Spatial competition and social welfare considering different feasible location regions

This research examines the location-price game of two firms, where consumers with quadratic transportation costs are dispersed along the linear city [0, 1], while firms can select their business sites on a continuous but arbitrarily constrained interval [ m , n ] or on a discontinuous interval separated by a continuous zoning area, in which business activities are prohibited. We find that at least one subgame perfect equilibrium in pure strategies exists. Multiple equilibria may emerge when the continuous location region is far from consumers with the remote firm earning a zero profit. When the continuous region is relatively small and not too far from consumers, two firms choose to locate separately at the endpoints of the interval. When considering the discontinuous location region, the highest social surplus can be achieved when both firms are located on one side of the zoning area.