A differential game theoretic model for duopolistic competition on design quality

In this paper we propose a differential game theoretic model to analyze the design quality and pricing decisions for a product over the product life cycle. The market is represented as a duopoly where our product competes against a similar product marketed by our competition. The duopolistic competition is modelled as a two-player nonzero sum noncooperative game. The resulting control theoretic model is solved under certain functional assumptions to describe the Nash equilibrium strategies of the two competitors. Finally, observations made on an extensive set of numerical experimentations over a variety of model parameters are summarized into a set of relevant managerial guidelines on developing design quality and pricing strategies.