Comparing customer taste distributions in vertically differentiated mobile service markets

Abstract

In this paper, we study a vertically differentiated duopoly market, where competitors (mobile service providers) offer mobile subscriptions to customers, who diversify in their preferences regarding price and quality. We consider a two-stage game where the players first select the quality and then begin a competitive process for the price or quantity, which is widely known as Bertrand or Cournot game, respectively. To capture the service provider strategy, we first introduce variable costs to improve the quality, which are linear in quality per a subscription, and then derive the market-related metrics of interest for the tractable uniform distribution of the customer’s taste parameter. Further relaxing this strong assumption, we provide with a numerical procedure that helps characterize an arbitrary taste distribution as well as an arbitrary cost function. Finally, selected numerical examples report on the comparison between the uniform and the truncated exponential distribution, thus accentuating the importance of choosing an appropriate customer taste model.