Stackelberg-Nash Equilibrium in the Linear City Model

In the paper [1], the spatial duopoly of firms under Stackelberg competition in which one of the firms is the leader, both by the volume of goods supply and location, was studied. In this paper, we consider the case of leadership only by the volume of goods supply. The Stackelberg-Nash equilibrium in the quantity and spatial strategies of firms are found. In the course of stability analysis of this equilibrium, it is proved that the transport tariff is a bifurcation parameter for firms. It is established that the change of the central agglomeration strategy into the differentiation strategy occurs at the point of transcritical bifurcation. The conditions for full coverage of the markets for both strategies are determined. As is demonstrated below, the Stackelberg information asymmetry leads to the asymmetry of equilibrium locations of firms.