Stability properties of a Cournot-type oligopoly model with time delay

Abstract

The paper studies a Cournot game involving n private firms, where the firms’ interactions are analyzed in a discrete-time setting with time delay. The past production levels of other private firms have an impact on the production levels of each private firm. We performed a local stability analysis on the nonlinear system associated with the model and found that it has only one equilibrium point, which is asymptotically stable if and only if some conditions involving the number of firms, the degree of product di erentiation and the time delay are fulfilled. In addition, numerical examples are presented in this paper, which illustrate the theoretical results obtained.

Keywords

• equilibrium point
• local stability
• oligopoly game
• bifurcations
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