Competitive location with dissimilar objectives

This paper studies a competitive location model on graphs in which one firm has a “public welfare maximization” objective that attempts to minimize the average distance to its own customers, while the other has a “profit/market share maximizing” objective that seeks to maximize the demand it serves. Nash Equilibrium pairs of locations are characterized for three classes of graphs: trees, cactus graphs and general graphs and it is shown that their existence can be determined in strongly polynomial time and that in the same time, all Nash Equilibria location pairs can also be determined, thereby allowing decision makers to use secondary criteria to choose among them. These results show that Nash Equilibrium location pairs are guaranteed to exist for trees and are characterized by a property analogous to the classical result in location theory (Goldman in Transp. Sci, 1971). Finally, a computational illustration of the main algorithm is also provided.