A cellular automaton for the simulation of competitive location

Since the seminal paper by Hotelling (1929) the principle of minimum differentiation has been accepted as one of the basic principles of theoretical and mathematical approaches to competitive location problems. However, despite its popularity, the principle is not robust: if the assumptions underlying the model are relaxed, the principle could be invalid. In this paper we propose an extension of the Hotelling model in the sense that more than two competitors are allowed and the space of the competition is a bidimensional discrete lattice. The discrete grid represents a product space where each firm locates a differentiated product. Competition is based on location only and each competitor can relocate in a finite subset of feasible locations, whenever it is advantageous. Given the discreteness of the space and the deterministic decision rule given to agents, the overall system can be seen as a specification of a cellular automaton. Cellular automata are dynamic systems capable of exhibiting the same kind of dynamics as partial differential equations. Furthermore, in some cases they seem to be capable of represening other behaviours, not detectable in systems of differential equations, such as self-organization. The results of some simulations are discussed both in terms of cellular automaton behaviour and in relation to other works reported in the literature. It was found that the dynamics of the system are quite regular and self-organization emerges.