NETWORK FACILITY‐LOCATION MODELS IN STACKELBERG‐NASH‐COURNOT SPATIAL COMPETITION

ABSTRACT A hierarchical mathematical programming approach is combined with sensitivity analysis (of variational inequalities) to formulate a facility-location model for a firm competing on a discrete network. It is assumed that the locating firm will act as the leader firm in an industry characterized by Stackelberg leader-follower(s) oligopolistic competition. The other n competitors in this industry are assumed to act as Cournot firms that each operate under the Coumoi assumption of zero conjectural variation with respect to their n–1 Cournot competitors. It is further assumed that the n Cournot firms will react to the location/production/shipping activities of the Stackelberg firm. Therefore, when the Stackelberg firm makes its location, production, and shipping decisions it takes into account the reaction of the n Cournot firms to its (the Stackelberg firm's) integrated location and distribution decisions. Specifically, a Cournot reaction function is developed and imbedded in the Stackelberg firm's profit-maximizing objective function to project the anticipated reaction of the Cournot firms to the Stackelberg firm's location decision.