On the management of open innovation

Research Policy 43 (2014) 903–913

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On the management of open innovation夽 Alfonso Gambardella ∗ , Claudio Panico Bocconi University, Italy

a r t i c l e

i n f o

Article history: Received 15 March 2013 Received in revised form 4 December 2013 Accepted 4 December 2013 Available online 23 January 2014 Keywords: Open innovation Decision rights Intellectual property rights Governance Incentives

a b s t r a c t In an open innovation relationship, the party that owns a key asset enjoys bargaining power that discourages the investments of the other party in the collaboration. We show that these incentives can be restored by conferring on the weak party the power to take decisions during the research process – e.g., a pharmaceutical firm with manufacturing and commercialization assets offers the direction of a joint research project to a biotech partner. However, on many occasions, the strong party still captures more value from the collaboration by retaining the power to take decisions during research even if it produces less innovation value and fewer aggregate profits. We conclude that the potential of open innovation is underexploited. In particular, owners may not release enough power to take decisions on the use of their assets. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Following Chesbrough’s (2003, 2006) pioneering contributions, open innovation literature has covered many topics. They range from the direction of knowledge flows (inward or outward), to the forms of openness (alliances, joint ventures, networks, etc.), the parties involved (suppliers, users, competitors, communities), or the impact of openness on innovation performance (e.g., von Hippel, 1988; Laursen and Salter, 2006; Dahlander and Gann, 2010; West and Bogers, 2013). However, other topics need attention. In particular, some open innovation scholars suggest that the future research agenda should delve into the incentives of firms to exchange knowledge (West et al., 2006; Erden et al., 2012). More generally, we lack a good understanding of the conditions under which firms or other agents engage in open relationships, the factors that affect their incentives to invest in these relationships, and the governance of open innovation systems.

夽 This paper benefitted from the very constructive guidance of the editor of this special issue, Ammon Salter, and the constructive and insightful comments of two anonymous reviewers. Ashish Arora also provided important suggestions. In addition, we benefited from the comments of many colleagues, including Massimo Colombo, Marco Giarratana, Cristina Rossi Lamastra, Isabella Leone, Raffaele Oriani and Giovanni Valentini, as well as seminar participants in the “Open Innovation Workshop,” Imperial College, London, June 25, 2012, at Catolica University, Lisbon, March 11, 2013, and the AIG Conference, Politecnico, Milan, October 18, 2013. Of course, none of them is responsible for our errors and omissions. We also acknowledge financial support from the Italian Ministry of University and Research (MIUR), PRIN 2012, “Market and Non-Market Mechanisms for the Exchange and Diffusion of Innovation: When Do They Work, When Do They Not Work, and Why Should We Care,” MIUR, Protocol N. 2010H37KAW 001. ∗ Corresponding author. E-mail address: [email protected] (A. Gambardella). 0048-7333/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.respol.2013.12.002

In this paper, a stylized model tries to address this gap. As one of the first attempts to formalize open innovation, we keep our model simple and study a research collaboration between a firm and a research unit. This is a familiar context for scholars of innovation. Typically, a specialized firm has technological capabilities but, unlike established companies, it does not control manufacturing or commercialization assets, or large scale research capabilities. The relationship between biotech companies and larger pharmaceutical firms is a good example of our framework and we will use it as our leading illustration in this paper. We study the governance of this collaboration and particularly how the parties allocate property rights and, separately, the rights to take decisions during the research process, which we label “decision rights.” This is an important distinction that we need to clarify at the outset of our analysis. A key argument of this paper is that the party holding the rights to make decisions on the use of an asset need not be the party that owns the asset. For example, a pharmaceutical firm owns a research lab, but offers the direction of the lab to an employee of a biotech company with which it collaborates. This enables the biotech firm to take decisions that capture more value from the collaboration than if the pharmaceutical manufacturer had kept the decision rights. In particular, as we shall see, the biotech firm enjoys spillovers on other internal projects. More generally, the reallocation of decision rights compensates the potentially weaker bargaining power of the biotech company due to the fact that it does not own the assets.1

1 To clarify our terminology, the property rights literature uses “control rights” to define the residual rights enjoyed by the owner of an asset when the parties negotiate ex post the allocation of the value that they create. But sometimes control rights are also referred to rights that do not pertain to the negotiation stage. We

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We ask three questions. Which allocation of property and decision rights yields the highest returns for the parties involved? Which allocation yields the highest innovation value? Which allocation yields the highest aggregate profits, i.e., it is efficient? These are central questions in understanding the governance of open innovation, as they investigate whether the parties have the right incentives to open up by starting a collaboration, and whether openness generates more valuable innovations and more profits. We model two types of benefits from a research project. First, the parties benefit from the output of their research, typically an innovation, which is the main target of the project. Second, they benefit from spillovers during the research process. The knowledge acquired in a research project can often be used in other research projects and even within the same project, researchers can push some goals rather than others. For example, according to Lerner and Malmendier (2010), biotech companies often cross-subsidize projects. The parties decide first whether to stipulate a contract to enter into a collaboration. The contract specifies which party has the right to take decisions during the research process. As noted, the contract may stipulate that the biotech firm directs the project carried out in collaboration with the pharmaceutical firm. If so, the biotech firm has greater opportunities of cross-subsidization, or spillovers. To streamline our analysis, we exclude financial transfers and initially we assume that there is no exchange of property rights. However, as we will see, these assumptions are not crucial for our results. In a context like research, contracts are incomplete (e.g., Teece, 1988). Therefore, apart from an ex-ante contract regarding the allocation of decision rights over research, the parties need to reach an agreement ex-post on how to share the final output of the collaboration (Grossman and Hart, 1986). Property rights on critical assets confer bargaining power in this ex-post negotiation. For example, a pharmaceutical firm that owns manufacturing and commercialization assets, can exploit the innovation even if it does not reach an agreement with the biotech firm. Thus, ex-ante contracting and ex-post bargaining allow us to distinguish between two sources of power in a open innovation context: the power to decide the allocation of decision rights when stipulating the contract, which we call contracting power; and the power to capture innovation value, which we call bargaining power. As noted, bargaining power depends on whether a party owns critical assets. We model contracting power as the power to make a take-it-or-leave-it offer to the other party. This power normally depends on whether the party has many alternative partners with which it could collaborate. If so, it will collaborate only if the other party accepts the offer. We identify the conditions under which the party with contracting power retains decision rights over research or relinquishes them to the other party. We find that most often it retains decision rights. However, sometimes it does not. The intuition is that contracting power and property rights confer strong bargaining power. This discourages the other party from investing in the collaboration because it will not capture enough value in the ex-post bargaining stage. In particular, we show that if the contribution of the weak party is important, the party with contracting power relinquishes decision rights over research so that the weak party enjoys research spillovers that compensate its lack of incentives. An interesting result of our analysis is that the allocation chosen by the party with contracting power does not always yield the highest innovation value or efficiency. This party may still capture more value by retaining decision rights even if giving decision rights to the other party creates higher innovation value and

eliminate this confusion and reserve the term “decision rights” to mean the rights to take interim decisions during the research process.

