Dynamic Location Games

We study a location game where consumers are distributed according to some density f and where market entry is costly and occurs sequentially. This permits an endogenous determination of the number of active ¯rms, their locations and the sequence in which these locations are occupied. While in general the analysis of such games is complicated by the fact that equilibrium locations and the sequence of settlement must be determined simul-taneously, we show that they can be independently derived for certain classes of densities including monotone and, under some additional restrictions, hump-shaped and U-shaped ones. For these classes we characterize the subgame perfect equilibrium outcome. More-over, when f is monotone and concave the equilibrium locations in areas where the density is larger tend to be more pro¯table. When f is uniform the number of ¯rms entering in equilibrium is minimal.