Heterogeneous duopoly with isoelastic demand function

Abstract

In this paper we analyze a duopolistic market with heterogeneous firms when the demand function is isoelastic (Puu, T., 1991. Chaos in duopoly pricing. Chaos, Solitons and Fractals 1, 573–581.). We consider the same heterogeneous firms of Zhang et al. (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148.) introducing a nonlinearity in the demand function instead of the cost function. Stability conditions of the Nash equilibrium and complex dynamics are studied. In particular we show two different routes to complicated dynamics: a cascade of flip bifurcations leading to periodic cycles (and chaos) and the Neimark-Sacker bifurcation which originates an attractive invariant closed curve. Comparisons with respect to the Puu model and the model of Zhang et al. are performed.