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The dynamics of a differentiated duopoly with quantity competition

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  • Fanti, Luciano
  • Gori, Luca

Abstract

We analyse the dynamics of a Cournot duopoly with heterogeneous players to investigate the effects of micro-founded differentiated products demand on stability. The present study, which indeed 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 behaviours. Since a higher degree of product differentiation implies weaker competition, then a theoretical implication of our findings, that also constitute a policy warning, is that a fiercer (weaker) competition tends to stabilise (destabilise) the unique positive Cournot–Nash equilibrium.

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Bibliographic Info

Article provided by Elsevier in its journal Economic Modelling.

Volume (Year): 29 (2012)
Issue (Month): 2 ()
Pages: 421-427

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Handle: RePEc:eee:ecmode:v:29:y:2012:i:2:p:421-427

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Web page: http://www.elsevier.com/locate/inca/30411

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Keywords: Bifurcation; Chaos; Cournot; Oligopoly; Product differentiation;

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References

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  1. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
  2. Wouter J. Denhaan, 2000. "The Importance Of The Number Of Different Agents In A Heterogeneous Asset-Pricing Model," Computing in Economics and Finance 2000 349, Society for Computational Economics.
  3. Häckner, Jonas, 1999. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Research Papers in Economics 1999:9, Stockholm University, Department of Economics.
  4. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, October.
  5. Qiu, Larry D., 1997. "On the Dynamic Efficiency of Bertrand and Cournot Equilibria," Journal of Economic Theory, Elsevier, vol. 75(1), pages 213-229, July.
  6. 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.
  7. Luciano Fanti & Nicola Meccheri, 2010. "The Cournot-Bertrand Profit Differential in a Differentiated Duopoly with Unions and Labour Decreasing Returns," Working Paper Series 36_10, The Rimini Centre for Economic Analysis.
  8. Lopez, Monica Correa & Naylor, Robin A., 2004. "The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining," European Economic Review, Elsevier, vol. 48(3), pages 681-696, June.
  9. 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.
  10. Ghosh, Arghya & Mitra, Manipushpak, 2010. "Comparing Bertrand and Cournot in mixed markets," Economics Letters, Elsevier, vol. 109(2), pages 72-74, November.
  11. 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.
  12. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
  13. 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.
  14. 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.
  15. 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.
  16. Huang, Weihong, 2008. "The long-run benefits of chaos to oligopolistic firms," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1332-1355, April.
  17. 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.
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Citations

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Cited by:
  1. Luciano Fanti, 2012. "The dynamics of a banking duopoly with capital regulations," Discussion Papers 2012/151, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  2. Fanti, Luciano & Gori, Luca, 2012. "The codetermined firm in a Cournot duopoly: A stability analysis," Economic Modelling, Elsevier, vol. 29(4), pages 1242-1247.
  3. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," MPRA Paper 37834, University Library of Munich, Germany.
  4. Fanti, Luciano, 2014. "The dynamics of a banking duopoly with capital regulations," Economic Modelling, Elsevier, vol. 37(C), pages 340-349.
  5. Luciano Fanti, 2012. "Environmental standards and Cournot duopoly: a stability analysis," Discussion Papers 2012/154, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  6. Du, Jian-guo & Fan, Yue-qian & Sheng, Zhao-han & Hou, Yun-zhang, 2013. "Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter," Economic Modelling, Elsevier, vol. 33(C), pages 507-516.
  7. Fanti, Luciano & Gori, Luca, 2011. "Cross-ownership and stability in a Cournot duopoly," MPRA Paper 34574, University Library of Munich, Germany.

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