Spatial price competition when stores are not certain to have what consumers want

This paper examines the Bertrand-Nash equilibrium prices charged by stores that are spaced evenly along an infinite roadway, assuming that each store has the product that any given consumer wants with probability w. A consumer either knows whether any particular store has the desired product, and the store's price for the product, or else is able to find out this information by making a costless phone call. The demand function facing any store is a linear function of all prices, with a negative coefficient on the store's own price, and positive coefficients on the prices of all other stores which decline geometrically as the stores become successively more distant. The Bertrand-Nash equilibrium price markup is inversely proportional to w. (C) 1998 Elsevier Science B.V.