On optimal location for three competitive facilities

The competitive facility location problems are investigated on many papers. In most of their papers the competitive location model with two competitors are investigated. In this paper three companies which are mutually competitive intend to locate their facilities on linear market. It is well-known that Nash equilibrium solution for location problem does not exist for three competitive facilities. In our model we assume that the demands are continuously distributed on the linear market and their facilities are locating according to specific order of sequence, A, B and C. In this paper we consider Stackelberg equilibrium solution for competitive location problems with three facilities. In our model we consider the decision problems of three stages. In the first stage problem we decide the location of the facility A which is optimally located for the remaining two facilities B and C. And in the second stage problem we decide the location of the facility B which is optimally located for C by utilizing the information on the location of facility A. Finally in the third stage problem we decide the location of the facility C which is optimally located by utilizing the information on the location of the facilities A and B.