A continuous time Cournot duopoly with delays

Gori, Luca and Guerrini, Luca and Sodini, Mauro (2015): A continuous time Cournot duopoly with delays. Forthcoming in: Chaos, Solitons & Fractals

Abstract

This paper extends the classical repeated duopoly model with quantity-setting firms of Bischi et al. (1998) by assuming that production of goods is subject to some gestation lags but exchanges take place continuously on the market. The model is expressed in the form of differential equations with discrete delays. By using some recent mathematical techniques and numerical experiments, results show some dynamic phenomena that cannot be observed when delays are absent. In addition, depending on the extent of time delays and inertia, synchronisation failure can arise even in the event of homogeneous firms.

• Item Type: MPRA Paper
• Language: English
• Keywords: Chaos; Cournot duopoly; Time delays
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets

References

Asea, P., Zak, P., 1999. Time to build and cycles. Journal of Economic Dynamics & Control 23, 1155--1175.

Bambi, M., Gori, F., 2014. Unifying time-to-build theory. Macroeconomic Dynamics 18, 1713--1725.

Berezowski, M., 2001. Effect of delay time on the generation of chaos in continuous systems. One-dimensional model. Two-dimensional model-tubular chemical reactor with recycle. Chaos, Solitons & Fractals 12, 83--89.

Bischi, G.I., Naimzada, A., Sbragia, L., 2007. Oligopoly games with Local Monopolistic Approximation. Journal of Economic Behavior & Organization 62, 371--388.

Bischi, G.I., Stefanini, L., Gardini, L., 1998. Synchronization, intermittency and critical curves in a duopoly game. Mathematics and Computers in Simulation 44, 559--585.

Chen, S., Shi, J., Wei, J., 2013. Time delay-induced instabilities and Hopf bifurcations in general reaction--diffusion systems. Journal of Nonlinear Science 23, 1--38.

Dixit, A.K., 1986. Comparative statics for oligopoly. International Economic Review 27, 107--122.

Ferrara, M., Guerrini, L., Sodini, M., 2014. Nonlinear dynamics in a Solow model with delay and non-convex technology. Applied Mathematics and Computation 228, 1-12.

Guerrini, L., Sodini, M., 2013. Dynamic properties of the Solow model with increasing or decreasing population and time-tobuild technology. Abstract and Applied Analysis, article ID 280925.

He, X.-Z., Li, K., 2012. Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model. Journal of Economic Dynamics & Control 36, 973--987.

He, X.-Z., Zheng, M., 2010. Dynamics of moving average rules in a continuous-time financial market model. Journal of Economic Behavior & Organization 76, 615--634.

Krawiec, A., Szydlowski, M., 1999. The Kaldor--Kalecki business cycle model. Annals of Operations Research 89, 89--100.

Lin, X., Wang, H., 2012. Stability analysis of delay differential equations with two discrete delays. Canadian Applied Mathematics Quarterly 20, 519--533.

Matsumoto, A., Szidarovszky, F., 2011. Delay differential neoclassical growth model. Journal of Economic Behavior & Organization 78, 272--289.

Matsumoto, A., Szidarovszky, F., 2012. Nonlinear delay monopoly with bounded rationality. Chaos, Solitons & Fractals 45, 507--519.

Matsumoto, A., Szidarovszky, F., 2014. Discrete and continuous dynamics in nonlinear monopolies. Applied Mathematics and Computation 232, 632--642.