This study considers an endogenous timing game of R&D decisions with research spillovers and compares the effects of output and research subsidies. We show that the simultaneous-move (sequential-move) game is an equilibrium if the spillover rate is low (high) under an output subsidy while this equilibrium is socially beneficial if the spillover rate is high or low enough. Under a research subsidy, however, the simultaneous-move game is a unique equilibrium regardless of the spillover rate, which is always socially beneficial. We also show that an output subsidy in the simultaneous-move game provides higher (lower) social welfare than a research subsidy if the spillover rate is low (high). Finally, we provide the robustness of our findings and some policy-relevant discussions.

中文翻译：

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具有溢出效应的研发决策的内生时机：产出与研究补贴

本研究考虑了研发决策与研究溢出的内生时间博弈，并比较了产出和研究补贴的影响。我们证明，如果在产出补贴下溢出率低（高），那么同时移动（顺序移动）博弈就是一个均衡，而如果溢出率足够高或足够低，这种均衡对社会是有益的。然而，在研究补贴下，同时移动博弈是一种独特的均衡，无论溢出率如何，这总是对社会有益的。我们还表明，如果溢出率低（高），同时移动博弈中的产出补贴比研究补贴提供更高（更低）的社会福利。最后，我们提供了我们的研究结果的稳健性和一些与政策相关的讨论。