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.

中文翻译：

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关于两个非线性古诺双寡头模型的比较

本文研究了基于Cobb–Douglas的基于对称效用函数构造的两个非线性双寡头模型之间的比较。第一个模型由两家公司组成，它们使用称为有界理性的基于梯度的机制来更新其产出。第二种模型包含一个有界理性公司，该公司与一个其竞争取决于市场份额最大化和利润最大化之间权衡的公司竞争。对于这两个模型，计算了不动点，并分析了它们的稳定性条件。获得的结果表明，如果第二家公司采用较低的权衡权重，则第二种模型更加稳定。我们表明，这两个模型只能通过翻转分叉来稳定。此外，