Nonlinear duopoly games with positive cost externalities due to spillover effects

A Cournot duopoly game is proposed where the interdependence between the quantity-setting firms is not only related to the selling price, determined by the total production through a given demand function, but also on cost-reduction effects related to the presence of the competitor. Such cost reductions are introduced to model the effects of know-how spillovers, caused by the ability of a firm to take advantage, for free, of the results of competitors' Research and Development (R&D) results, due to the difficulties to protect intellectual properties or to avoid the movements of skilled workers among competing firms. These effects may be particularly important in the modeling of high-tech markets, where costs are mainly related to R&D and workers' training. The results of this paper concern the existence and uniqueness of the Cournot–Nash equilibrium, located at the intersection of non-monotonic reaction curves, and its stability under two different kinds of bounded rationality adjustment mechanisms. The effects of spillovers on the existence of the Nash equilibrium are discussed, as well as their influence on the kind of attractors arising when the Nash equilibrium is unstable. Methods for the global analysis of two-dimensional discrete dynamical systems are used to study the structure of the basins of attraction.