Innovation race under revenue and technology uncertainty of heterogeneous firms where the winner does not take all

Abstract

ABSTRACT We analyze the competitive investment behavior on innovative products or services under revenue and technology uncertainty for heterogenous firms. Firms make a decision on how much to invest in research and development of an innovative technology at the beginning of the time horizon. They discover the technology at an uncertain time in the future. The time of successful discovery depends on the amount of investment and the characteristics of the firms. All firms collect revenues even though they are not winners. Although there can be positive or negative external shocks, the potential revenue rates decrease in time and the first firm to adopt the technology is less prone to negative shocks and benefits more from positive shocks. Therefore, the competition is a stochastic race, where all firms collect some revenue once they adopt. We show the existence of a pure strategy Nash equilibrium for this game in a duopoly market under general assumptions and provide more structural results when the time to successfully innovate is exponentially distributed. We show the uniqueness of the equilibrium for an arbitrary number of symmetric firms. We argue that for sufficiently efficient firms who are resilient against market shocks, consolidating racing firms will decrease their expected profits. We also provide an illustrative computational analysis for comparative statics, where we show the non-monotonic behavior of equilibrium investment levels as examples. It appears that the equilibrium investment level behavior in innovation can be highly dependent on firm characteristics.