A Note on the Effect of Sequential Entry on Choice of Location

Abstract

AN important and neglected aspect of economics arises when entry into a market of sharply differentiated products is sequential and essentially irrevocable. One particularly important question is how far this leads to a less than optimal state of affairs. An approach to the investigation of this kind of problem is offered by the theory of spatial competition, which provides examples that are easily quantifiable and so enables us to study the phenomenon in relatively pure form. The spatial analogy has been widely used by Hotelling [8], Chamberlin [2], and Lerner and Singer [9], among others, to investigate product differentiation and, either implicitly or explicitly, the related problem of excess capacity. Hotelling and Chamberlin considered cases involving small numbers of infinitely mobile competitors, each choosing his location on the assumption that rivals' locations remain unchanged. Lerner and Singer considered some general conditions necessary for the existence of spatial equilibrium for larger numbers, but on the same behavioural assumptions. In all three of these important analyses individual location choices can be assumed to be made sequentially, in the sense that each seller chooses his location given the locations of rivals. But since relocation is assumed costless the final outcome in each case does not depend upon the sequential nature of the decision process, and the result is the same as that which would obtain if all sellers, choosing simultaneously, established the equilibrium set of locations at the outset. [5, 6, 6a, 7, I4, I5] are restricted to duopoly problems on varying assumptions on demand and foresight with regard to rival behaviour. But here, too, the assumption of infinite mobility leads to neglect of important problems arising from irrevocable sequential choices. [4, I3, i6, i8] consider problems involving foresight for somewhat larger numbers, but only [I3, i6] assume that locations, once selected, are fixed. In both cases, however, the authors assume a type of expectation formation different from that which we shall consider here. Finally, it is worth noting that [3, I I 12, I7] consider various aspects of the use of the spatial analogy in the explicit investigation of the problems of excess capacity and the efficiency of competition. Although we shall not concern ourselves with these last two questions, except insofar as they are implicit in non-optimal location, the results given in this paper may be regarded, in part, as a contribution to this literature. * This paper embodies an early result obtained in research for the Ph.D. degree in the Faculty of Economics and Politics in the University of Cambridge. I owe a great debt to my supervisor, M. J. Farrell, for his help and encouragement.