in the case where the previous leader share his knowledge alone than the prot in the case where no one share his knowledge. However, this result seems not realistic for the reason that obtaining a higher market share is heavily strategic for multiple reasons such as, for example, the bargaining power. 5 Conclusion In this paper we analyze rms already in R&D cooperation and that compete in the same market. In the aim of creating an innovation, rms have to share their knowledge but this imply spillovers that involve a higher competition. In this framework we try to understand whether rms are incited to share their knowledge through a theoretical model. In the theoretical model, both rms can choose whether their share their knowledge in a rst step, and compete in Cournot framework in a second step. We introduce two spillovers: a negative spillover increasing the competition and a positive spillover raising the demand. We found that spillovers involve by knowledge sharing have negative impacts on the choice of sharing knowledge when rms compete with substitute products. Moreover, the more the competition is between rms before the cooperation, the less 18

19 competitors share their knowledge. Furthermore, rms with a larger market share keeps knowledge sharing with higher competition than rms with a lower market share. Indeed, it is riskier to share the knowledge for a small rm as long as the larger rm can catch her market. 19

20 References Branstetter, L. G. and M. Sakakibara (2002). When do research consortia work well and why? evidence from japanese panel data. The American Economic Review 92 (1), Cantner, U. and H. Graf (2006). The network of innovators in jena: An application of social network analysis. Research Policy 35 (4), Cellini, R. and L. Lambertini (2009). Dynamic R&D with spillovers: Competition vs cooperation. Journal of Economic Dynamics and Control 33 (3), Cohen, W. M. and D. A. Levinthal (1989). Innovation and learning: the two faces of R&D. The economic journal 99 (397), d'aspremont, C. and A. Jacquemin (1988). Cooperative and noncooperative R&D in duopoly with spillovers. The American Economic Review 78 (5), Ding, X.-H. and R.-H. Huang (2010). Eects of knowledge spillover on interorganizational resource sharing decision in collaborative knowledge creation. European Journal of Operational Research 201 (3), Gomes-Casseres, B., J. Hagedoorn, and A. B. Jae (2006). Do alliances promote knowledge ows? Journal of Financial Economics 80 (1), Goyal, S. and S. Joshi (2003). Networks of collaboration in oligopoly. Games and Economic Behavior 43 (1), Goyal, S. and J. L. Moraga-González (2001). R&D networks. Economics 32 (4), RAND Journal of Hagedoorn, J. (2002). Inter-rm R&D partnerships: an overview of major trends and patterns since Research policy 31 (4), Hanaki, N., R. Nakajima, and Y. Ogura (2010). The dynamics of R&D network in the IT industry. Research Policy 39 (3),

21 Kamien, M. I., E. Muller, and I. Zang (1992). Research joint ventures and R&D cartels. The American Economic Review 82 (5), Katz, M. L. (1986). An analysis of cooperative research and development. The RAND Journal of Economics 17 (4), Katz, M. L., J. A. Ordover, F. Fisher, and R. Schmalensee (1990). R&D cooperation and competition. Brookings papers on economic activity. Microeconomics 1990, Letterie, W., J. Hagedoorn, H. van Kranenburg, and F. Palm (2008). Information gathering through alliances. Journal of Economic Behavior & Organization 66 (2), Motta, M. (1992). Cooperative R&D and vertical product dierentiation. International Journal of Industrial Organization 10 (4), Petit, M. L. and B. Tolwinski (1999). R&D cooperation or competition? European Economic Review 43 (1), Sakakibara, M. (2003). Knowledge sharing in cooperative research and development. Managerial and Decision Economics 24 (2-3), Salant, S. W. and G. Shaer (1998). Optimal asymmetric strategies in research joint ventures. International Journal of Industrial Organization 16 (2), Samaddar, S. and S. S. Kadiyala (2006). An analysis of interorganizational resource sharing decisions in collaborative knowledge creation. European Journal of operational research 170 (1), Singh, N. and X. Vives (1984). Price and quantity competition in a dierentiated duopoly. The RAND Journal of Economics 15 (4), Spence, M. (1984). Cost reduction, competition, and industry performance. Econometrica: Journal of the Econometric Society 52 (1), Suzumura, K. (1992). Cooperative and noncooperative R&D in an oligopoly with spillovers. The American Economic Review 82 (5),

