The dynamics of a differentiated duopoly with quantity competition

Posted by D. Daniel Sokol

Luciano Fanti (Department of Economics, University of Pisa) and Luca Gori (Department of Law and Economics "G.L.M. Casaregi", University of Genoa) describe The dynamics of a differentiated duopoly with quantity competition.

ABSTRACT: We analyse the dynamics of a Cournot duopoly game with heterogeneous players to investigate the effects of micro-founded differentiated products demand. The present analysis, which modifies and extends Zhang et al. (2007) (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148) and Tramontana, F., (2010) (Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357), reveals that a higher degree of product differentiation may destabilise the market equilibrium. Moreover, we show that a cascade of flip bifurcations may lead to periodic cycles and ultimately chaotic motions. Since a higher degree of product differentiation implies weaker competition, then a theoretical implication of our findings, that also constitute a policy warning for firms, is that a fiercer (weaker) competition tends to stabili! se (destabilise) the unique positive Cournot-Nash equilibrium of the economy.