Dynamic stability of Stackelberg equilibrium in mixed oligopolies: The role of social responsibility, marginal costs, and market structure

This paper investigates how corporate social responsibility, marginal costs, and market structure affect the stability of the Stackelberg equilibrium in mixed oligopolies. To achieve this, we develop dynamic mixed duopoly and triopoly models, showing that the Stackelberg equilibrium is locally asymptotically stable when the adjustment speed is below a threshold. The stability of the equilibrium is enhanced by increased marginal costs, stronger commitment to social responsibility, and the presence of a sophisticated follower in the triopoly setting. However, when the adjustment speed exceeds the threshold and the equilibrium becomes unstable, we introduce a control term into the dynamic model to restore stability. The implications of our analysis highlight the importance of firms avoiding excessive cost cutting in favor of innovation driven competition. Additionally, fostering social responsibility and moderate market competition plays a critical role in sustaining stable markets over the long term.