Computational complexity of the discrete competitive facility location problem

We consider the discrete competitive facility location problem with finitely many consumers and finitely many locations of the facilities. Two competing companies are opening the facilities in some of these locations consequently; i.e., the first company does it first, then does second company. The goal of both is to maximize their profit obtained from serving the consumers, provided that each of the consumers chooses exactly one of the facilities opened by both companies, based on his known preferences. The complexity status is identified for two particular cases of this problem. © 2014, Pleiades Publishing, Ltd.