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Heterogeneity and the (de)stabilizing role of rationality

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  • Cavalli, Fausto
  • Naimzada, Ahmad
  • Pireddu, Marina

Abstract

In this paper we study oligopolies of generic size consisting of heterogeneous firms, which adopt best response adjustment mechanisms with either perfect foresight (rational firms) or static expectations (naive firms). Assuming an isoelastic demand function and possibly different marginal costs for the two groups of firms, we focus on the local stability of the Nash equilibrium. We show that, with respect to the oligopoly composition, described in terms of the fraction of rational firms, different scenarios are possible. We find that a high rationality degree may not always guarantee stability, in particular when rational firms have sufficiently larger marginal costs. In fact, in this situation, increasing the fraction of rational firms can even introduce instability. Besides the usual scenarios in which replacing some naive firms with rational ones leads to a stabilization of (or at least keeps unchanged) the dynamics, we provide a family of situations, characterized by costs ratio favorable to naive firms, in which equilibrium loses its stability when naive firms are replaced by rational ones. The results we present are both analytical and simulative.

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  • Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    • Handle: RePEc:eee:chsofr:v:79:y:2015:i:c:p:226-244
    DOI: 10.1016/j.chaos.2015.05.017
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    1. Akio Matsumoto & Ferenc Szidarovszky, 2011. "Stability, Bifurcation, and Chaos in N -Firm Nonlinear Cournot Games," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-22, February.
    2. Anufriev, Mikhail & Kopányi, Dávid & Tuinstra, Jan, 2013. "Learning cycles in Bertrand competition with differentiated commodities and competing learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2562-2581.
    3. 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.
    4. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
    5. 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.
    6. Ahmad Naimzada & Marina Pireddu, 2013. "Dynamics in a nonlinear Keynesian good market model," Working Papers 254, University of Milano-Bicocca, Department of Economics, revised Sep 2013.
    7. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    8. Banerjee, Abhijit & Weibull, Jorgen W., 2000. "Neutrally Stable Outcomes in Cheap-Talk Coordination Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 1-24, July.
    9. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    10. Naimzada, Ahmad & Pireddu, Marina, 2014. "Dynamic behavior of product and stock markets with a varying degree of interaction," Economic Modelling, Elsevier, vol. 41(C), pages 191-197.
    11. Lampart, Marek, 2012. "Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1081-1085.
    12. Akio Matsumoto, 2004. "Statistical Dynamics In Piecewise Linear Cournot Game With Heterogeneous Duopolists," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 295-321.
    13. Naimzada, Ahmad K. & Tramontana, Fabio, 2009. "Controlling chaos through local knowledge," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2439-2449.
    14. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    15. G.‐I. Bischi & M. Gallegati & A. Naimzada, 1999. "Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games," Annals of Operations Research, Springer, vol. 89(0), pages 252-271, January.
    16. Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    17. 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.
    18. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    19. Angelini, Natascia & Dieci, Roberto & Nardini, Franco, 2009. "Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3179-3196.
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    1. Andrea Caravaggio & Lorenzo Cerboni Baiardi & Mauro Sodini, 2021. "A note on symmetry breaking in a non linear marketing model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 507-531, December.
    2. Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    3. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    4. Fausto Cavalli & Ahmad Naimzada & Mauro Sodini, 2018. "Oligopoly models with different learning and production time scales," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 297-312, November.

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