We analyze firm research and development investment incentives in a framework in which only one innovation can be undertaken. We assume that the probability of discovering the innovation depends on a parameter that represents the technical difficulty of innovating. We show that patent protection is not always necessary for investments to be made. With patent protection, research and development competition leads to a symmetric equilibrium. Moreover, firms over-invest in marginal innovation but under-invest in difficult innovation, which explains why and how public authorities should intervene to promote specific research in certain economic sectors.