greater efficiency. Contractual relationships between the parties may therefore dampen the potential of open innovation because of an unbalanced initial allocation of power, a point also made by Aghion and Tirole (1994) with respect to the efficiency of the ownership pattern. We also find that the thrust of these results does not change if the parties can exchange property rights. Our model lies at the heart of the literature on open innovation. Chesbrough and Rosenbloom (2002) see open innovation as a profit-maximizing strategy that targets both value creation and value appropriation. Value creation stems from the fact that knowledge sharing enhances the synergies and the opportunities of companies. As we will see, our model posits that there is complementarity between the investments of the firm and the unit. Value appropriation, instead, speaks to the way in which they share this value. This suggests that we also need to understand how to orchestrate a system of relationships in which different agents motivated by different incentives for value creation, can claim part of that value. These factors are key for the success of an open innovation strategy and for the ability of firms to enjoy the benefits of openness. They can be even more important than technological capabilities (Christensen, 2006). We bring another novelty to the open innovation literature. By studying formally the organization of innovation across firm boundaries, we bridge the open innovation literature with organizational economics and the property rights approach (Grossman and Hart, 1986; Hart and Moore, 1990; Aghion and Tirole, 1994). The next section summarizes the main features of our model and it acknowledges some background literature. Sections 3 and 4 present our model. Section 5 extends the model to the exchange of property rights. Section 6 provides a final discussion, along with the limitations of our analysis.

2. Background and literature In the spirit of Aghion and Tirole (1994), our model studies the relationships between a firm and a research unit that can develop an innovation project either independently or in collaboration. As in their paper, the firm is an established company, while the unit is a specialized research enterprise. This is not central to our model. However, as in Aghion and Tirole (1994), it enables us to exemplify some scenarios. Our focus on decision rights over the research process marks a distinction compared to Aghion and Tirole (1994) and the propertyrights approach more generally, and it has both conceptual and empirical justifications. Conceptually, both property rights and decision rights allow for an allocation of non-contractible benefits. But while ownership confers ex-post bargaining power after the research process is completed and the parties negotiate on how to share the value produced by the collaboration, decision rights pertain to an interim stage that precedes the bargaining. As noted in Section 1, according to Lerner and Malmendier (2010) biotech firms often use the financing or the knowledge related to a project with a drug company, to support other internal projects. In addition, biotech firms usually want to linger on the more academic aspects of the project. Decision rights over research can therefore be an instrument for the provision of incentives because it affects the extent to which biotech firms can enjoy these private benefits. Empirically, decision rights are distinct from property rights. A party can have the right to make decisions in a project even if it does not own the relevant assets. For example, a biotech and a pharmaceutical company may conduct research at the premises of the drug firm or use its equipment, while the direction of the project is assumed by an employee of the biotech firm. Similarly, the team may be composed of researchers from both firms, but the head of the team, who directs the research, is an employee of

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one or the other. Chesbrough himself noted that the presence of Xerox’s managers in the board of its spinoffs favored the pursuit of projects closer to Xerox interests (Chesbrough, 2003). Moreover, as noted by Lerner and Merges (1998), contracts specify decision rights carefully, especially in research. Examples include the right to patent the outcome of the collaboration, the right to sublicense, the right to terminate the alliance, the right to manufacture or market the product (see also Adegbesan and Higgins, 2010). Panico (2011) discusses the example of a research contract between Pfizer and Coley, a small biotech research specialist. The contract specifies several decision rights attributed to Coley, like the right to use Pfizer’s library of compounds, the right to conduct research, or to take several decisions regarding assets owned by Pfizer. Lerner et al. (2003) further investigate how financial markets influence the contractual allocation of decision rights. Before moving to the model, we acknowledge the vast theoretical literature on control and delegation of decisions rights, using both a complete and an incomplete contract setting. Aghion and Tirole (1997) focus on an agent with the authority to select one from many projects, and the decision to delegate depends positively on the extent of the (non-contractible) benefits the agent obtains from decision authority. They investigate how delegation increases the agent’s initiative to acquire information (or exert effort). In the same vein of incomplete contracts, Rajan and Zingales (1998) focus on the access to resources rather than property rights. Privileged access confers the opportunity of specializing in the resources but no additional residual right of control. Panico (2011, 2012) discusses an incentive scheme that combines contingent payments and the non-pecuniary benefits of decision rights when they can be freely divided between a principal and a agent, in a world of incomplete and complete contracts. Along the same line, Gambardella et al. (2010) and Gambardella et al. (2013) consider the allocation of decision rights in relation to the strategic management of human capital. Other studies consider the allocation of control and decision rights in a principal-agent setting with adverse selection. Dessein (2005) addresses the allocation of control in a relationship between an investor firm and a privately informed entrepreneur that releases control to signal alignment of interests with the firm. Alonso and Matouschek’s (2008) paper considers a setting in which two parties have different preferences and the principal sets delegation and a non-contingent payment when facing a privately informed agent.

3. The model 3.1. Set-up We study a customer firm (F) and a research unit (R) that consider the possibility of starting a collaboration to produce an innovation. They hold property rights on some relevant assets for the production of this innovation. To fix ideas, we focus on IPR. We model three open innovation modes. First, F owns IPR on an invention and collaborates with R to produce an innovation that builds on the early IPR. Because F’s initial knowledge flows outside its boundaries, we call this case outbound innovation. Second, R owns the IPR, but F does not. This is the case of inbound innovation. Third, both F and R own IPR and pool assets and knowledge to conduct additional research. We call this case bidirectional innovation. Outbound/inbound is a terminology often used by the open innovation literature (e.g., Enkel et al., 2009). There are three stages in this process: ex ante, in which the parties reach an agreement; interim, in which the parties conduct research and invest; and ex post, in which the parties negotiate after they produce the innovation. Similarly to Aghion and Tirole

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(1994), we distinguish between ex-ante and ex-post bargaining power. As noted in Section 1, we use the terminology contracting power and bargaining power. Ex-ante, the party with contracting power makes a take-it-or-leave-it offer to the other. Typically, this is a stylized way to capture the idea that this party can sign alternative collaborative agreements. In other words, the party with contracting power is less substitutable in the collaboration than the party without contracting power. As noted, ex-post bargaining power depends, instead, on the ability of a party to preserve the use of its assets if F and R do not reach any ex-post agreement. We model decision rights during the research process with  ∈ {0, 1};  is equal to 1 (or 0) if F (or R) collects decision rights. The allocation of interim decision rights is contractible and it is established ex-ante. After choosing , in the interim stage, F and R invest. Following the terminology of the contractual literature, we call these investments “efforts” and we represent them with E and e. These efforts are decided independently and simultaneously by the parties. Their costs are (E2 /2) and (e2 /2). We separate the benefits of open innovation in two parts: one that accrues entirely to the party that collects interim decision rights, due to its ability to direct the process and one that stems from the appropriation of a share of the product created by the collaboration according to ex-post bargaining. While a simplification, this separation clarifies the effects of decisions associated with the research process and decisions that depend on ex-post negotiation on the value of the innovation. The total value of the product of the collaboration is V(E, e), increasing and concave in both arguments and with a positive cross-derivative, such that there is complementarity between efforts. Because of contract incompleteness, the parties cannot specify contractually either the research efforts, E and e, or how they will share the value of the innovation, V(E, e). To work with closed-form solutions, we assume that V (E, e) = E + eE + ˛e

