A discontinuous model of duopoly with isoelastic demand and innovation costs

The paper studies the dynamic properties of a duopoly game in which firms strategically compete in quality-enhancing innovation investments and quantities. Market demands are assumed to be isolastic (reciprocal to the price) functions. The non-linearity of the demand functions, as already highlighted by T. Puu in [11], suggests the existence of complicated dynamics (cyclical or chaotic) in a standard dynamic Cournot duopoly. In addition to this, competition in innovation introduces the presence of discontinuities in the best response functions, expanding the set of possible equilibria (including asymmetric and multiple ones) of the standard Cournot duopoly and further enriching the dynamic features of the model.