On competitive sequential location in a network with a decreasing demand intensity

We introduce and analyze a Hotelling like game wherein players can locate in a city, at a fixed cost, according to an exogenously given order. Demand intensity is assumed to be strictly decreasing in distance and players locate in the city as long as it is profitable for them to do so. For a linear city (i) we explicitly determine the number of players who will locate in equilibrium, (ii) we fully characterize and compute the unique family of equilibrium locations, and (iii) we show that players’ equilibrium expected profits decline in their position in the order. Our results are then extended to a city represented by an undirected weighted graph whose edge lengths are not too small and co-location on nodes of the graph is not permitted. Further, we compare the equilibrium outcomes with the optimal policy of a monopolist who faces an identical problem and who needs to decide upon the number of stores to open and their locations in the city so as to maximize total profit.