Research and Development with a Generalized Hazard Function

Previous work in this area has analyzed research and development as a stochastic racing game where the strategy is the rate of investment on the innovation, conditional on no success to date. This paper generalizes this work in several ways; first, we use a more general hazard function, although we retain the assumption that it depends only upon current investment. We find that when patent protection is perfect, equilibrium investment rates are monotonically increasing over time. Second, we allow for the possibility that some firms are currently receiving profits from the sale of a product which will be replaced by the innovation. This allows us to determine whether current industry leaders will tend to be more or less innovative than firms with smaller current market shares. We find that, in a stationary equilibrium, current industry leaders will tend to invest at a lower rate than those firms which currently have smaller market shares. We also remark that a stationary equilibrium implies that the random success date follows an exponential distribution, an assumption which is ubiquitous in the earlier theoretical work on this subject.