When to adopt a service innovation: Nash equilibria in a competitive diffusion framework

Abstract

We study the optimal timing of adoption of a service innovation that a new entrant firm brings to a market populated by two incumbent firms. Our analysis is based on a model of competitive diffusion dynamics that extends the monopolistic Bass model to include customer churn processes, as well as a potential market expansion driven by the innovation. We obtain expressions for the time trajectories of the customer bases, i.e., the numbers of customers that use old and new service processes for the competing firms, as well as sharper, closed-form characterizations for the setting with a stable market and homogeneous imitation process.In modeling competitive dynamics we consider settings where incumbents anticipate a potential failure of the innovation. We use the trajectories for the customer bases to model an optimal adoption response problem faced by one of the incumbent firms when the adoption time for the other incumbent can be anticipated or is pre-announced, and analyze this problem in the absence of market expansion or intra-generational customer churn. Using the optimal response results, we provide the Nash equilibrium analysis of the adoption decisions by competing incumbent firms and derive sufficient conditions for the “now-now”, “now-never” and “never-never” adoption equilibria. We use the trading volume data from the foreign exchange markets to estimate the parameters of the competitive diffusion dynamics for our model and to conduct a numerical investigation of the impact of the uncertainty associated with the success of the innovation on the incumbents’ Nash equilibrium adoption times.