Dynamic analysis of discontinuous best response with innovation

We study a Cournot duopoly where firms can decide to incur fixed costs in activities that improve their competitiveness (i.e. product development or process innovation). Innovation costs generate discontinuities in the firms' quantity best response functions and, in turn, a variety of equilibrium configurations, including multiple equilibria. We provide a dynamic global analysis of the equilibria and show the way in which firms' initial expectations regarding the rival's level of output are crucial in defining the configuration of the long run equilibrium.