On Comparing between Two Nonlinear Cournot Duopoly Models

The comparison between two nonlinear duopoly models constructed based on symmetric utility function that is derived from Cobb–Douglas is investigated in this paper. The first model consists of two firms which update their outputs using gradient-based mechanism called bounded rationality. The second model contains a bounded rational firm that is competing with a firm whose outputs depend on a trade-off between market share maximization and profit maximization. For the two models, the fixed points are calculated and their conditions of stability are analyzed. The obtained results show that the second model is more stabilizing provided that the second firm adopts low weights of trade-offs. We show that the two models can be destabilized via flip bifurcation only. Furthermore, the noninvertibility of the two models that can give rise to several stable attractors is discussed.