On the Dynamics of a Duopoly Game with Differentiated Goods

The present study extends Fanti, Gori, 2012 (L. Fanti, L. Gori, 2012. The dynamics of a differentiated duopoly with quantity competition, Economic Modelling, 29, 421-427). In this study we investigate the dynamics of a nonlinear discrete-time duopoly game with differentiated goods, linear demand and quadratic cost functions. The game is modeled with a system of two difference equations. Existence and stability of equilibria of this system are studied. We show that the model gives more complex chaotic and unpredictable trajectories as a consequence of change in the parameter of horizontal product differentiation and a higher (lower) degree of product differentiation (weaker or fiercer competition) destabilize (stabilize) the economy. The chaotic features are justified numerically via computing Lyapunov numbers and sensitive dependence on initial conditions. Also, we show that in the case of quadratic costs there are stable trajectories and a higher (lower) degree of product differentiation does not tend to destabilize the economy.