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Decisions in Economics and Finance

, Volume 41, Issue 2, pp 259–275 | Cite as

A continuous-time heterogeneous duopoly model with delays

  • Serena Brianzoni
  • Giovanni CampisiEmail author
  • Luca Guerrini
Article
  • 18 Downloads

Abstract

In this paper, the continuous-time version with delays of the model of Tramontana (Econ Model 27(1):350–357, 2010) is presented. The stability of the equilibrium point is discussed by analyzing the distribution of roots of associated characteristic equation. It is found that combining marginal costs with time delays gives rise to different economic scenarios, where stability switches may appear and Hopf bifurcations occur within certain range of parameters.

Keywords

Heterogeneous players Duopoly model Time delay 

Notes

Acknowledgements

The authors gratefully acknowledge two anonymous reviewers for comments and suggestions. The usual disclaimer applies.

References

  1. Bischi, G.I., Naimzada, A.K., Sbragia, L.: Oligopoly games with local monopolistic approximation. J. Econ. Behav. Organ. 62(3), 371–388 (2007)CrossRefGoogle Scholar
  2. Bischi, G.I., Lamantia, F., Radi, D.: An evolutionary cournot model with limited market knowledge. J. Econ. Behav. Organ. 116, 219–238 (2015)CrossRefGoogle Scholar
  3. Dieci, R., Westerhoff, F.: Stability analysis of a cobweb model with market interactions. Appl. Math. Comput. 215(6), 2011–2023 (2009)Google Scholar
  4. Ezekiel, M.: The cobweb theorem. The Quarterly Journal of Economics, pages 255–280 (1938)Google Scholar
  5. Gori, L., Guerrini, L., Sodini, M.: A continuous time cournot duopoly with delays. Chaos Solitons Fract. 79, 166–177 (2015a)CrossRefGoogle Scholar
  6. Gori, L., Guerrini, L., Sodini, M.: Hopf bifurcation and stability crossing curves in a cobweb model with heterogeneous producers and time delays. Nonlinear Anal. Hybrid Syst. 18, 117–133 (2015b)CrossRefGoogle Scholar
  7. Gori, L., Guerrini, L., Sodini, M.: Different modelling approaches for time lags in a monopoly. Essays in Economic Dynamics, pp. 81–98. Springer (2016)Google Scholar
  8. Gori, L., Guerrini, L., Sodini, M.: A characterisation of duopoly dynamics with frictions in production adjustments. J. Evolut. Econ. 27(5), 963–988 (2017)CrossRefGoogle Scholar
  9. Hommes, C.H.: Adaptive learning and roads to chaos: the case of the cobweb. Econ. Lett. 36(2), 127–132 (1991)CrossRefGoogle Scholar
  10. Hommes, C.H.: Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand. J. Econ. Behav. Organ. 24(3), 315–335 (1994)CrossRefGoogle Scholar
  11. Matsumoto, A., Nakayama, K.: Nonlinear cobweb model with time delays.International Conference on Modeling, Simulation and AppliedMathematics, pages 402–406. (2015)Google Scholar
  12. Matsumoto, A., Szidarovszky, F.: Nonlinear delay monopoly with bounded rationality. Chaos Solitons Fract. 45(4), 507–519 (2012)CrossRefGoogle Scholar
  13. Matsumoto, A., Szidarovszky, F.: Discrete and continuous dynamics in nonlinear monopolies. Appl. Math. Comput. 232, 632–642 (2014)Google Scholar
  14. Matsumoto, A., Szidarovszky, F.: The asymptotic behavior in a nonlinear cobweb model with time delays. Discrete Dynamics in Nature and Society, 2015 (2015)Google Scholar
  15. Pecora, N., Sodini, M.: A heterogenous cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves. Commun. Nonlinear Sci. Numer. Simul. 58, 36–46 (2018)CrossRefGoogle Scholar
  16. Puu, T.: The chaotic monopolist. Chaos Solitons Fract. 5(1), 35–44 (1995)CrossRefGoogle Scholar
  17. Ruan, S., Wei, J.: On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Continuous Discrete Impuls. Syst. Ser. A 10, 863–874 (2003)Google Scholar
  18. Tramontana, F.: Heterogeneous duopoly with isoelastic demand function. Econ. Model. 27(1), 350–357 (2010)CrossRefGoogle Scholar

Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2018

Authors and Affiliations

  1. 1.Department of ManagementPolytechnic University of MarcheAnconaItaly
  2. 2.Department of Agricultural, Food and Environmental SciencesPolytechnic University of MarcheAnconaItaly

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