(1)

where ˛ ≥ 0 is a productivity parameter that measures the relative importance of R’s effort. If ˛ > 1, then coeteris paribus the marginal impact of R’s effort on the final innovation is larger than F’s, while the opposite is true if ˛ < 1. This is a simple way to capture the asymmetry in the importance of the marginal effort of the two parties. Also, the term eE captures the complementarity between efforts. This term was absent in the payoff from the collaboration in Aghion and Tirole (1994), who assume a separable payoff function in the efforts of the two parties. Thus, we tackle more directly the strategic interaction between the parties. The total value produced during the research process is simply (1/2)V(E, e). It is natural to assume that spillovers during the research stage are proportional to the total value of the final innovation and for simplicity we set the proportionality factor equal to 1/2. We also assume that the party that collects decision rights captures all this value; that is, F and R enjoy, respectively, a benefit from making the preferred decisions during the research process equal to (/2)V(E, e) and (1 − /2)V(E, e), with  equal to 1 or 0. This means that the total benefits accruing to one party from the collaboration is (/2)V(E, e) or (1 − /2)V(E, e) plus the share of the innovation value that the party can appropriate when bargaining, that is a share of V(E, e), as defined by Eq. (1).2 When they contract, F and R can remain closed and obtain payoffs  > 0 and u > 0. These payoffs depend on property rights, as it is natural to assume that a party that owns assets or previous IPR incurs lower costs when it innovates. They engage in open

2 We could introduce a parameter ˇ ∈ [0, 1] that captures the importance of the benefits from controlling research relatively to the final innovation, but we do not get much additional insight.

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innovation only if the payoff from collaborating exceeds the payoffs of closed innovation. After the contracting stage, the parties choose the effort levels. We look for Nash equilibria. Finally, when they bargain ex-post, the parties’ outside options depend on property rights, as a party that owns initial IPR or manufacturing and commercial assets enjoys greater benefits from the project when working independently. Specifically, we assume that F’s and R’s best alternatives when they bargain are positive only if a party holds property rights and they are equal to the value of the innovation when the counterpart’s effort is set to zero. They are, respectively,  V(E, 0) =  E and V(0, e) = ˛e, where  ,  ∈ {0, 1}. The variables  and  identify the case of outbound, inbound, and bidirectional open innovation that correspond to the combinations ( , ) = (1, 0), ( , ) = (0, 1), and ( , ) = (1, 1). We will not discuss the case ( , ) = (0, 0) as it is less interesting and has the same intuitions as the case ( , ) = (1, 1). Note also that this highlights why we specify a complementarity effect eE in Eq. (1). This is not an ad hoc addition to introduce complementarity, but it is a fundamental feature of the structure of an open innovation process. From above, if the parties do not reach an agreement when they bargain, their payoff is  V(E, 0) =  E and V(0, e) = ˛e. The collaboration has two benefits with respect to independence. First, the two firms share knowledge, information, and assets, which creates synergies. The complementarity between e and E, that is the term eE, captures this synergy. Second, if one party is offered decision rights over research, not only can it use its own assets to capture value, but also the assets of the other party. This is bound to create more benefits than if the party only controls its own assets, as in the closed innovation mode. In other words, our model captures the essence of the benefits produced by open innovation, and clarifies them: on the one hand, firms benefit from synergies and sharing of knowledge and assets; on the other hand, the party that holds decision rights can use more assets than just its

opportunity cost of collaborating,  and u. In this case, both parties can innovate. Clearly, they both capture the benefits of the research process because they direct their own research. We make the reasonable assumption that the party that has already generated an invention incurs lower costs to innovate; thus, F’s and R’s cost decrease respectively with  and . To simplify, we assume that the parties’ research costs are equal (2 −  )/2E2 and (2 − )/2e2 , so that they coincide with the research costs of collaborating if the parties own the initial IPR. F’s and R’s reservation payoffs are then =

1 E2 3 2− 2 V (E, 0) + V (E, 0) − (2 −  ) = E − E 2 2 2 2

(2)

1 e2 3 2− 2 V (0, e) + V (0, e) − (2 − ) = ˛e − e . 2 2 2 2

(3)

and u=

By maximizing Eqs. (2) and (3), F’s and R’s reservation payoffs are ( ) =

9 1 8 2−

(4)

9 ˛2 . 8 2−

(5)

and u() =

4. Analysis of the open innovation modes 4.1. Payoffs To understand the function of the different innovation modes, we study the equilibria of three ownership patterns ( , ) = {(1, 0), (0, 1), (1, 1)}, and two allocations of decision rights,  = 0, 1. The general form of F’s and R’s payoff function is (6)

(7) own to produce idiosyncratic benefits when conducting research. For example, it can also rely on the researchers of the other party to produce spillover innovations that may benefit its own business, and not the business of the partner (Lerner and Malmendier, 2010). We must also be more explicit about our assumptions. First, the ownership pattern affects the parties’ outside options, but not directly the value of the innovation, as in Grossman and Hart (1986) and Aghion and Tirole (1994). Second, the allocation of decision rights does not affect the additional value created, but only who captures this additional value. These two assumptions allow us to exclude more obvious considerations from the analysis, as for example the fact that if the innovation value is higher when both parties have invented, they exert greater efforts. Our model highlights the incentives and the tension between value creation and appropriation as the key factors that affect the function of open innovation.

3.2. Benchmark: closed innovation We start with the benchmark in which F and R can conduct research without collaborating. This determines the parties’

where the first terms in Eqs. (6) and (7) relate to the benefits captured by the party that collects decision rights; the second terms relate to the negotiation payoffs, which correspond to the Nashbargaining solution and depend on the allocation of property rights; and the last terms are the costs of effort. For each specification of the model, we compute the firm’s and the unit’s effort that correspond to the Nash equilibrium, and the resulting payoffs. We then study: i) the optimal allocation of decision rights chosen by the party with contracting power; ii) the allocation of decision rights that maximizes innovation value; iii) the efficient allocation of decision rights, i.e., the allocation that maximizes aggregate equilibrium profits. 4.2. Bidirectional innovation We start by considering the case in which the firm and the unit own IPR, so that  =  = 1 and their best alternatives when collaborating are V(E, 0) = E and V(0, e) = ˛e. By Eqs. (6) and (7), F’s and R’s payoffs with bidirectional innovation, bid and ubid , are bid =





 1 1 · (E + eE + ˛e) + E + eE − E 2 2 2 2

(8)

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and ubid =



 1

1− 1 · (E + eE + ˛e) + ˛e + eE − e2 . 2 2 2

(9)

