Spillovers, disclosure lags, and incentives to innovate. Do oligopolies over-invest in R&D?

We develop a dynamic duopoly, where firms have to take into account a technological externality, that reduces over time their innovation costs, and an inter-firm spillover, that lowers only the second comer's R&D cost. This spillover exerts its effect after a disclosure lag. We identify three possible equilibria, which are classified, according to the timing of R&D investments, as early, intermediate, and late. The intermediate equilibrium is subgame perfect for a wide parameters range. When the innovation size is large, it implies that the duopolistic market equilibrium involves underinvestment. Hence, even in presence of a moderate degree of inter-firms spillover, the competitive equilibrium calls for public policies aimed at increasing the research activity. When we focus on minor innovations -- the case in which, according to the earlier literature, the market equilibrium underinvests -- our results imply that the policies aimed at stimulating R&D have to be less sizeable than suggested before, despite the presence of an inter-firm spillover.