Spillovers, Product Innovation and R&D Cooperation: a Theoretical Model

In this paper, we deal with the impact of post-innovation knowledge spillovers on private firms decisions to invest in R&D and cooperate, forming a Research Joint Venture (RJV). In particular, we analyze the case of two potential investors involved in a non-tounament competition for a stochastic product innovation in a market where imitation is possible, proposing a theoretical model where cooperation may emerge as subgame perfect Nash equilibrium of a three stage game: in the first stage, firms decide whether cooperate or not; in the second, they decide whether invest on; in the third, they compete in the market. We show that firms cooperate in R&D when spillovers are high enough and the fixed costs associated to R&D activities are low enough; however, our analysis suggests that cooperation in R&D may not always be optimal and, as a consequence, subsidizing any form of R&D cooperation is not efficient. Starting from the possible equilibria of the game, we propose an optimal scheme of subsides, which should be designed according to the intensity of spillovers, the level of R&D costs, and the probability to succeed in innovation. Finally, when we introduce collusion in the market stage, the private incentive to invest increases, reducing the cases where firms need public subsidies to cooperate in R&D. When subsides are costly tolerating collusion may be a second best solution.