Cooperative Location for Competing Firms under Delivered Pricing and Demand Linear in Price

The location-price decision problem for competing firms can be reduced to a location game if firms compete on delivered pricing. This game has often been studied for non-cooperative firms where the Nash equilibrium is used as solution concept. However, it may occurs that there exist alternative locations for which all firms get higher payoffs than those prescribed by the equilibrium. This fact has been shown by the authors for joint profit maximization locations when demand is fixed and firms set equilibrium prices. In this paper, we study the location game considering that demand is linear in price and firms cooperate by setting the monopoly price at each market instead of the equilibrium price. Two Mixed Integer Linear Programming location models are developed to maximize the joint profit for different and equal production costs, respectively. An empirical investigation is performed to compare the joint profit of the firms, which is obtained by the solutions of the proposed location models, with the one obtained by the Nash equilibrium solution that is obtained if the firms do not cooperate.