Location Equilibria Under Alternative Solution Concepts

We provide a comparison of the location equilibria in a duopoly model under three alternative solution concepts. The first one is a simultaneous price and location game, the second is a two-stage location-then-price game. Third, we introduce a new solution concept, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the first two solution concepts when products are homogenous. We show this is also true for the third concept. However, introducing sufficient product heterogeneity in a specific manner restores the existence of equilibrium in each case. We argue that, under certain "regularity" conditions, equilibrium locations are farther apart under the location-then-price game than in the simultaneous game. We provide simulation results for a specific functional form (the logit model) which illustrates this result, and show that locations in the price-then-location game may be either closer or farther from the center than simultaneous game. Another contribution of the paper is to introduce a no-purchase option into the logit model of spatial competition.