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The dynamics of a differentiated duopoly with quantity competition

Fanti, Luciano and Gori, Luca (2011): The dynamics of a differentiated duopoly with quantity competition.

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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 stabilise (destabilise) the unique positive Cournot-Nash equilibrium of the economy.

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