### Abstract

Oligopolies are a fundamental economic market structure in which the number of competing firms is sufficiently small so that the profit of each firm is dependent upon the interaction of the strategies of all firms. There are alternative behavioral assumptions one may employ in forming a model of spatial oligopoly. In this chapter, we study the classical oligopoly problem based on Cournot’s theory. The Cournot-Nash solution of oligopoly models assumes that firms choose their strategy simultaneously and each firm maximizes their utility function while assuming their competitor’s strategy is fixed. We begin this chapter with the basic definition of Nash equilibrium and the formulation of static spatial and network oligopoly models as variational inequality (VI) which can be solved by several numerical methods that exist in the literature. We then move on to dynamic oligopoly network models and show that the differential Nash game describing dynamic oligopolistic network competition may be articulated as a differential variational inequality (DVI) involving both control and state variables. Finite-dimensional time discretization is employed to approximate the model as a mathematical program which may be solved by the multi-start global optimization scheme found in the off-the-shelf software package GAMS when used in conjunction with the commercial solver MINOS. We also present a small-scale numerical example for a dynamic oligopolistic network.

Original language | English (US) |
---|---|

Title of host publication | Handbook of Regional Science |

Publisher | Springer Berlin Heidelberg |

Pages | 237-258 |

Number of pages | 22 |

ISBN (Electronic) | 9783642234309 |

ISBN (Print) | 9783642234293 |

DOIs | |

State | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Economics, Econometrics and Finance(all)
- Business, Management and Accounting(all)

### Cite this

*Handbook of Regional Science*(pp. 237-258). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-23430-9_105

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*Handbook of Regional Science.*Springer Berlin Heidelberg, pp. 237-258. https://doi.org/10.1007/978-3-642-23430-9_105

**Computable models of static and dynamic spatial oligopoly.** / Meimand, Amir H.; Friesz, Terry Lee.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Computable models of static and dynamic spatial oligopoly

AU - Meimand, Amir H.

AU - Friesz, Terry Lee

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Oligopolies are a fundamental economic market structure in which the number of competing firms is sufficiently small so that the profit of each firm is dependent upon the interaction of the strategies of all firms. There are alternative behavioral assumptions one may employ in forming a model of spatial oligopoly. In this chapter, we study the classical oligopoly problem based on Cournot’s theory. The Cournot-Nash solution of oligopoly models assumes that firms choose their strategy simultaneously and each firm maximizes their utility function while assuming their competitor’s strategy is fixed. We begin this chapter with the basic definition of Nash equilibrium and the formulation of static spatial and network oligopoly models as variational inequality (VI) which can be solved by several numerical methods that exist in the literature. We then move on to dynamic oligopoly network models and show that the differential Nash game describing dynamic oligopolistic network competition may be articulated as a differential variational inequality (DVI) involving both control and state variables. Finite-dimensional time discretization is employed to approximate the model as a mathematical program which may be solved by the multi-start global optimization scheme found in the off-the-shelf software package GAMS when used in conjunction with the commercial solver MINOS. We also present a small-scale numerical example for a dynamic oligopolistic network.

AB - Oligopolies are a fundamental economic market structure in which the number of competing firms is sufficiently small so that the profit of each firm is dependent upon the interaction of the strategies of all firms. There are alternative behavioral assumptions one may employ in forming a model of spatial oligopoly. In this chapter, we study the classical oligopoly problem based on Cournot’s theory. The Cournot-Nash solution of oligopoly models assumes that firms choose their strategy simultaneously and each firm maximizes their utility function while assuming their competitor’s strategy is fixed. We begin this chapter with the basic definition of Nash equilibrium and the formulation of static spatial and network oligopoly models as variational inequality (VI) which can be solved by several numerical methods that exist in the literature. We then move on to dynamic oligopoly network models and show that the differential Nash game describing dynamic oligopolistic network competition may be articulated as a differential variational inequality (DVI) involving both control and state variables. Finite-dimensional time discretization is employed to approximate the model as a mathematical program which may be solved by the multi-start global optimization scheme found in the off-the-shelf software package GAMS when used in conjunction with the commercial solver MINOS. We also present a small-scale numerical example for a dynamic oligopolistic network.

UR - http://www.scopus.com/inward/record.url?scp=85027000431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027000431&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-23430-9_105

DO - 10.1007/978-3-642-23430-9_105

M3 - Chapter

AN - SCOPUS:85027000431

SN - 9783642234293

SP - 237

EP - 258

BT - Handbook of Regional Science

PB - Springer Berlin Heidelberg

ER -