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

Abstract

We formulate a dynamic facility location model for a firm locating on a discrete network. It is assumed that this locating firm will act as the leader firm in an industry characterized by Stackelberg leader–follower competition. The firm’s I competitors are assumed to act as Cournot firms 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 firm’s location decision. In the second half of this paper, we use these models to illustrate through a numerical example the insights yielded by our approach.