22 Tomasello, M. V., M. Napoletano, A. Garas, and F. Schweitzer (2016). The rise and fall of R&D networks. Working Paper. Ziss, S. (1994). Strategic R&D with spillovers, collusion and welfare. The Journal of Industrial Economics 42 (4),

23 A Thresholds of the game The rst threshold is when rm 1 want to share their knowledge when the rm 2 shares it such that Π A 1 > Π B 1 α 1 > 1 2δ(4γ + 3δ) ( 2( 4 + γ2 )(2γλ + ( 2 + γ)ω) + (2α 2 (4 + γ 2 ) 8( 2 + γ + γ 2 )λ 3( 4 + γ 2 )ω)δ ( 3α 2 γ + (6 + 5γ)λ + (2 + γ)ω)δ 2 + (α 2 λ)δ 3 ), where the right hand side of this inequality is denoted T 1. The second threshold is when rm 1 want to share their knowledge when the rm 2 does not such that Π C 1 > Π D 1 α 1 > 1 2δ(4γ + 3δ) ( 2( 4 + γ2 )(2γλ + ( 2 + γ)ω) + (2α 2 (4 + γ 2 ) ( 4 + γ 2 )(2λ + ω))δ + α 2 γδ 2 ), where the right hand side of this inequality is denoted T 2. The third threshold is when rm 2 want to share their knowledge when the rm 1 shares it such that Π A 2 > Π C 2 α 1 < 1 δ(8 + γ(2γ + δ)) (2( 4 + γ2 )(2γλ + ( 2 + γ)ω) + (8α 2 γ + 8( 2 + γ + γ 2 )λ + 3( 4 + γ 2 )ω)δ + (6α 2 + (6 + 5γ)λ + (2 + γ)ω)δ 2 + λδ 3 ), where the right hand side of this inequality is denoted T 3. The fourth threshold is when rm 2 want to share their knowledge when the rm 1 does not such that Π B 2 > Π D 2 α 1 < 2( 4 + γ2 )(2γλ + ( 2 + γ)ω) + (8α 2 γ + ( 4 + γ 2 )(2λ + ω))δ + 2α 2 δ 2 δ(8 + γ(2γ + δ)) where the right hand side of this inequality is denoted T 4. We can calculate 23

24 partial derivatives for each threshold with respect to λ: T 1 λ = 4γ(4 γ2 ) + 8(1 γ)(2 + γ)δ δ 2 (6 + 5γ) δ 3, 2δ(4γ + 3δ) is positive for 0 < γ < 2 and 0 < δ < 2 γ. T 2 λ = 4γ(4 γ2 ) + 2(4 γ 2 )δ, 2δ(4γ + 3δ) is positive for 0 < γ < 2 and δ > 0. T 3 λ = 4γ(4 γ2 ) 2(8 4γ(1 + γ)) + δ 2 (6 + 5γ) + δ 3, δ(8 + (γ + δ)(γ + δ)) is negative 0 < γ < 2 and 0 < δ < 2 γ. T 4 λ = 4γ(4 γ2 ) 2(4 γ 2 )δ, δ(8 + γ(2γ + δ)) is negative for 0 < γ < 2 and δ > 0. Thus a rise of λ increases T 1, T 2 and decreases T 3 and T 4. 24

