Dynamics of a discrete-time mixed oligopoly Cournot-type model with three time delays.

This paper analyzes a discrete-time Cournot competition model with time delays taking into consideration the dynamics of market interactions involving one public firm and multiple private firms. The model assumes that the production output of the public firm is influenced by the past output levels of the private firms. The output levels of the private firms are affected by the past production outputs of both the public firm and their private competitors. The study identifies two equilibrium states within the nonlinear system: a positive equilibrium and a boundary equilibrium. Through a stability analysis, it is established that the boundary equilibrium is a saddle point. In the absence of time delays, the stability region for the positive equilibrium is determined. The research explores various specific delay scenarios, finding conditions under which the positive equilibrium is asymptotic stability. Additionally, the occurrence of flip and Neimark–Sacker bifurcations are examined. In order to illustrate the complex dynamics, the paper provides a series of numerical examples. • We explore Cournot competition with delays, involving both public and private firms. • Two equilibria are found: positive and boundary, with boundary as a saddle point. • Stability of positive equilibrium is analyzed, with and without time delays. • Flip/Neimark–Sacker bifurcations are investigated supported by numerical examples. [ABSTRACT FROM AUTHOR]