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

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.

[1]  Thomas L. Magnanti,et al.  Sensitivity Analysis for Variational Inequalities , 1992, Math. Oper. Res..

[2]  Anna Nagurney,et al.  Variational Inequalities , 2009, Encyclopedia of Optimization.

[3]  Patrick T. Harker,et al.  Alternative Models of Spatial Competition , 1986, Oper. Res..

[4]  J. Pang.  Solution differentiability and continuation of Newton's method for variational inequality problems over polyhedral sets , 1990 .

[5]  P. Marcotte.  Algorithms for the Network Oligopoly Problem , 1987 .

[6]  Thomas L. Magnanti,et al.  Sensitivity Analysis for Variational Inequalities Defined on Polyhedral Sets , 1989, Math. Oper. Res..

[7]  Jerzy Kyparisis,et al.  Sensitivity analysis framework for variational inequalities , 1987, Math. Program..

[8]  T. Friesz,et al.  Incorporating competitors' reactions in facility location decisions: A market equilibrium approach , 1995 .

[9]  Stella Dafermos,et al.  Sensitivity Analysis in Variational Inequalities , 1988, Math. Oper. Res..

[10]  Hanif D. Sherali,et al.  A mathematical programming approach for determining oligopolistic market equilibrium , 1982, Math. Program..

[11]  Roger L. Tobin,et al.  A Dynamic Spatial Cournot-Nash Equilibrium Model and an Algorithm , 1997 .

[12]  Terry L. Friesz,et al.  STACKELBERG GAMES ON A NETWORK WITH COURNOT‐NASH OLIGOPOLISTIC COMPETITORS , 1991 .

[13]  A. Nagurney,et al.  Oligopolistic and competitive behavior of spatially separated markets , 1987 .

[14]  Engelbert J. Dockner,et al.  A Dynamic Theory of Conjectural Variations , 1992 .

[15]  James W. Friedman,et al.  Oligopoly and the theory of games , 1977 .

[16]  Anna Nagurney,et al.  A dynamical systems approach for network oligopolies and variational inequalities , 1994 .

[17]  T. Friesz,et al.  Equilibrium Facility Location on Networks , 1995 .

[18]  T. Miyagi.  A computational procedure for determination of oligopolistic spatial price equilibrium , 1991 .

[19]  Alain Haurie,et al.  On the relationship between Nash - Cournot and Wardrop equilibria , 1983, Networks.

[20]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[21]  Terry L. Friesz,et al.  Network facility-location models in Stackelberg-Nash-Cournot spatial competition , 1992 .

[22]  Anna Nagurney,et al.  Algorithms for oligopolistic market equilibrium problems , 1988 .

[23]  Patrick T. Harker,et al.  A variational inequality approach for the determination of oligopolistic market equilibrium , 1984, Math. Program..