Nonlinear duopoly games with positive cost externalities due to spillover effects

A Cournot duopoly game is proposed where the interdependence between the qu antity-setting firms is not only related to the selling price, determined b y the total production through a given demand function, but also on cost-re duction effects related to the presence of the competitor. Such cost reduct ions 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 compet itors' Research and Development (R&D) results, due to the difficulties to p rotect 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 wo rkers' training. The results of this paper concern the existence and unique ness of the Cournot-Nash equilibrium, located at the intersection of non-mo notonic reaction curves, and its stability under two different kinds of bou nded rationality adjustment mechanisms. The effects of spillovers on the ex istence of the Nash equilibrium are discussed, as well as their influence o n the kind of attractors arising when the Nash equilibrium is unstable. Met hods for the global analysis of two-dimensional discrete dynamical systems are used to study the structure of the basins of attraction. (C) 2001 Elsev ier Science Ltd. All rights reserved.