Equilibrium Existence in the Linear Model of Spatial Competition.

This paper considers a generalization of the Hotelling model of spatial competition. It is shown that a pure strategy perfect equilibrium in the two-stage location-price game exists only under very stringent conditions. These conditions are in fact the conditions for profit to be concave in price for any given location pair. When the solution concept is extended to allow for mixed strategies, there is no symmetric equilibrium involving pure strategies if transport costs are not sufficiently convex. The convexity of transport costs is crucial in determining whether there is excessive or insufficient diversity of products. Copyright 1988 by The London School of Economics and Political Science.