As a first step, we derive the Nash equilibrium efforts as a function of , Ebid () and ebid (). Then, we look for the optimal allocation of decision rights. Lemma 1. With bidirectional innovation, the equilibefforts are rium Ebid () = (4 + 2 + ˛(1 + )(3 − )/2) and ebid () = ((2 − )(2 + ) + 2˛(3 − ))/2. In discussing the results below, it is useful to distinguish between two effects on the parties’ incentives when decision rights are transferred from F to R. The direct effect implies that the firm has fewer incentives, while the unit has more incentives, simply because decision rights allow to capture the additional benefits from conducting research. The indirect effect stems from the complementarity between efforts. Given the specification of the model, the efforts are strategic complements, i.e., if one party increases the effort, the optimal response of the other party is to increase effort as well. Because of this complementarity, the negative effect on F’s effort when it does not collect decision rights is partly compensated by the higher effort exerted by R when it collects decision rights. The direct incentive effect prevails on the indirect one, and we can check from Lemma 1 that a party always exerts a greater effort when it holds decision rights. Proposition 1. With bidirectional innovation, the party with contracting power retains decision rights. In this case, both the firm and the unit prefer to collaborate, as opposed to the alternative of closed innovation, independently of who holds decision rights. The allocation of decision rights therefore depends only on the initial distribution of the contracting power. The next question is how innovation value and the aggregate profits originating from the equilibrium efforts relate to the allocation of decision rights. With bidirectional innovation the parties have equal bargaining positions because they both own an IPR. Thus, in the spirit of the standard property rights model, allocation of decisions rights to F yields more valuable innovations if ˛ ≤ 1 because the party whose effort is more important (the firm) has greater incentives to invest. Proposition 2. With bidirectional innovation, allocation of decision rights to the firm yields a more valuable innovation and it is efficient if ˛ ≤ 1. The thrust of Proposition 2 is that in order to maximize innovation value and efficiency, the party whose effort is more important has to hold decision rights. This is the firm if ˛ < 1 or the unit if ˛ > 1. However, according to Proposition 1, the party with contracting power retains decision rights. Therefore, some scenarios are undesirable. In particular, we observe higher innovation value and efficiency only when the party whose effort is more important, also has contracting power. The two conditions are not perfectly correlated. For example, a biotech company may have critical competencies in a research project performed in collaboration with a pharmaceutical manufacturer. However, there can be many biotech firms with such competencies. In this case, the drug manufacturer has contracting power because it can resort to other biotech firms, if the focal one does not accept its offer, and thus it will retain decision rights – for instance by keeping the direction of the project. While this optimizes the returns of the pharmaceutical firm, the biotech firm will not exert enough effort to maximize innovation value and efficiency. We will see in the next section that with outbound and inbound innovation, the parties have asymmetric bargaining positions because only one of them owns an IPR. Therefore, the

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configuration of decision rights that maximizes innovation value or efficiency does not mirror the relative importance of the parties’ effort. 4.3. Outbound innovation The firm F owns the IPR, that is,  = 1. Its best alternative when it bargains is V(E, 0) = E. The unit R has no IPR, that is,  = 0, and its best alternative ex post is 0. By Eqs. (6) and (7), F’s and R’s payoffs with outbound innovation, out and uout , are:





out =

 1 1 · (E + eE + ˛e) + E + (eE + ˛e) − E 2 , 2 2 2

(10)

uout =

1− 1 1 · (E + eE + ˛e) + (eE + ˛e) − e2 . 2 2 2

(11)





Let Eout () and eout () be the equilibrium level of effort with outbound innovation. Lemma 2. With outbound innovation, the equilibrium efforts are Eout () = (4 + 2 + ˛(1 + )(2 − ))/2 and eout () = ((2 +  + 2˛)(2 − ))/2. Proposition 3. With outbound innovation, if the firm has contracting power, it releases decisions rights if ˛ > ˛out > 1. If the unit has contracting power, it retains decision rights. Outbound innovation is the only case in which the allocation of decision rights may not reflect the initial distribution of contracting power. Thus, unlike bidirectional innovation, where the parties never release decision rights when they have contracting power, now F releases decision rights when the contribution of the unit is very important – that is, ˛ is well above 1. As shown in the Appendix, the firm always prefers to engage in open collaboration, whether or not it collects decision rights, while the unit always prefers to collaborate if it collects decision rights. If, instead, it does not collect decision rights and it is disproportionately more efficient than the firm, it prefers closed innovation. Because the firm is financially constrained, the only way to convince the unit to collaborate is to relinquish decision rights. Thus, if ˛ > ˛out , the unit would rather choose closed innovation because the firm’s effort does not contribute much to the final innovation. Therefore, although the firm has contracting power, it must compensate the unit for its weak bargaining position. We now consider efficiency and innovation value. Proposition 4. With outbound innovation, allocation of decision rights to the unit yields a more valuable innovation if ˛ > 1/2, and it is efficient if ˛≥˛ ˜ out , ˛ ˜ out < (1/2). According to Proposition 2, with bidirectional innovation allocation of decision rights to the firm produces a more valuable innovation and higher efficiency if ˛ ≤ 1. With outbound innovation, Proposition 4 states that allocation of decision rights to the firm is less desirable. It is desirable only when F’s contribution is very important, that is ˛ is small. The threshold is higher for value than efficiency, but the thrust of the argument is that allocation of decision rights to R can produce higher innovation value and efficiency even when R’s effort is less important – that is, when ˛ is below 1. The intuition is that with outbound innovation R’s bargaining position is weaker because it does not own IPR. Then, R’s control of the research process balances the parties’ incentives. Propositions 3 and 4 highlight the potential mismatch between the choice of the party with contracting power and the desirable choice at the aggregate level. Firstly let us consider the case in which F has contracting power. By Proposition 3, it releases decision rights on the research process only if the contribution of the unit to the collaboration is very important, most notably ˛ > ˛out > 1. However, to maximize innovation value and efficiency, it should

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release decision rights for any ˛≥˛ ˜ out . Since ˛ ˜ out < ˛out , this implies the following. When the contribution of the firm or the contribution of the unit to the collaboration is very important – that ˜ out or ˛ > ˛out – the decision of a firm with contracting is, ˛ < ˛ power and bargaining power (outbound innovation) also maximizes innovation value and efficiency. When ˛ < ˛ ˜ out it correctly retains decision rights, and when ˛ > ˛out it assigns them to the unit. The problem is when ˛ ˜ out ≤ ˛ ≤ ˛out . In this case the firm with contracting power and property rights does not relinquish decision rights, which implies less innovation value and efficiency than if the unit had decision rights. Interestingly, it is not difficult to see from Propositions 3 and 4 that if the unit had contracting power, it would correctly keep decision rights if ˛ ˜ out ≤ ˛. However, the unit with contracting power would inefficiently keep decision rights even when F’s contribution is very important, that is, when ˛<˛ ˜ out . As an illustration of these scenarios, consider the case in which a pharmaceutical firm owns critical manufacturing and commercialization assets, or key IPR, and there are many biotech firms with important research competencies that the pharmaceutical firm does not have. The choice among many biotech firms confers contracting power on the firm. If the contribution of the biotech firms to the collaboration is very important, that is, ˛ is high, and particularly ˛ > ˛out , the firm will relinquish decision rights to the biotech firm with which it collaborates. The problem is when the biotech firm’s contribution is important but not that important, to wit ˛ ˜ out ≤ ˛ ≤ ˛out . In this case, in the ideal situation a unique biotech firm negotiates with many potential drug manufacturers. The biotech firm would have contracting power and it would keep decision rights. Notice that, in practice, this scenario is unlikely. Albeit the level of ˛ and the allocation of contracting power are conceptually distinct, a very competent biotech firm will probably not have many rivals, and it will be sought as a partner by many drug manufacturers. In contrast, there could be more biotech ˜ out ≤ ˛ ≤ ˛out . firms with smaller levels of ˛, and particularly ˛ This suggests that in an open innovation environment the problem of too few incentives to the technology specialists can be a serious issue. In particular, they do not receive enough decision rights over the research process. Simply put, we ought to see more research labs owned by pharmaceutical firms, directed by biotech firms. 4.4. Inbound innovation With inbound innovation, F has no IPR, or  = 0, and its best alternative when bargaining is 0. The unit R owns the IPR, or  = 1, and its outside option is V(0, e) = ˛e. By Eqs. (6) and (7), F’s and R’s payoffs with inbound innovation, in and uin , are



