Location and Price Competition on a Uniform Path with Different Pricing Policies

This paper models duopolistic competition between an online retailer and a physical store retailer with the online retailer modelled as a firm with uniform delivered pricing policy and the physical store as a firm with a mill pricing policy. Both firms seek to maximize their respective profits through an appropriate choice of location and price. The market is assumed to be given by a “uniform path” - a tree whose node weights and arc lengths are equal. Modelling reality, we consider two alternate types of transportation costs faced by the online retailer: either dependent on the relative location of the firm and a customer or independent of it. Beginning with the framework of a Stackelberg, i.e., sequential game, optimal location and price strategies are analytically derived for both sequences of market entry by the two competitors. Cases in which the leader faces the first entry paradox or can become a monopolist by strategically deterring entry by the follower are delineated. Thereafter, Nash Equilibrium solutions to the simultaneous game are identified. Salient insights from the results include: (a) the competitive pressure faced by the physical store in the presence of online competition (b) the inability of an online retailer to compete in “large” markets under the first type of transportation cost and (c) the advantage to the physical retailer of being a market leader.