25 B Comparison of thresholds In order to nd Nash equilibrium of the game we need to know how thresholds evolve. We compare thresholds with the parameter λ: - T 1 < T 3 For λ < (4 2γ δ)((2+γ)ω α 2δ) 4γ(2+γ)+4(2+γ)δ+δ 2, the right hand side of this inequality is denoted λ 1. - T 2 < T 4 For λ < (4 2γ δ)((2+γ)ω α 2δ) 2(2+γ)(2γ+δ), the right hand side of this inequality is denoted λ 2. - T 1 < T 4 For λ < (4 γ 2 δ)((2+γ)ω α 2 δ) 8γ+8γ 2 +2γ 3 +8δ+6γδ+3γ 2 δ+γδ 2, the right hand side of this inequality is denoted λ 3. - T 2 < T 3 For λ < (4 γ 2 δ)((2+γ)ω α 2 δ) 2(4γ+4γ 2 +γ 3 +2δ+5γδ+γ 2 δ+δ 2 ), the right hand side of this inequality is denoted λ 4. - T 2 < T 1 For λ < (4 2γ δ)((2+γ)ω α 2δ) 8γ 2 +2δ+7γδ+δ 2, the right hand side of this inequality is denoted λ 5. - T 3 < T 4 For λ > 2(4 2γ δ)((2+γ)ω α 2 δ) 16 24γ+4γ 2 +2γ 3 +16δ+2γδ+3γ 2 δ+γδ 2 and γ < γ, 2(4 2γ δ)((2+γ)ω α 2 δ) or for λ < and γ > γ, 16 24γ+4γ 2 +2γ 3 +16δ+2γδ+3γ 2 δ+γδ 2 where γ = δ ( 3δ 4) ( 3δ 2 12δ+128) 3 +( 36δ 2 576δ+3328) 2 576δ δ 2 12δ /3 3 6, 36δ 2 + 4( 3δ 2 12δ+128) 3 +( 36δ 2 576δ+3328) 2 576δ+3328 the right hand side of the rst inequality is denoted λ 67. We nd also for ω > - λ 1 < λ 3 αδ (2+γ) For 0 < δ < 1 and 3δ 4 < γ < 2 (the innovation is high enough) that 6 Note that for δ = 0, then γ = 0.59 and for δ = 1, then γ = 0. 7 λ 6 is negative, decreasing and concave for γ [0, γ] and positive, decreasing and convex for γ [γ, 1]. 25

26 that - λ 3 < λ 4 For δ > 0 and c < 2 δ - λ 4 < λ 2 For 0 < δ < 8/3 and δ 4 < γ < 2 δ - λ 2 < λ 5 For δ < 8/3 and δ 4 < γ < 2 δ - λ 1 > λ 6 For < δ < 1 and 1 2 ( 2 δ) + 1 δ < γ < γ - λ 5 < λ 6 For 0 < δ < and γ < γ < 2 δ All the conditions found respect the constraints of parameters. We can conclude - For γ < γ and ((2 + γ)ω αδ) > 0 Then λ 6 < 0 < λ 1 < λ 3 < λ 4 < λ 2 < λ 5 - For γ > γ and ((2 + γ)ω αδ) > 0 Then 0 < λ 1 < λ 3 < λ 4 < λ 2 < λ 5 < λ 6 26

27 C Nash equilibrium - For 0 < λ < λ 1 Then T 4 > T 3 > T 1 > T 2 For α 1 > T 3 Then Firm 1 shares and Firm 2 does not share. For T 3 > α 1 > T 1 Then Firm 1 and Firm 2 share. For α 1 < T 1 Then Firm 1 does not share and Firm 2 shares; - For λ 1 < λ < λ 3 Then T 4 > T 1 > T 3 > T 2 For α 1 > T 1 Then Firm 1 shares and Firm 2 does not share. For T 1 > α 1 > T 3 Multiple equilibrium : one of them shares. For α 1 < T 3 Then Firm 1 does not share and Firm 2 shares. - For λ 3 < λ < λ 4 Then T 1 > T 4 > T 3 > T 2 For α 1 > T 4 Then Firm 1 shares and Firm 2 does not share. For T 4 > α 1 > T 3 Multiple equilibrium : one of them shares. For α 1 < T 3 Then Firm 1 does not share and Firm 2 shares. - For λ 4 < λ < λ 2 Then T 1 > T 4 > T 2 > T 3 27

28 For α 1 > T 4 Then Firm 1 shares and Firm 2 does not share. For T 4 > α 1 > T 2 Multiple equilibrium : one of them shares. For α 1 < T 2 Then Firm 1 does not share and Firm 2 shares. - For λ 2 < λ < λ 5 Then T 1 > T 2 > T 4 > T 3 - And for γ < γ and λ > λ 5 Then T 2 > T 1 > T 4 > T 3 - And for γ > γ and λ 5 < λ < λ 6 Then T 2 > T 1 > T 4 > T 3 - And for γ > γ and λ > λ 6 Then T 2 > T 1 > T 3 > T 4 - In these four situations For α 1 > T 2 Then Firm 1 shares and Firm 2 does not share. For T 2 > α 1 > T 4 Then no one share. For α 1 < T 4 Then Firm 1 does not share and Firm 2 shares. 28