in



1  1 (E + eE) − E 2 = · (E + eE + ˛e) + 2 2 2

and uin =



(12)



1− 1 1 · (E + eE + ˛e) + ˛e + (E + eE) − e2 . 2 2 2

(13)

Compared to outbound innovation, the unit has a better bargaining position and for a given allocation of decision rights it has stronger incentives to invest, while F has fewer incentives. At the same time, the unit (the firm) has a greater (lower) reservation utility because it incurs lower (higher) costs. Let Ein () and ein () indicate the equilibrium efforts with inbound innovation. Lemma 3. With inbound innovation, the equilibrium efforts are (1+)(2−)+2˛(3−) Ein () = (2 + 2 + ˛(3 − )(1 + ))/2 and ein () = . 2

Proposition 5. With inbound innovation, the party with contracting power retains decision rights. As with outbound innovation, both the firm and the unit prefer to collect decision rights. However, now collaboration is always preferred to closed innovation by both parties, irrespective of the configuration of decision rights. This means that the parties do not have to be compensated to be induced to collaborate. The allocation of decision rights reflects the initial power distribution. Proposition 6. With inbound innovation, allocation of decision rights to the unit leads to a more valuable innovation if ˛ > 2, and it is never efficient. Since the unit now has better bargaining position, we obtain the opposite result of outbound innovation. The firm has to have decision rights to produce a higher innovation value even if its effort is moderately less important, or ˛ ≤ 2. The intuition is again that the allocation of decision rights to the less efficient party balances the parties’ incentives. At the same time, efficiency requires that decision rights are allocated to the firm. As an illustration, now the biotech firm holds a critical IPR for the new innovation performed in collaboration. If many drug manufacturers seek to collaborate with this firm, it inefficiently retains decision rights, and the venture produces a less valuable innovation unless ˛ > 2. The scenario would be more aligned with general interest if the biotech firm is in a field where only one or very few drug manufacturers operate and there are quite a few biotech companies holding critical IPR. 5. Extension: reallocating IPRs So far we have emphasized allocation of decision rights. However, the literature on property rights economics has focused on the allocation of property rights. In this section we show that even if the parties trade initial property rights when they contract, the main thrust of our results does not change. This extension has another interesting interpretation. As noted, in an innovation context, intellectual property is an important type of property right. In this respect, our previous sections studied the governance of open innovation when markets for technology are underdeveloped and therefore trade in IPR are not possible. In this section we study whether well functioning markets for technology affect the governance of open innovation. Proposition 7. If both decision rights and IPR can be reallocated, then: (i) with outbound innovation, if the firm has contracting power, it retains decisions rights, but reallocates IPR to the unit when ˛ > (5/3); (ii) with inbound innovation, if the unit has contracting power, it retains decisions rights, but reallocates IPR to the firm when ˛ < (3/2). This Proposition says that when offered a choice between transferring decision rights or property rights, the parties prefer to relinquish the latter. Keeping the property of the technology is less important than keeping control over research. This suggests that when they exist, markets for technology improve the governance of open innovation. When the unit is particularly efficient (˛ > (5/3)), the firm will earn greater returns if the unit invests more. The solution is to sell IPR to the efficient unit. Notice that this suggests a new explanation for markets for technology, other than comparative advantages in exploiting IPR between research specialists and manufacturers or comparative advantages in enforcing IPR (Galasso et al., 2013). In the context of open innovation, markets for technology are an instrument to generate incentives and therefore to improve the governance of open innovation systems. They enable the stronger parties to reinforce the bargaining power of the weaker parties when their contribution to the collaboration is important. Moreover, trade in IPR is preferred to releasing decision

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rights. When the unit has contracting power and decision rights, it reallocates IPR, unless the unit’s contribution is so important that incentives to the firm are not particularly valuable to raise the unit’s returns. Next we consider the allocation of IPR and decision rights that maximizes innovation value and aggregate profits. Proposition 8. In order to maximize innovation value, IPR and decision rights should be allocated to: (i) the firm if ˛ ≤ 21 ; (ii) the firm and the unit if (1/2) < ˛ ≤ 1; (iii) the unit and the firm if 1 < ˛ < 2; (iv) the unit if ˛ ≥ 2. The thrust of Proposition 8 is that reallocation of property rights does not rule out suboptimal innovation values. The result that we obtained when we only looked at the allocation of decision rights is robust to this extension. To illustrate this point, consider the extreme cases. When ˛ ≥ 2, the unit should hold both IPR and decision rights. However, according to Proposition 7, the firm only releases IPR. Similarly, when ˛ ≤ (1/2), the firm ought to keep IPR and decision rights, but the unit only releases IPR. In the intermediate cases, when 1 < ˛ ≤ (5/3), according to Proposition 8 the unit should hold IPR and the firm should hold decision rights, but according to Proposition 7 the firm with contracting power holds both – and similarly for other cases. The individual decisions and the configuration that maximizes innovation value coincide only under some circumstances. An interesting case is when (5/3) < ˛ < 2 and the firm holds complementary IPR and contracting power. This is a common case in practice. Biotech firms can provide fairly important – though not crucial – contributions in a research collaboration with a drug manufacturer. However, there are quite a few of them and thus drug manufacturers hold contracting power. Moreover, the drug firms hold complementary IPR. In this case, they can choose markets for technology to provide incentives and improve the governance of open innovation. In addition, by releasing the IPR to the biotech firm (and by retaining decision rights) they maximize innovation value. Notice that when the biotech firm produces a crucial contribution to the collaboration, that is, ˛ ≥ 2, this is not enough. In this case, to maximize innovation value, the unit should hold contracting power. This is the scenario in which the biotech firm has unique competencies and many drug manufacturers want to collaborate with it. Moreover, the biotech firm should hold the key IPR. If so, the biotech firm retains both decision right and IPR, which also maximizes innovation value. Proposition 9. In order to maximize efficiency, IPR and decision rights should be allocated to: (i) the firm if ˛ ≤ ˛T  0.72; (ii) the firm and the unit if ˛T < ˛ ≤ ˛ ˜ out ; (iii) the unit if ˛ > ˛T . The same remarks that we have just made apply to efficiency. In particular, the extension to reallocation of property rights does not rule out potential inefficiencies. Finally, in an extension available from the authors upon request, we studied the case in which the firm can make monetary transfers to the unit. Like in Aghion and Tirole (1994) we ruled out the case in which the research unit, typically a smaller concern, can make monetary transfers to the larger downstream manufacturer. We show that when it can make a monetary payment, the firm is less likely to transfer decision rights and prefers to pay the unit rather than loosing control of the decision process. This confirms the importance of decision rights. When other instruments are available, the parties prefer not to release them. However, the main results of this paper still hold. In particular, the parties release decision rights during the research process, though less frequently. Moreover, the decisions of the parties do not always coincide with the ideal governance of open innovation in terms of innovation value or efficiency.

