Spatial Cournot competition and agglomeration in a model of location choice

Consider a two-stage non-cooperative Cournot game with location choice involving n greater than or equal to 2 competing firms. There are spatially contiguous markets along the interval [0,1] with relative size of the markets described by a continuous density function phi(x). The demand function for each individual consumer is the same in each market. Each firm first selects the location of its facility and then selects the quantities to supply to the markets, so as to maximize its profit. Earlier works on Cournot competition in spatial models have shown, assuming that the consumers are distributed uniformly over the markets, that firms typically tend toward central agglomeration. This paper extends the previous work by establishing the robustness of the agglomeration equilibrium to a broad class of density functions. Derived here are conditions under which: (i) agglomeration of all n firms is an equilibrium, (ii) agglomeration of duopolists is the only equilibrium, and (iii) duopolists exhibit a dispersed equilibrium. Examples of partial agglomeration are also constructed.