A Heterogeneous Duopoly Game under an Isoelastic Demand and Diseconomies of Scale

In this paper, we investigate a duopolistic market with heterogeneous firms under the assumptions of an isoelastic demand and quadratic costs. We obtain the sufficient and necessary condition of the local stability of the Cournot-Nash equilibrium and analytically compare it with that of the analogue model under linear rather than quadratic costs. By approaches of symbolic computation, we prove that diseconomies of scale have an effect of stabilizing the game provided that the cost parameters are large enough. Moreover, by means of numerical simulations, we find that our model loses its stability only through a period-doubling bifurcation, which is different from its analogue having two possible routes to chaotic dynamics.