R&D collaboration networks in mixed oligopoly.

• Author: Zikos, Vasileios

1. Introduction

   In advanced industrial economics, R&D collaboration plays a crucial role for the creation, exploitation, and diffusion of knowledge. Firms participating in collaboration agreements innovate more frequently than others and discover more original innovations (Beise and Stahl 1999). In doing so, collaborating firms are able to increase their profitability and achieve superior economic performance than their noncollaborating counterparts.

   An important feature of collaboration agreements is that they often engage both private and public firms. Mixed oligopoly is a very common form of market in Europe and in Japan following the introduction of competition into traditional state monopolies. An example of R&D collaboration in mixed oligopoly is the Norwegian industry for fuel cells and hydrogen technologies. In particular, Norway's portfolio includes a variety of R&D projects aimed at the development of environmentally clean and efficient energy technologies (see Godo et al. 2003). These projects are organized as research consortia between R&D-intensive firms including state-owned companies such as Statoil.

   The objective of this article is to explore the role of a public firm in influencing the structure of the network, and the potential implications of a public firm's presence for the relationship between equilibrium industry structure and performance, two key issues of the literature on R&D networks. The most natural way of studying which network architectures will materialize is to adopt Jackson and Wolinsky's (1996) concept of pairwise stability. It requires that a network is pairwise stable if no firm has an incentive to delete one of its existing links and no pair of firms want to establish a new link. Note that this condition is quite weak and thus should be seen only as a necessary condition for stability. Pairwise stability allows for deviations by a pair of firms. However, it could be the case that a group of firms can improve their competitive position by deleting or adding several links, which is not a possible deviation in the context of pairwise stable networks. To this end, Jackson and van den Nouweland (2005) introduced the concept of strong stability: We say that a network is strongly stable if it survives all possible deviations by a coalition of firms. (1)

   In particular, we are primarily interested in the following questions:

   (i) What are the incentives of competing firms that pursue efficiency-enhancing innovations to create networks for the purpose of sharing new knowledge? What is the architecture of the networks that will endogenously emerge?

   (ii) How does the presence of a state-owned company affect the network structure, and are individual incentives to form networks adequate from an efficiency point of view?

   To answer these questions, we consider an environment with a public firm and two private firms. The timing of moves is as follows. In stage one, prior to competing in the product market, firms create collaboration ties. The purpose of collaboration agreements is the sharing of know-how about a cost-reducing technology. Six conceivable network structures arise from this stage. Under the complete network all firms are connected, whereas under the empty network there are no collaborative ties. A star network entails that there is a "hub" firm, either public or private, that maintains a direct link with two "spoke" firms, whereas the latter are indirectly connected via the "hub." Finally, under a partial network there is only a pair of firms with a collaborative link. In stage two, firms choose a noncooperative level of R&D effort. A firm's own R&D effort, together with the effort of its partners and the structure of the network, determine its operating costs. In the last stage, firms compete in the market of a homogeneous good by choosing their quantities.

   Our first result concerns the relationship between the level of collaborative activity and individual R&D effort. We find that even though R&D effort decreases with the number of alliances of a private firm, it increases with the number of alliances of the public firm. (2) To see intuitively why this happens, notice that the formation of a link implies two effects. On the one hand, as a firm establishes a link, it drives down its own production costs and expands its output. On the other hand, the costs of partner firms become lower too, which makes them tougher competitors. It turns out that this negative effect cannot be outweighed by the positive effect of collaboration on a firm's own quantity, thereby leading a private firm to exert a lower R&D effort. By contrast, both effects pull in the same direction when the public firm engages in collaborations and thus lead to a greater R&D effort. Although this is so in the absence of R&D subsidies, it turns out that the provision of an R&D subsidy encourages not only the public firm but also the private firms to put in a higher effort when they engage in collaborations.

   Our second result explores the stability properties of R&D networks. In particular, we show that the complete network is the unique pairwise stable and strongly stable network. This finding is mainly driven by the fact that the public firm is an aggressive competitor as it produces more output than a private firm. A higher output induces the private firms to form links in order to limit the competitive strength of the public firm. Thus our result can be interpreted in the following natural way: The stability of the complete network is not due to any enhancing effect of public ownership on the private firms' incentives to collaborate. Rather, it is due to the maximizing behavior of the public firm, which encourages collaboration by leaving a small residual demand to the private firms.

   Our next result looks at the efficiency properties of R&D networks. In particular, we establish that the complete network is Pareto efficient, independently of the extent of technological spillovers. The private partial network and the private-hub star network are also Pareto efficient but within a smaller range of spillover values. More interestingly, when R&D subsidies are provided by the regulator, the complete network becomes the unique Pareto efficient network. Taken together, these results carry an important message: They suggest that a public firm can reconcile individual incentives for collaboration with the objective of efficiency, independently of whether R&D is subsidized (Table 1).

   Our article contributes to the growing literature on R&D networks. This literature focuses mainly on the analysis of the network architectures that will endogenously emerge and on the efficiency properties of the resulting networks. Goyal and Moraga-Gonzalez (2001) do so in a setting with an arbitrary number of horizontally related firms and symmetric networks. They also analyze the three-firm case, which focuses on strategic incentives for collaboration by allowing firms to gain competitive advantages. Since this study it has been widely accepted that stable and efficient networks can differ. Goyal and Moraga-Gonzalez (2001) find that such a conflict arises when spillovers are not too small. Mauleon, Sempere-Monerris, and Vannetelbosch (2008) provide a corresponding finding in a setting where each firm sets its own wage.

   Song and Vannetelbosch (2007) investigate the possibility of resolving the potential conflict between stable and efficient networks by means of an R&D subsidization policy. In particular, using a setting with three firms located in different countries and selling a (homogeneous) good within an internationally integrated product market, they show that the likelihood of a conflict is reduced, but it is still present in the cases of very small or quite large spillovers. (3) In light of this, our result yields an insight into the role of a public firm as policy instrument in regulating innovative activity. It suggests that a public firm can align individual incentives for collaboration with the objective of efficiency, independently of whether R&D subsidies are provided by the regulator. Other authors have reported similar conclusions though in a different context. In particular, Mauleon, Sempere-Monerris, and Vannetelbosch (2008) find that the complete network emerges as the unique stable architecture when the labor market is unionized and wages are set at the firm level. Also, the complete network maximizes industry profits and so is the unique (strongly) efficient network.

   Our article also contributes to the R&D literature in mixed oligopolies. Delbono and Denicolo (1993) examine the role of a public firm in regulating innovative activity in a mixed duopoly with perfectly protected innovations. They show that a welfare-maximizing firm can alleviate the overinvestment problem in the private duopoly. Poyago-Theotoky (1998) investigates the case of easy imitation in R&D, showing that most of the results of Delbono and Denicolo (1993) can actually be reversed. (4) Our approach is richer in the sense that the strategic effects of the R&D are mediated through a network of R&D collaboration within which the place firms occupy and the structure of the network play an important role. This in turn may give us a more comprehensive view of how research incentives are shaped in the present context. (5)

   The remainder of the article is organized as follows. Section 2 presents the model. The next section contains our results on the stability and efficiency properties of R&D networks. In section 4, we consider extensions of our model, and in section 5, we conclude. The equilibrium of the different network structures is characterized in appendix 1, and the proofs that are not included in the main text are relegated to appendix 2.

2. The Model

   We consider a model of endogenous network formation. Firms create collaboration links to transfer knowledge on a new technology that enhances their productive efficiency and, hence, lowers...