Reaction Function Based Dynamic Location Modeling in Stackelberg-Nash-Cournot Competition

We formulate a dynamic facility location model for a …rm locating on a discrete network. It is assumed that this locating …rm will act as the leader …rm in an industry characterized by Stackelberg leader-follower competition. The …rm’s I competitors are assumed to act as Cournot …rms and are each assumed to operate under the assumption of zero conjectural variation with respect to their I 1 Cournot competitors. Using sensitivity analysis of variational inequalities within a hierachical mathematical programming approach, we develop reaction function based dynamic models to optimize the Stackelberg …rm’s location decision. In the second half of this paper, we use these models to illustrate through a numerical example the enhanced insights yielded by a reaction based, dynamic approach