Analysis of a nonlinear mixed Cournot game with boundedly rational players

•A dynamic nonlinear mixed Cournot game with a semipublic firm and a private firm is developed.•The stability of the Nash equilibrium and complex dynamic features are discussed.•The production adjustment costs are proved to inhibit the stability of the Nash equilibrium sometimes.

In this paper, we consider a creative case where one semipublic firm endeavors to maximize the weighted average on social welfare and its own profit while the other private firm only intends to maximize its own profit, so we bring in a dynamic nonlinear mixed Cournot model with bounded rationality. The locally asymptotical stability of the unique Nash equilibrium is also investigated and complex dynamic features including period doubling bifurcations, strange attractors and chaotic phenomena are also discussed. Furthermore, by introducing production adjustment costs into the model, we will show that sometimes they violate the locally asymptotical stability of the Nash equilibrium, compared to the well-known results under the best response dynamic when these costs act as a stabilizing factor.