909

6. Discussion and final remarks Our model of innovation across firm boundaries connects the open innovation literature with the property rights view of the firm. We maintain the perspective of open innovation as a profitmaximizing strategy that targets both value creation and value appropriation (Chesbrough and Rosenbloom, 2002). Contracting and the provision of incentives are critical for the effective management of cooperative innovation processes, but they have not been deeply investigated (West and Bogers, 2013). We model the relationship between a firm and a research unit in the spirit of Grossman and Hart’s (1986) seminal work on incomplete contracts, and on Aghion and Tirole’s (1994) subsequent analysis of management of innovation. We also build on Panico’s (2011) analysis of governance in research collaborations. Like the standard property rights approach, in our model property rights influence ex-post bargaining. However, we show that the allocation of decision rights during the research process is another important means of providing incentives. Our contribution to the literature on open innovation is twofold. First, along with ex-post bargaining power, we highlight the role of contracting power – that is, the power to retain or release decision rights at the outset of the collaboration. The contracting power depends on the extent to which a party can resort to an alternative partner. We show that the party endowed with contracting power tends to retain decision rights. It releases them when the bargaining power of the other party is weak because it does not hold property rights and its effort has to be supported by adequate incentives because its contribution is important. Interestingly, we may stigmatize the behavior of a company that cross-subsidizes its own projects with the knowledge or financial resources acquired during a collaboration. We show that, in fact, this means restoring its incentives, if the company does not have enough contracting or bargaining power, and especially if its contribution is important. This has important managerial implications. A party that tightly monitors a weak but competent partner during the research process may obtain fewer returns. The lower investment of the partner reduces the value of the final output, which the monitoring party could instead capture. Second, we find that the partner with contracting power and property rights may not choose the allocation of decision rights that creates the highest innovation value or efficiency. This is not a problem when dealing with a very competent biotech firm. If the established company holds contracting power and property rights, it will release decision rights to the biotech firm, which is also desirable to maximize innovation value and efficiency. However, a common situation in many high-tech industries is that there are many technology specialist firms with good but not blockbusting competencies. Because they are competent firms, the more established partner with contracting power and property rights should offer them decision rights in order to maximize innovation value and efficiency. However, they are not so competent that the partner finds it desirable to relinquish decision rights. Thus, the potential of open innovation to produce high innovation value may suffer from the fact that established firms do not let their research partners direct activities that involve the use of their assets. As noted earlier in the paper, we would like to see more research labs owned by pharmaceutical firms but directed by biotech firms. This problem is even more severe when the parties can exchange property rights or the established firm can make a monetary transfer to the research unit. We have shown that if they have contracting power they will never release decision rights. However, in both cases, there are circumstances in which maximization of innovation value or efficiency requires transfer of decision rights. To sum up, the problem of “research labs of pharmaceutical firms not directed

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by biotech companies” may really be a serious impediment to the full fledged benefits of open innovation. Several extensions of our stylized model could improve our understanding of the governance of open innovation. They also mark the limitations of our analysis. First, we offer no solution to the wedge between the actions of companies and the more general interest toward reallocation of decision rights, particularly from established firms to research units. This rich area for future research in open innovation is central to understanding how to remove impediments to the benefits of openness. While policy is an obvious solution, future research could study more sophisticated contractual instruments. For example, this paper assumes that all decision rights are allocated to one party or the other. However, the parties could share decision rights. This could balance incentives better and produce better outcomes, including a reduction of the wedge between actual and desired choices. Another direction is to study non-economic factors, like sociological or other reasons that may induce greater release of decision rights to maximize innovation value and efficiency. A second natural extension is to a multi-party setting, in which several agents participate in the production of a common outcome while maintaining their own objectives. Competition is a third extension. Future research may study the strategic interactions between incumbents that compete in the product market and collaborate with research units. The following step would be to consider competition and collaboration among incumbents. Another set of extensions may study the relationships between open innovation and markets for technology. In this paper, we have sketched a distinction between them. Markets for technology focus on the exchange of property rights, typically IPR. Open innovation, instead, is really about the allocation of decision rights. The spirit of Chesbrough’s original idea, and the ensuing literature, is that parties share knowledge or other assets independently of ownership. Thus, for instance, even if a pharmaceutical firm owns IPR, they are used by other parties as well. In this respect, this paper has shown that open innovation is not ruled out by markets for technology and markets for technology can co-exist with open innovation. However, more can be done. In particular, uncertainty about the best innovation value produced by many research units generates a trade-off. In open innovation, the ex-ante governance created by the established firm ensures that the research unit picked as partner invests enough in the collaboration to maximize the established firm’s returns. However, after the collaboration, the established firm may prefer to use the innovation produced by another research unit that reveals itself to be superior. If there are switching costs, picking the new solution may be inefficient, or at least more costly than if the established firm waits until uncertainty disappears. In markets for technology, firms exchange existing innovations (IPR). Thus, the research takes place in advance and it is not motivated by an optimal governance that induces the licensor to invest as much as the licensee would like. Future research may compare open innovation systems, in which ex-ante governance produces better organizational designs at the cost of irreversibility in the choice of supplier, and markets for technology, which offer better opportunities to pick valuable solutions ex-post at the cost of limited ex-ante incentives.

Proof of Lemma 1 Proof. Taking the first order condition for Eq. (8) and (9), we obtain the following best response functions, 2+ 1+ + e 2 2

ebid (E) = ˛

3− 2− + E 2 2

(A.1)

(A.2)

Substituting (A.2) into (A.3) and solving for E and e, the equilibrium efforts that correspond to a given allocation of decision rights are 4 + 2 + ˛(1 + )(3 − ) 2

(A.3)

(2 − )(2 + ) + 2˛(3 − ) . 2

(A.4)

E bid () = and ein () = 

Proof of Proposition 1 Proof. By (A.3) and (A.4), when F collects the decision rights the equilibrium efforts are E bid (1) = 3 + 2˛;

ebid (1) =

3 + 2˛. 2

(A.5)

Substituting (A.5) into Eq. (8) and (9), F’s and R’s equilibrium payoffs when F collects the decision rights write as

bid (1) =

2 1 · [3E bid (1) + 2E bid (1) · ebid (1) + ˛ebid (1) − (E bid (1)) ] 2



27 1 9+ ˛ + 6˛2 2 2

=



(A.6)

and

U bid (1) =

2 1 [2˛ebid (1) + E bid (1) · ebid (1) − (ebid (1)) ] 2

=

1 2

9 4



+ 6˛ + 4˛2 .

