Purpose The purpose of this study is to analyze comparatively the properties of open-loop and closed-loop equilibria in a dynamic oligopoly model with price dynamics and reflexive behavior of market agents. Design/methodology/approach To consider dynamic competitive markets, the authors focus on a differential game theory in oligopolistic structures, using analytical models to illustrate how advertising effort, good differentiation and price stickiness interact simultaneously in the open-loop and the closed-loop Nash equilibria. The comparative assessment of these equilibria obtains some significant results. Findings An optimization model that enriches the continuous time is presented. Under the open-loop and the closed-loop, Nash equilibrium showed an increase in the total output, advertising in price stickiness and promotional efficiency, while there was a decrease in product differentiation and advertising promotional efficiency. However, the open-loop equilibrium levels are larger than the closed-loop equilibrium. Under the closed-loop information, the long-run equilibrium was faster than the opened-loop in a dynamic oligopoly. The graphical illustration was used to present the behavior of the model parameters. Practical implications This study helps managers to choose an appropriate price and advertising adjustment to maximize profit. The obtained results may help firms to make the smart decision and may provide managers the valuable tool for making decisions in the competitive market environments. Originality/value This is a first attempt to analyze a dynamic oligopoly in the differentiated market environment. It considers a joint action of the output and advertising in shaping the closed-loop and the open-loop equilibria with N competitors in a dynamic competitive setting.