Decisions in Economics and Finance

, Volume 41, Issue 2, pp 297–312 | Cite as

Oligopoly models with different learning and production time scales

  • Fausto CavalliEmail author
  • Ahmad Naimzada
  • Mauro Sodini


We propose a modelling approach to study Cournotian oligopolies of boundedly rational firms which continuously update production decisions on the basis of information collected periodically. The model consists of a system of differential equations with piecewise constant arguments, which can be recast into a system of difference equations. Considering different economic settings, we study the local stability of equilibrium, proving the destabilizing role of the time lag between two consecutive learning activities. We investigate some particular families of oligopolies showing the occurrence of both flip and Neimark–Sacker bifurcations, as well as the evidence of multistability with the coexistence between different attractors, occurring when oligopolies consisting of both technologically different and identical firms are studied.


Cournot oligopolies Learning and production decisions Differential equations with piecewise constant argument Stability Bifurcations Multistability 

JEL Classification

L13 C62 



The authors wish also to thank the anonymous Reviewers and Professor Anufriev, Guest Editor of the Special Issue on “Stability and Bifurcations in Nonlinear Economic Systems”, for the useful suggestions.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Mathematical Finance and EconometricsCatholic University of Sacred HeartMilanItaly
  2. 2.DEMSUniversity of Milano-BicoccaMilanItaly
  3. 3.Department of Economics and ManagementUniversity of PisaPisaItaly

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