(A.7)

Equivalently, when R collects the decision rights the equilibrium efforts are E bid (0) = 2 +

3 ˛; ebid (0) = 2 + 3˛, and 2

(A.8)

Substituting (A.8) into Eqs. (8) and (9), F’s and R’s equilibrium payoffs when R collects the decision rights write as

bid (0) =

2 1 [2E bid (0) + E bid (0) · ebid (0) − (E bid (0)) ] 2

=



9 1 4 + 6˛ + ˛2 2 4



(A.9)

and

U bid (0) =

2 1 bid [E (0) + 2E bid (0) · ebid (0) + 3˛ebid (0) − (ebid (0)) ] 2

=

Appendix A.

E bid (e) =

and





27 1 6+ ˛ + 9˛2 . 2 2

(A.10)

It can be easily checked that bid (1) > bid (0) > (1), and U bid (0) > U bid (1) > u(1), meaning that both parties always prefers inbound innovation to closed innovation, and that they are better off when they collect decision rights. Thus, the party having the contracting power always retains decision rights.  Proof of Proposition 2

A. Gambardella, C. Panico / Research Policy 43 (2014) 903–913

Proof. Substituting (A.5) and (A.8) into Eq. (1), when F and R collect the decision rights the innovation value is, respectively, V (E bid (1), ebid (1)) =

15 25 + ˛ + 6˛2 2 2

(A.11)

and 2

U out (0) = [E out (0) + 2E out (0) · eout (0) + 2˛eout (0) − (eout (0)) ] =

and V (E

bid

(0), e

bid

25 21 2 (0)) = 6 + ˛+ ˛ . 2 2

Proof of Lemma 12 Proof. Taking the first order condition for (Eq. (10)) and (Eq. (11)), we obtain the following best response functions, 2+ 1+ + e 2 2 2− 2− ˛+ E. 2 2

(A.14)

4 + 2 + ˛(1 + )(2 − ) 2

(A.15)

and e

out

Proof of Proposition 4 Proof. Substituting (A.17) and (A.20) into Eq. (1), when F and R collect the decision rights the innovation value is, respectively,

Substituting (A.14) into (A.13) and solving for E and e, the equilibrium efforts that correspond to a given allocation of decision rights are E out () =

(A.22)

It can be easily checked that out (1) > out (0) > (1), meaning that F always prefers outbound innovation to closed innovation, and that it is better off when it collects the decision rights. Moreover, Uout (0) > Uout (1), meaning that R is also better off when it collects decision rights. But whereas U out (0) > u(0), meaning that R prefers outbound innovation to closed innovation if it collects decision rights, we can note that U out (1) < u(0) if ˛ > ˛out  24.73. Thus, if ˛ > ˛out , F can only relinquish control to R to convince it to collaborate. 

(A.13)

and eout (E) =

1 [6 + 9˛ + 4˛2 ]. 2

(A.12)

By comparing (A.11) and (A.12), it can be easily checked that the innovation value is maximal when F has the decision rights if ˛ ≤ 1. By considering the aggregate profits, it is immediate to check that bid (1) + Ubid (1) ≥ bid (0) + Ubid (0) if ˛ ≤ 1. 

E out (e) =

911

V (E out (1), eout (1)) = E out (1) + E out (1)eout (1) + ˛eout (1) = 2˛2 + 7˛ +

15 2

(A.23)

and V (E out (0), eout (0)) = E out (0) + E out (0)eout (0) + ˛eout (0)

(2 +  + 2˛)(2 − ) () = . 2

= 4˛2 + 9˛ + 6

(A.16)

(A.24)

 Proof of Proposition 3 Proof. By (A.18) and (A.16), when F collects the decision rights the equilibrium efforts are E out (1) = 3 + ˛, eout (1) =

3 + ˛. 2

(A.17)

Substituting (A.17) into Eq. (10) and (11), F’s and R’s equilibrium payoffs when F collects the decision rights are out (1) =



1 2 3E out (1) + 2E out (1) · eout (1) + 2˛eout (1) − (E out (1)) 2 =

 1 9 + 9˛ + 3˛2 2



(A.18)

U



 2 1 (1) = E out (1) · eout (1) + ˛eout (1) − eout (1) 2 =

1 2

9 4



+ 3˛ + ˛2 .

E

(0) = 2 + ˛, e

out

(A.19)

(0) = 2 + 2˛,

(A.20)

and substituting (A.20) into Eqs. (10) and (11), F’s and R’s equilibrium payoffs are

1 [4 + 6˛ + 3˛2 ] 2

E in (e) =

1+ 1+ + e 2 2

(A.25)

and 3− 2− + E. 2 2

(A.26)

E in () =

(1 + )(2 + ˛(3 − )) 2

(A.27)

2˛(3 − ) + (2 − )(1 + ) . 2

(A.28)

and ein () =  Proof of Proposition 5 Proof. By (A.27) and (A.28), when F collects the decision rights the equilibrium efforts are

2

out (0) = [2E out (0) + eout (0) · E out (0) + ˛eout (0) − (E out (0)) ] =

Proof. Taking the first order condition for (Eq. (12)) and (Eq. (13)), we obtain the following best response functions,

Substituting (A.26) into (A.25) and solving for E and e, the equilibrium efforts that correspond to a given allocation of decision rights are



Equivalently, by (A.15) and (A.16) when F collects the decision rights the equilibrium efforts are out

Proof of Lemma 3

ein (E) = ˛

and out

By comparing (A.23) and (A.24), it can be easily checked that the innovation value is maximal when F collects the decision rights if ˛ ≤ (1/2). Also, by considering the aggregate profits, it is easily checked that out (1) + Uout (1) > out (0) + Uout (0) if ˛ < ˛ ˜ out  0.32. 

(A.21)

E in (1) = 2 + 2˛, ein (1) = 1 + 2˛.

(A.29)

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Substituting (A.29) into Eq. (12) and (13), F’s and R’s equilibrium payoffs when F collects the decision rights are in (1) =

2 1 · [2E in (1) + 2E in (1) · ein (1) + ˛ein (1) − (E in (1)) ] 2

=

1 · [4 + 7˛ + 6˛2 ] 2

(A.30)

Proof of Proposition 8

and 2 1 U (1) = (E in (1) + E in (1) · ein (1) + 2˛ein (1) − (ein (1)) ) 2 in

=

1 [3 + 6˛ + 4˛2 ]. 2

(A.31)

Equivalently, by (A.27) and (A.28) when R collects the decision rights the equilibrium efforts are E out (0) = 1 +

3 ˛, eout (0) = 1 + 3˛. 2

(A.32)

Substituting (A.32) into Eq. (12) and (13), F’s and R’s equilibrium payoffs when R collects the decision rights are in (0) =





2 1 in 1 9 1 + 3˛ + ˛2 [E (0) + E in (0) · ein (0) − (E in (0)) ] = 2 2 4 (A.33)

and U in (0) =

Consider now the case of inbound innovation. First, by Proposition 5, with inbound innovation the unit optimally retains decision rights and obtains profits Uin (0). Second, if the unit can also relinquish the IPR to the firm, by Proposition 3 it optimally retains decision rights and obtains profits Uout (0). Finally, Uout (0) ≥ Uin (0) provided that ˛ ≤ 32 . Thus, the unit always retains the decision rights, and relinquishes the IPR if ˛ ≤ 32 . 

