Hotelling?s theory of spatial competition has a very interesting implication in that it predicts that there will be too little product differentiation in terms of firms? locations.

Suppose that the consumer?s are located uniformly along a line of unit length, and each consumer?s demand is s decreasing function of the final price which includes the price of the product plus the product of travel cost and distance traveled. In such a situation if all firms have constant costs and are forced to charge a common price, then consumers purchase from the seller closest to him. The efficient outcome in this context is the one that minimizes the sum of consumer?s travel costs, by having firms equally placed. However, when two sellers are equally spaced at locations of 0.25 and 0.75 on the line, both have a unilateral incentive to increase sales by moving towards the center. The Nash prediction for the single period game is for each firm to locate at the center and consequently choose to have very little product differentiation. The choice of location here is the analogous of the choice of product characteristics.

Brown-Kruse, Cronshaw and Schenk (1993) conducted a duopoly experiment with a similar structure as above in mind. They imposed a random stopping rule to terminate the market if a red ball was drawn with replacement from an urn where 1/8th of the balls were red. The resulting probability of continuation (7/8) was high enough to support the efficient outcome (locations at 0.25 and 0.75) as a Nash Equilibrium, with trigger strategies specifying a punishment location of 0.5 following any deviation. However the experiment results found an overwhelming support for subjects to locate at the center (0.5). Unfortunately this is one of many examples of the non-cooperative stage game outperforming the suggested trigger strategy. There was a second series of sessions with non-binding communications via a early version of a chat program where the predominant locations came out as 0.25 and 0.75.

Reference

Brown-Kruse, Jamie L., Mark B. Cronshaw, and David J. Schenk (1993). Theory and experiments on spatial competition. Economic Inquiry, vol. 31:1, pp. 139-65.