Heterogeneous duopoly with isoelastic demand function
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.
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- Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
- Agliari, Anna & Gardini, Laura & Puu, Tönu, 2005. "Some global bifurcations related to the appearance of closed invariant curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(3), pages 201-219.
- Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-22, February.
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- Gian-Italo Bischi & Ahmad K. Naimzada & Lucia Sbragia, 2004. "Oligopoly Games with Local Monopolistic Approximation," Working Papers 81, University of Milano-Bicocca, Department of Economics, revised Nov 2004.
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"Cournot Duopoly when the Competitors Operate Multiple Production Plants,"
0809, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
- Agiza, H.N. & Hegazi, A.S. & Elsadany, A.A., 2002. "Complex dynamics and synchronization of a duopoly game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 133-146.
- Anna Agliari & Laura Gardini & Tonu Puu, 2006. "Global Bifurcations In Duopoly When The Cournot Point Is Destabilized Via A Subcritical Neimark Bifurcation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-20.
- Ahmad Naimzada & Fabio Tramontana, 2008. "Controlling Chaos Through Local Knowledge," Working Papers 0810, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
- Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
- Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
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