R&D rivalry with the interaction of output subsidies in an extensive endogenous timing game

This study investigates strategic interplay between government's output subsidies and firms' R&D rivalry in an extensive endogenous timing game. We find that research spillovers are crucial in determining multiple equilibria of the game, which yields different welfare consequences. We show that a simultaneous-move game appears at equilibrium if the spillovers rate is extremely low, but it is always socially undesirable. We also show that the government plays as a leader or a follower at equilibrium, while it could cause welfare loss unless spillovers rate is either high or sufficiently low. Our findings suggest that the appropriate role of the government in providing output subsidies should be based on the rate of research spillovers when the firms strategically choose their endogenous timings of R&D activities.