Abstract
Although oligopoly theory is generally concerned with the single-product firm, what is true in the real word is that most of the firms offer multiproducts rather than single products in order to obtain cost-saving advantages, cater for the diversity of consumer tastes, and provide a barrier to entry. We develop a dynamical multiproduct Cournot duopoly model in discrete time, where each firm has an owner who delegates the output decision to a manager. The principle of decision-making is bounded rational. And each firm has a nonlinear total cost function due to the multiproduct framework. The Cournot Nash equilibrium and the local stability are investigated. The tangential bifurcation and intermittent chaos are reported by numerical simulations. The results show that high output adjustment speed can lead to output fluctuations which are characterized by phases of low volatility with small output changes and phases of high volatility with large output changes. The intermittent route to chaos of Flip bifurcation and another intermittent route of Flip bifurcation which contains Hopf bifurcation can exist in the system. The study can improve our understanding of intermittent chaos frequently observed in oligopoly economy.
Highlights
Dynamic Cournot model is a typical nonlinear discrete time varying system which takes output as its decision variable
In the period window, with the increase of α1, the periodic orbit which is caused by tangential bifurcation shows bifurcation, and the structure of this bifurcation has a self-similar construction with the main bifurcation which evolves into chaos via Flip bifurcation
In this paper we propose a multiproduct Cournot duopoly model with relative profit delegation
Summary
Dynamic Cournot model is a typical nonlinear discrete time varying system which takes output as its decision variable. Tramontana and Elsadany [2] proposed a three oligopoly market with heterogeneous expectations, analyzed double routes to chaos (Hopf and Flip bifurcation), and presented the differences of the two routes from the economic view. Xin et al [4] built a nonlinear discrete output game model for two oligopolistic firms whose products are adnascent and investigated its complex dynamics. We build a duopoly multiproduct output model which extends the models of [1,2,3,4,5,6,7], which consider single-product firm, and introduce the managerial delegation to the multiproduct model which modifies the models of [1,2,3,4,5,6].
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