A R&D Race with Dual Uncertainties: Technical (In)Feasibility and Timing of Innovation

This paper develops a simple model of a R&D race with two sources of uncertainty about the innovation. The first is about its technical feasibility, and, the second, if the innovation is technically feasible, about its timing. Firms have prior beliefs that the innovation is technically feasible. As the race continues without success, firms become increasingly pessimistic that the innovation is technically feasible, which impacts investment, modeled as feedback strategies. Closed form solutions are developed, which include several earlier models as special cases. It is shown that the equilibrium path of research intensities under technical feasibility uncertainty: (a) lies below that of technical feasibility, (b) may rise or fall over time, and (c) will converge to a ‘steady state’ level in the long run. Increased rivalry raises innovative activity in the short run, but dampens it in the long run, implying that the equilibrium paths of research intensities for various number of rivals will cross. Allowing for an endogenous market structure: (a) under free entry, a competitive market structure emerges but the race lasts for an instant, and (b) under fixed cost of entry, a finite number of firms participate, where this number is a function of how optimistic firms are that the innovation is technically feasible.