Proof. Propositions 4 and 6 inform us about the allocation of decision rights that maximizes the innovation value with outbound and inbound innovation. It then suffices to compare V(Eout (0), eout (0)) and V(Ein (1), ein (1)), and note that the former is not lower than the latter provided that ˛ ≤ 1. Thus, the innovation value is greater when the firm collects the IPR whenever ˛ ≤ 1.  Proof of Proposition 9 Proof. By Proposition 6, with inbound innovation it is always efficient that F collects the decision rights. Moreover, by Proposition 4, with outbound innovation it is efficient that F collects the deci˜ out , ˛ ˜ out < (1/2). It can be easily checked that sion rights if ˛ < ˛ in (1) + Uin (1) > out (0) + Uout (0) provided that ˛ > ˛T  1.39, which is greater than ˛ ˜ out . Thus, if ˛ > ˛T , the aggregate profits are greater when the unit collects both the IPR and the decisions rights.  Appendix B. B.1. On the role of complementarity

2 1 · [2E in (0) + 2E in (0) · ein (0) + 2˛ein (0) − (ein (0)) ] 2

=

1 [3 + 8˛ + 6˛2 ]. 2

(A.34)

It can be easily checked that in (1) > in (0) > (0), and U in (0) > U in (1) > u(1), meaning that both parties always prefers inbound innovation to closed innovation, and that they are better off when they have decision rights. Thus, the party having the contracting power always retains decision rights.  Proof of Proposition 6 Proof. Substituting (A.29) and (A.32) into Eq. (1), when F and R collect the decision rights the innovation value is, respectively, V (E in (1), ein (1)) = 4 + 9˛ + 6˛2

(A.35)

and V (E in (0), ein (0)) = 2 + 7˛ +

15 2 ˛ . 2

(A.36)

By comparing (A.35) and (A.36), it can be easily checked that the innovation value is maximal when F collects the decision rights if ˛ < 2. Also, by considering the aggregate profits, it is easily checked that in (1) + Uin (1) > in (0) + Uin (0).  Proof of Proposition 7 Proof. First, by Proposition 3, with outbound innovation at the optimum the firm retains decision rights and obtains profits out (1) if ˛ ≤ ˛out  24.73, whereas it relinquishes decision rights if ˛ > ˛out and obtains profits out (0) < out (1). Second, if the firm can also relinquish the IPR to the unit, by Proposition 5 it always retains decision rights and obtains profits in (1). Finally, it can be easily checked that in (1) > out (1) provided that ˛ > 53 , which is smaller than ˛out . Thus, the firm optimally retains the IPR and the decision rights if ˛ ≤ 53 , and relinquishes the IPR but retains the decision rights if ˛ > 53 .

There are two major differences between our model and Aghion and Tirole’s (1994) model of innovation. First, we account for the possibility that the two partners innovate by themselves, such that the closed innovation stands as the outside option for collaborating. Second, we introduce complementarity effects through the term eE that enters into all the payoff functions when the parties collaborate. What would happen if, as in Aghion and Tirole, there was no complementarity effect between the research efforts? The payoff from collaborating decrease, whereas the outside option of closed innovation would stay the same, on so we expect that the parties collaborate less often. We can prove the following result: Proposition 10. Absent complementarity between research efforts, there cannot be a collaboration with outbound, inbound, and bidirectional innovation, and therefore closed innovation is the only possible outcome. Proof. We just prove that closed innovation is the only outcome with outbound innovation. The same reasoning applies to the cases of inbound and bidirectional innovation. First, absent complementarity, by Eqs. (10) and (11), F’s and R’s payoffs with outbound innovation write as ˜ out = 

 1 1 · (E + ˛e) + E + ˛e − E 2 , 2 2 2

(B.1)

u˜ out =

1− 1 1 · (E + ˛e) + ˛e − e2 . 2 2 2

(B.2)

The equilibrium efforts are  2

(B.3)

˛(2 − ) . 2

(B.4)

E˜ out () = 1 + and e˜ out () =

Second, substituting (B.3) and (B.4) into (B.1) and (B.2), and setting  = 1, the profits when F collects the decision rights are 9 + (˛2 /2) for F and (˛2 /8) for R. When R collects the decision rights 8

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instead,  = 0, the profits are (1 + ˛2 )/2 for both parties. Note that both parties prefer to collect decision rights. Third, it is easily checked that when they do not collect decision rights, F and R prefer to engage in instead open innovation (5/4) and ˛ < (1/8), of choosing closed innovation if ˛ > respectively. These two conditions are incompatible. Therefore, each party prefers to collect decision rights when having the contracting power, but the other party is better off when with closed innovation, and so the collaboration is never started. We can apply the same argument to the case of inbound and bidirectional innovation, and conclude that absent complementarity in the research efforts, there cannot be open innovation.  References Adegbesan, A., Higgins, M., 2010. The intra-alliance division of value created through collaboration. Strategic Management Journal 32, 187–211. Aghion, P., Tirole, J., 1994. On the management of innovation. Quarterly Journal of Economics 109, 1185–1207. Aghion, P., Tirole, J., 1997. Formal and real authority in organizations. The Journal of Political Economy 105-1, 1–29. Alonso, R., Matouschek, N., 2008. Optimal delegation. The Review of Economic Studies 75-1, 259–293. Chesbrough, H., 2003. Open Innovation: The New Imperative for Creating and Profiting from Technology. Harvard Business School Press, Boston, MA. Chesbrough, H., 2006. Open innovation: a new paradigm for understanding industrial innovation. In: Chesbrough, H., Vanhaverbeke, W., West, J. (Eds.), Open Innovation: Researching a New Paradigm. Oxford University Press, Oxford, pp. 1–12. Chesbrough, H., Rosenbloom, R.S., 2002. The role of the business model in capturing value from innovation: evidence from Xerox Corporation’s technology spin-off companies. Industrial and Corporate Change 11 (3), 529–555. Christensen, J., 2006. Whither core competency for the large corporation in an open innovation world? In: Chesbrough, H., Vanhaverbeke, W., West, J. (Eds.), Open Innovation: Researching a New Paradigm. Oxford University Press, Oxford, pp. 35–61. Dahlander, L., Gann, D., 2010. How open is innovation? Research Policy 39 (6), 699–709. Dessein, W., 2005. Information and control in ventures & alliances. Journal of Finance 60, 2513–2550.

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