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
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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.
Bischi, G., Chiarella, C., Kopel, M., Szidarowski, F.: Nonlinear Oligopolies—Stability and Bifurcations. Springer, Berlin (2010)CrossRefGoogle Scholar
Cavalli, F., Naimzada, A.: Effect of price elasticity of demand in monopolies with gradient adjustment. Chaos Solitons Fractals 76, 47–55 (2015)CrossRefGoogle Scholar
Cavalli, F., Naimzada, A.: A multiscale time model with piecewise constant argument for a boundedly rational monopolist. J. Differ. Equ. Appl. 22, 1489–1580 (2016)CrossRefGoogle Scholar
Cavalli, F., Naimzada, A., Pireddu, M.: Heterogeneity and the (de) stabilizing role of rationality. Chaos Solitons Fractals 79, 226–244 (2015)CrossRefGoogle Scholar
Howroyd, T.D., Russell, A.M.: Cournot oligopoly models with time delays. J. Math. Econ. 13, 97–103 (1984)CrossRefGoogle Scholar
Howroyd, T.D., Rickard, J.A., Russell, A.M.: The effects of delays on the stability and rate of convergence to equilibrium of oligopolies. Econ. Rec. 62, 194–198 (1986)CrossRefGoogle Scholar
Lamantia, F., Radi, D.: Exploitation of renewable resources with differentiated technologies: an evolutionary analysis. Math. Comput. Simul. 108, 155–174 (2015)CrossRefGoogle Scholar
Matsumoto, A., Szidarovszky, F.: Dynamics in linear Cournot duopolies with two time delays. Comput. Econ. 38, 311–327 (2011)CrossRefGoogle Scholar
Mooradian, T., Matzler, K., Ring, L.: Strategic Marketing. Pearson, London (2014)Google Scholar
Quandt, R.E.: On the stability of price adjusting oligopoly. South. Econ. J. 33, 332–336 (1967)CrossRefGoogle Scholar
Wiener, J.: Generalized Solutions of Functional Differential Equations. World Scientific, Singapore (1993)CrossRefGoogle Scholar