I study a dynamic variant of the Dixit–Stiglitz (Am Econ Rev 67(3), 1977) model of monopolistic competition by introducing price stickiness à la Fershtman and Kamien (Econometrica 55(5), 1987). The analysis is restricted to bounded quantity and price paths that fulfill the necessary conditions for an open-loop Nash equilibrium. I show that there exists a symmetric steady state and that its stability depends on the degree of product differentiation. When moving from complements to perfect substitutes, the steady state is either a locally asymptotically unstable (spiral) source, a stable (spiral) sink or a saddle point. I further apply the Hopf bifurcation theorem and prove the existence of limit cycles, when passing from a stable to an unstable steady state. Lastly, I provide a numerical example and show that there exists a stable limit cycle.

我通过引入价格粘性àla Fershtman和Kamien（Econometrica 55（5），1987），研究了Dixit-Stiglitz（Am Econ Rev 67（3），1977）模型的动态变化。该分析仅限于满足开环纳什均衡必要条件的有限数量和价格路径。我表明存在一个对称的稳态，其稳定性取决于产品的差异程度。当从补码到完美替换时，稳态是局部渐近不稳定（螺旋形）源，稳定（螺旋形）沉点或鞍点。我进一步应用了霍普夫分支定理，并证明了从稳定状态转变为不稳定状态时极限环的存在。最后，我提供了一个数值示例，并表明存在一个稳定的极限环。