R&D Competition and Cooperation with Distance-Dependent Spillovers

We study a continuous-time duopoly model of process innovation with R&D spillovers, comparing noncooperative R&D with cooperative research regimes. We extend the standard constant-spillover framework by allowing knowledge transmission to decay with technological distance and to favor followers over leaders in asymmetric specifications. In a global Markov-perfect model, firms may invest before production is viable, enter or exit production as costs evolve, and converge to no-market, monopoly, or duopoly outcomes. State-dependent spillovers change R&D incentives, catch-up dynamics, long-run market structure, and the welfare effects of research cooperation. In the computed equilibria, more follower-favoring spillovers weaken the leader's private incentive to invest but accelerate catch-up, shorten monopoly phases, and make eventual duopoly more likely. When spillovers are weak, cooperation mainly softens dynamic rivalry; when information sharing is substantial, cooperation expands market formation, lowers long-run costs, and can raise both consumer and total surplus, especially under the research-joint-venture regime. The value of R&D cooperation depends on the direction and persistence of knowledge flows, not only on their average intensity.