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The paper analyzes the interactions among one public firm and $n$ privatefirms on the market, in the framework of a discrete-time Cournot game with timedelay. The production of the public firm is influenced by previous outputlevels of private firms. The productions of private companies are influenced bythe past productions of the public company, as well as by the previousproductions of the other private companies. The associated nonlinear systemadmits two equilibrium points: the positive one and the boundary equilibrium.After the stability analysis, we obtained that the boundary equilibrium pointis a saddle point. If there is no delay, for the positive equilibrium point wehave determined the stability region. Then, for different particular cases ofdelays, we found the conditions for which the positive equilibrium isasymptotically stable. The flip and Neimark-Sacker bifurcations areinvestigated. In addition, numerous numerical examples are performed to revealthe complex dynamic behavior of the system.

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