上下游企业间R&D合作网络形成及其社会福利

研发（Research and Development，R&D）合作网络的形成是企业在创新活动中进行合作的一个重要特征，数据表明，上下游主体间的垂直R&D合作比位于同一市场层面主体间的横向R&D合作网络更普遍。针对企业间R&D合作网络的内生形成问题，首先，建立上游供应商与下游竞争厂商之间同时选择R&D合作链接和R&D投入水平的博弈模型；然后，通过比较所有可能存在的网络结构下各企业的均衡利润水平，识别稳定网络结构并分析R&D投资的效率；接下来，分析稳定网络结构随着横向R&D合作溢出效应和垂直R&D合作溢出效应的演化；最后，通过比较各网络结构下的社会福利，分析稳定网络结构的有效性。结果表明：（1）垂直合作链接促进合作双方的R&D投入，提高合作双方的均衡利润水平；横向合作链接阻碍竞争厂商的R&D投入，随着横向R&D合作溢出效应的增加，厂商R&D投入的竞争效应逐渐高于其成本降低的效应，从而厂商的利润先增加后减小；（2）在适当的溢出效应参数范围内，完全合作网络是唯一的成对稳定网络结构；但是当供应商与其中一个厂商的垂直R&D合作溢出率较高时，稳定网络结构将会发生演化。（3）社会福利分析的结果表明成对稳定网络未必总是最有效的合作网络结构。

Formation and Social Welfare of R&D Networks among Upstream and Downstream Firms

This paper contributes to the increasing literature on modelling R&D network formation among firms using game theory approach. What distinguishes this paper from existing ones is that it allows the firms to form or delete links with both their suppliers and their competitors simultaneously. In a benchmark model, we try to highlight the pair-wise stable networks among all the possible formations and to characterize the properties of the pair-wise stable networks. Moreover, we try to verify the impacts of R&D collaborations'spillover on the formation of pair-wise stable networks and the social welfares.In a two-tier industry with one supplier S and two manufacturers M_i,(i=1,2), the four-step game proceeds as follows: at step 1, the supplier and the two manufacturers select their vertical and horizontal R&D links simultaneously. The R&D collaboration between the manufacturers and the supplier is called vertical links, and the one between two manufacturers is called horizontal link. At step 2, knowing the R&D network structure, the three firms (S, M₁, and M₂) choose the optimal R&D efforts to maximize their own profits. At step 3, the supplier S chooses to provide the quantity of inputs to two downstream manufacturers. At step 4, M₁ and M₂ compete in a Cournot market to choose the quantities of production simultaneously.In this benchmark model, there are 8 possible networks and 6 of them have different results at equilibrium. Under each network structure, the model is solved by using backward induction. First, the quantity of each manufacturer at equilibrium is worked out. Then the optimal R&D efforts for the three firms is solved, and thereby their profits under each network are computed. Finally, pair-wise stable network under Goyal and Joshi's concept is verified.The main finding is that the complete network is the unique pair-wise stable network if the R&D spillover rate between the two downstream competitors is not smaller than the one between the supplier and the manufactories. However, the unique pair-wise stable network may not always be the most efficient one from the social welfare point of view. Our results verify the empirical findings that R&D collaboration is ubiquitous in the industry and vertical collaboration is more prevalent than horizontal collaboration. Furthermore, a new perspective for further research on the R&D network of upstream and downstream firms is provided.