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 microfounded 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 CournotNash equilibrium of the economy.
Item Type:  MPRA Paper 

Original Title:  The dynamics of a differentiated duopoly with quantity competition 
English Title:  The dynamics of a differentiated duopoly with quantity competition 
Language:  English 
Keywords:  Bifurcation; Chaos; Cournot; Oligopoly; Product differentiation 
Subjects:  L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L13  Oligopoly and Other Imperfect Markets D  Microeconomics > D4  Market Structure and Pricing > D43  Oligopoly and Other Forms of Market Imperfection C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  33477 
Depositing User:  Luca Gori 
Date Deposited:  17. Sep 2011 18:51 
Last Modified:  13. Feb 2013 03:35 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/33477 