中文摘要：

将垂直溢出纳入到产业链纵向研发合作中，讨论了由M 个上游企业、1个中游企业和N 个下游企业构成的三级产业链中，中游企业采取独立研发策略或费用分摊策略时，垂直溢出对研发合作产出的影响，并进行了对比分析。研究结果表明：无论中游企业采取独立研发或费用分摊策略，垂直溢出都会促进中游企业增加研发投入、研发产出，提高三级产业链的总利润和总产量，降低终端市场产品价格；相比于独立研发策略，在费用分摊策略下，中游企业研发投入规模更大、研发产出效果更好，产业链总产量更大，下游企业终端市场产品价格更低。但只有垂直溢出超过特定临界值时，采取费用分摊策略时，产业链总利润才会高于独立研发策略，此时选择纵向研发合作更为有利。

英文摘要：

Base on vertical spillovers, this study establishes a vertical R＆amp;D collaboration model in a three-level supply chain, which consists of M upstream enterprises, one midstream enterprise, and N downstream enterprises, and the midstream enterprise can adopt either independent R＆amp;D strategy or cost sharing strategy to help form the vertical R＆amp;D alliance. Then we discuss the effects of midstream enterprise＇s two R＆amp;D strategies on its own＇ R＆amp;D outputs, the three-level supply chain＇s total profits and total output, and the downstream enterprises＇ product price. The results show that： first of all, vertical spillovers help to improve midstream enterprise＇s R＆amp;D output, en-hance total output and total profit of the three-level supply chain, and reduce the downstream enterprises＇ product price. Secondly, the cost sharing strategy is more effective than the independent R＆amp;D strategy to create effective R＆amp;D for the midstream enterprise, to enhance total output and total profit of the three-level supply chain, and to reduce the downstream enterprises＇ product price. Furthermore, only if vertical spillovers is high enough, the cost sharing strategy is more effective than the independent R＆amp;D strategy to enhance the total profit of the whole sup-ply chain.