The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions.

中文翻译：

---

动态双头垄断模型：当企业以一定利润分享市场时

本文分析了古诺双寡头博弈的竞争，其参与者（公司）在具有等弹性需求函数和线性成本的市场中是异质的。第一家公司采用基于理性的梯度机制，而第二家公司选择以一定的利润分享市场以更新其生产。它在利润和市场份额最大化之间进行权衡。计算了拟议博弈的平衡点，并研究了其稳定性条件。我们的研究表明，平衡点通过倍增周期和Neimark-Sacker分叉变得不稳定。此外，描述拟议博弈的地图是非线性且不可逆的，这导致了几个稳定的吸引子。和文学一样